Study Abroad Curriculum Mapping with Selected Partner

Study Abroad Curriculum Mapping

with Selected Partner Institutions

Department of Chemical and Biochemical Engineering

Rutgers University

September 2014

Studying abroad is an enriching experience. In the past years, many chemical engineering

students have spent a year, a semester, or a summer studying at a partner institution abroad.

Before leaving for study abroad, a student will need to select the courses that he or she will

enroll in at the partner institution. This may be a tedious process since the student may not be

familiar with the courses offered overseas.

In order to assist each student who are interested in studying abroad, the Department of

Chemical and Biochemical Engineering has developed a “Curriculum Mapping Document” that

identifies the courses at partner institutions that are equivalent to the required courses at Rutgers

Chemical Engineering. This document is meant to be used as a guide. The information

contained in this document was obtained from the course websites of the selected partners. To

obtain the most up-to-date course offerings, please contact Rutgers Center for Global Education

(Rutgers Study Abroad Office) at 102 College Avenue, New Brunswick, NJ 08901-8543.

Important Notes:

In this document, Rutgers Chemical Engineering courses are listed on the left, and the equivalent

course at the partner institution is listed on the right. There are a couple important things to keep

in mind when using the Curriculum Mapping:

1. This document includes courses offered by nine (9) partner institutions. You may study

abroad at a partner institution not listed here. To receive the most up-to-date course

syllabus and course offerings of a partner university, visit the website of the partner

institution. You may contact Rutgers Center of Global Education.

2. The courses offered at partner institutions are subject to change. If an equivalent course is

no longer being offered at the partner institute, it is the student’s responsibility to make

sure that an equivalent course is taken. Students should consult with Director of

Undergraduate Programs of Chemical Engineering and Dean of Undergraduate Education

for advice. Final approval of course equivalency is made by both the undergraduate

director or the dean.

3. Only required chemical engineering courses are mapped in this document. You may take

non-chemical engineering or elective courses at the partner school. To determine the

credits of courses not listed in this document, consult the Undergraduate Director and

Associate Dean of Undergraduate Education.

4. The information contained in this document is subject to change. Use this document as a

guide to identify the courses that you may take while studying abroad.

Understanding the Curriculum Mapping:

Below is a sample of the curriculum mapping for the University College Dublin:

In the first box, the two courses Advanced Calc. for Eng. (3 credits, offered in both the

spring and fall) and Multivariable Calculus (4 credits, offered in both the spring and fall) have

one equivalent course, Multivar. Calculus Eng. II (5 University of College Dublin Credits,

offered only in the fall). This means taking ACM30030 (Multivar. Calculus Eng. II ) would

count for credit towards 01:640:421 and 01:640:251 (Advanced Calc. for Eng. and Multivariable

Calculus). Organic Chemistry I (4 major credits, offered in both the spring and fall), Organic

Chemistry II (4 major credits, offered in both the spring and fall), and Organic Chemistry Lab (2

major credits, offered in both the spring and fall) have two equivalent courses, Basis of Organic

& Biological Chemistry and Structure and Reactivity in Organic Chemistry (5 University of

College Dublin credits, offered in the fall). Analytical Physics does not have an equivalent

course, and Physical Chemistry has one equivalent course, Quantum Mechanics & Molecular

Spectroscopy. Information about the credit system, and particular courses are listed in the

footnotes. Course calendar information is listed on page 5. Course description information is

listed at the end of the document. You may double click on the endnote superscript towards the

top right of the equivalent course to jump to the course description. Make sure to verify the

term each course is offered in the University Calendar.

Rutgers University Curriculum University College Dublin Equivalent Courses

Course Number Course Name Credits Term Course Number Course NameCourse Description

Credits‡ Term

01:640:421 Advanced Calc. for Eng. 3.0 Fall &

Spring ACM30030 Multivar. Calculus Eng. II 5.0 Fall

01:640:251 Multivariable Calculus 4.0

01:750:229 Analytical Physics II Lab 1.0 Fall No equivalent course for 01:750:229, Analytical Physics II Lab

01:160:307 Organic Chemistry I M 4.0

Fall &

Spring

CHEM10050 Basis of Organic &

Biological Chemistry 5.0

Fall 01:160:308 Organic Chemistry II M 4.0

CHEM20040 Structure and Reactivity in

Organic Chemistry 5.0

01:160:311 Organic Chemistry Lab M 2.0

01:160:328 Physical Chemistry M 4.0 Spring CHEM30060* Quantum Mechanics &

Molecular Spectroscopy 5.0 Fall

Table of Contents University Calendar

University of Manchester … United Kingdom

Curriculum Mapping

Course Descriptions

University of Birmingham… United Kingdom

Curriculum Mapping

Course Descriptions

University College London… United Kingdom

Curriculum Mapping

Course Descriptions

University College Dublin … Ireland

Curriculum Mapping

Course Descriptions

HKUST … China

Curriculum Mapping

Course Descriptions

Pohang University… South Korea

Curriculum Mapping

Course Descriptions

University of Melbourne… Australia

Curriculum Mapping

Course Descriptions

University of Queensland… Australia

Curriculum Mapping

Course Descriptions

University of Auckland… New Zealand

Curriculum Mapping

Course Descriptions

University Calendar

University of Manchester

Semester 1- September until January, Christmas Break for one month

Semester 2- January until June, Easter Break for 3 weeks

University of Birmingham

Semester 1-September until December, 3 weeks for Christmas break

Semester 2-January until March

Exams May until June

University College London

Semester 1 September until December. Two week break for Christmas

Semester 2 January-March. One week for Easter.

University College Dublin

Semester 1-September until December (12 weeks), 1 month for Christmas

Semester 2-January until May, 2 weeks for Easter

HKUST

Fall-September until December. Two Weeks for Finals. One month and two weeks for Christmas.

Spring- February until May. Two weeks for finals. One week Spring break.

Pohang University

Semester 1- March until August (15 weeks)

Semester 2- September until February. (15 weeks)

University of Melbourne

Semester 1-March until June Finals in mid-June. 8 week winter break recess.

Semester 2- July until October. Finals in November.

University of Queensland

Semester 1- March until June

Semester 2- July until November

University of Auckland

Semester 1- March until June. Finals in Mid June. Two week break in July

Semester 2-July until November. Finals at end of October. Two week break in September

Study Abroad Curriculum

Mapping for The University Of Manchester

B.S. Program, Chemical Engineering

‡ A University of Manchester 10 credit course equates to around 100 total hours of work. For reference, a 10 credit

Manchester course equals 3 credits at Rutgers. A 15 credit course equals 4 Rutgers credits, and 20 credit course equals 5

Rutgers credits. 45 University of Manchester credits per semester is the minimum credit load to achieve full-time status

Rutgers University Curriculum The University of Manchester Equivalent

Courses

Course

Number Course Name Credits Term Course Number Course Name

Course Description Credits

‡ Term


Spring CHEN20041 Mathematical Methods 2

1 10.0 Fall

14:155:201 Analysis I M 3.0 Fall CHEN10041 Chemical Eng. Design 12 10.0 Fall

14:155:307 Analysis II M 3.0 Fall

CHEN10011 Engineering Mathematics 13 10.0 Fall

CHEN10072 Engineering Mathematics 24 10.0 Spring

01:750:227 Analytical Physics II 3.0 Fall PHYS10342 Electricity and Magnetism5 10.0 Spring


14:155:324 Design Separ. Process M 4.0 Spring CHEN20072 Distillation & Absorption6 10.0 Spring

01:640:244 Differ. Equat. Eng. &

Physics 4.0 Spring MATH10232 Calculus and Applications B

7 15.0 Spring

01:220:102 Microeconomics 3.0 Fall &

Spring ECON10041 Microeconomic Principles

8 10.0 Fall

01:640:251 Multivariable Calculus 4.0 Fall &

Spring MATH10121 Calculus and Vector A

9 20.0 Fall

01:160:307 Organic Chemistry I M 4.0 Fall &

Spring CHEM10101 Introductory Chemistry

10 30.0 Fall

01:160:308 Organic Chemistry II M 4.0 Fall &

Spring CHEM10412 Organic Chemistry

11 10.0 Spring

01:160:311 Organic Chemistry Lab M 2.0 Fall &

Spring No equivalent course for 01:160:311 Organic Chemistry Lab

01:160:328 Physical Chemistry M 4.0 Spring CHEM10212 Basic Physical Chemistry12

10.0 Spring

14:155:208 Thermodynamics I M 3.0 Spring CHEN10082 Fundamentals of

Thermodynamics13

10.0 Spring

14:155:309 Thermodynamics II M 3.0 Fall CHEN20091 Chem. Thermodynamics14

10.0 Fall

14:155:303 Transport Phenomena I M 3.0 Fall CHEN10031 Transport Phenomena 115

10.0 Fall

14:155:304 Transport Phenomena II M 3.0 Spring CHEN10092 Transport Phenomena 216

10.0 Spring


Mapping for The University Of Birmingham


^ Courses marked LI are linked and must be taken together

* 06 22493 is a Full Term Course. It is advised that Students take Part A, offered in the Fall, equivalent to 01:640:421, Advanced Calc. for Eng

** 04 23779 is a Full Term Course. It is advised that Students take Part A, offered in the Fall , equivalent to,14:155:307, Analysis II. Students may not

supplement Part B for 06 25667, LI Multivariable & Vector Analysis, The University of Birmingham equivalent of 01:640:251, Multivariable Calculus

*** 04 17126 is a Full Term Course. It is advised that students take Part B, offered in Semester 2, as Part B of the course equivalent to 14:155:324, Design

Separation Process

‡ A University of Birmingham 10 credit course equates to around 100 total hours of work per semester. For reference, a 10 credit Birmingham course is

equivalent a 3.0 credit course at Rutgers University. A 15.00 credit course equates to 4.0 Rutgers credit course, and a 20 credit course equates to a 5.0

Rutgers University credit course

Rutgers University Curriculum The University of Birmingham Equivalent Courses

Course Number Course Name Credits Term Course Number Course NameCourse Description

Credits‡ Term


Spring 06 22493*

Transform Theory and Number

Methods in Linear Algebra1

20.0 Full Term

14:155:201 Analysis I M 3.0 Fall No equivalent course for 14:155:201 Analysis I

14:155:307 Analysis II M 3.0 Fall 04 23779** Engineering Math A&B2 20.0 Full Term

01:750:227 Analytical Physics II 3.0 Fall 03 00953 Electromagnetism 23 10.0 Spring

01:750:229 Analytical Physics II Lab 1.0 Fall 03 00943 Physics Laboratory 24 10.0 Fall

14:155:324 Design Separ. Process M 4.0 Spring 04 17126*** Process Integration and Unit

Operations5

20.0 Full

Term


Physics 4.0 Spring 06 25670^ LI Differential Equations

6 20.0

Full

Term


Spring

08 03338 Microeconomics A7 10.0 Fall

08 03342 Microeconomics B8 10.0 Spring


Spring 9) 06 25667^ Multivariable & Vector Analysis

9 20.0

Full

Term


Spring 03 21440 Synthesis & Mechanism

10 20.0

Full

Term


Spring

03 25338^ LI Synthesis and Mechanism IIa11

10.0 Fall

01:160:311 Organic Chemistry Lab M 2.0 03 25339^ LI Synthesis and Mechanism IIb12

10.0 Spring

01:160:328 Physical Chemistry M 4.0 Spring

03 19718 Quantum Mechanics & Optics &

Waves13

10.0 Fall

03 17273 Quantum Mechanics 214

10.0 Fall

03 00498 Quantum Mechanics 315

10.0 Fall

14:155:208 Thermodynamics I M 3.0 Spring

04 21831

Fluid Flow, Thermodynamics,

and Heat Transfer16

(grouping

of Thermodynamics I, Transport

Phenomena I, and part of

Transport II)

20.0 Full Term 14:155:303 Transport Phenomena I M 3.0 Fall

14:155:304 Transport Phenomena II M 3.0 Spring

14:155:309 Thermodynamics II M 3.0 Fall 04 22992 Chem. Eng. Thermodynamics 217

10.0 Fall


Mapping for University College London


* CENG 1004, Introduction to Chemical Engineering, contains material relevant to 14:155:208, 14:155:309, Thermodynamics I and II,

14:155:303, 14:155:304, Transport I and II, and 14:155:324, Design Separation Process

** CENG 2002, Mass Transfer Operations, contains material relevant to 14:155:303, Transport I, and 14:155:309, Thermodynamics II

*** The curriculum for MATH 1402, Mathematical Methods 2, only partially covers its equivalent course, 01:640:244, Differ. Equat. Eng. & Physics

**** MATH 1402, Mathematical Methods 2 contains material relevant to 01:640:421, Advanced Calc. for Eng

*****CHEM 1201, Basic Organic Chemistry and CHEM 2201, Organic Chemistry both contain a laboratory component.

‡ A 4.0 credit course at University College London is equivalent to a 3.0 credit course at Rutgers University. Full-time status at University College

London requires students to take 12 credits per semester

Rutgers University Curriculum University College London Equivalent Course

Course

Number Course Name Credits Term Course Number Course Name


‡ Term


Spring MATH 7402 Mathematical Methods 4

1 4.0 Spring

14:155:201 Analysis I M 3.0 Fall CENG 1004* Introduction to Chem.

Eng.2

4.0 Full

Year

14:155:307 Analysis II M 3.0 Fall MATH 3603 Numerical Methods3 4.0 Fall

01:750:227 Analytical Physics II 3.0 Fall PHAS 2201 Electricity and Magnetism4 4.0 Fall


14:155:324 Design Separ. Process M 4.0 Spring CENG 2002** Mass Transfer Operations5 4.0

Full

Year


Physics 4.0 Spring MATH 3401*** Mathematical Methods 5

6 4.0 Fall


Spring ECON 1602 Basic Microeconomic Concepts

7 4.0 Spring


Spring MATH 1402**** Mathematical Methods 2

8 4.0 Spring


Fall &

Spring

CHEM 1201***** Basic Organic Chemistry9 4.0 Spring

01:160:308 Organic Chemistry II M 4.0

CHEM 2201***** Organic Chemistry10

8.0 Full

Year 01:160:311 Organic Chemistry Lab M 2.0

01:160:328 Physical Chemistry M 4.0 Spring PHAS 2222 Quantum Physics

11 4.0 Fall

PHAS 2224 Atomic& Molecular Physics12

4.0 Spring

14:155:208 Thermodynamics I M 3.0 Spring CENG 1002 Thermodynamics

13 4.0

Full

Year 14:155:309 Thermodynamics II M 3.0 Fall

14:155:303 Transport Phenomena I M 3.0 Fall CENG 1001 Transport Processes I14

4.0

Full

Year 14:155:304

Transport Phenomena

II M 3.0 Spring

CENG 2006 Process Heat Transfer15

4.0

CENG 3005 Transport Processes III16

4.0


Mapping for The University College Dublin


* CHEM20120, Physical Chemistry, is accepted in place of CHEM30060

‡ A 5.0 credit University College of Dublin course is equivalent to a 3.0 credit Rutgers University course

The University College of Dublin semester is fifteen weeks long (twelve weeks learning, one week review for

finals, two weeks for final examination.

Rutgers University Curriculum University College Dublin Equivalent Courses

Course Number Course Name Credits Term Course

Number Course Name


‡ Term


Spring ACM30030 Multivar. Calculus Eng. II

1 5.0 Fall

01:640:251 Multivariable Calculus 4.0

14:155:201 Analysis I M 3.0 Fall CHEN10010 Chem. Eng. Process Principles2 5.0 Spring

14:155:307 Analysis II M 3.0 Fall CHEN30160 Computational Methods in

Chemical & Bioprocess Eng. 3

5.0 Spring

01:750:227 Analytical Physics II 3.0 Fall PHYC30070 Electromagnetism4 5.0 Spring


14:155:324 Design Separ. Process M 4.0 Spring CHEN30020 Unit Operations5 5.0 Spring


Physics 4.0 Spring ACM10060 Applications of Diff. Equat.

6 5.0 Spring


Spring ECON10010 Principles of Microeconomics

7 5.0

Fall &

Spring


Fall &

Spring

CHEM10050 Basis of Organic & Biological

Chemistry8

5.0

Fall 01:160:308 Organic Chemistry II M 4.0

CHEM20040 Structure and Reactivity in

Organic Chemistry9

5.0 01:160:311 Organic Chemistry Lab M 2.0

01:160:328 Physical Chemistry M 4.0 Spring CHEM30060* Quantum Mechanics &

Molecular Spectroscopy10

5.0 Fall

14:155:208 Thermodynamics I M 3.0 Spring CHEN20030 Chem. Eng. Thermodynamics

& Kinetics11

5.0 Fall

14:155:309 Thermodynamics II M 3.0 Fall CHEN30030 Chemical & Bioprocess Eng.

Thermodynamics12

5.0 Fall

14:155:303 Transport Phenomena I M 3.0 Fall CHEN20060 Transport Phenomena13

5.0 Spring

14:155:304 Transport Phenomena II M 3.0 Spring CHEN30130 Heat Transfer and Fluid

Mechanics14

5.0 Spring


Mapping for Hong Kong University of Science & Technology

(HKUST)


* In order to fulfill the requirement for 14:155:309, Thermodynamics II, both CENG 2210, Chem. Eng.

Thermodynamics and CENG 3210, Separation Process must be taken, starting with CENG 2210

** MATH2021, Multivar. & Vector Calculus, is accepted in place of MATH2023. MATH2021 is a full-year course

‡ The credit system at Hong Kong University of Science & Technology is equivalent to that at Rutgers University

Rutgers University Curriculum Hong Kong University Equivalent Courses

Course

Number Course Name Credits Term

Course

Number Course Name


‡ Term


Spring MATH 4052 Partial Differential Equations

1 3.0 Fall

14:155:201 Analysis I M 3.0 Fall CENG 2010 Chem. Process Principles2 3.0 Spring

14:155:307 Analysis II M 3.0 Fall MATH 3311 Intro to Numerical Methods3 2.0 Spring

01:750:227 Analytical Physics II 3.0 Fall PHYS 1114 General Physics II4 3.0 Spring

01:750:229 Analytical Physics II Lab 1.0 Fall PHYS 1115 Lab for General Physics II5 1.0 Spring

14:155:324 Design Separ. Process M 4.0 Spring

CENG 3210* Separation Process6 3.0 Fall

14:155:208 Thermodynamics I M 3.0 CENG 2210* Chem. Eng. Thermo.

7 3.0

Fall &

Spring 14:155:309 Thermodynamics II M 3.0 Fall


Physics 4.0 Spring MATH 2350

Applied Linear Algebra and

Differential Equations8

4.0 Fall


Spring ECON 2103 Principles of Microeconomics

9 3.0 Fall


Spring MATH 2023** Multivar. Calculus

10 4.0

Fall &

Spring


Spring CHEM 2118 Organic Chemistry I

11 4.0 Fall


Spring CHEM 3120 Organic Chemistry II

12 3.0 Spring


Spring CHEM 2151 Organic Chemistry Lab

13 2.0 Fall

01:160:328 Physical Chemistry M 4.0 Spring CHEM 3420 Physical Chemistry II14

3.0 Spring

14:155:303 Transport Phenomena I M 3.0 Fall CENG 2220 Process Fluid Mechanics15

3.0 Fall &

Spring

14:155:304 Transport Phenomena II M 3.0 Spring CENG 3220 Heat and Mass Transfer16

3.0 Spring


Mapping for Pohang University of Science & Technology


* Students may take MECH 250, Thermodynamics, a 3.0 credit course offered in Semester 1 as an equivalent to 14:155:208,

Thermodynamics I

** MATH 200, Differential Equations, and PHYS 206, General Physics II contain a one-hour per week lab component.

*** MATH 110, Calculus, contains around six week of material that would be review to those who have taken 01:640: 152, Calculus II for

the Mathematical and Physical Sciences

‡ The credit system at Pohang University of Science & Technology is equivalent to that at Rutgers University. The fall semester begins

September 1st and ends February 28th, while the spring semester begins March 1st and ends August 31s

Rutgers University Curriculum Pohang University Equivalent Courses

Course


Course

Number Course Name


‡ Term


Spring MATH 200* Differential Equations

1 3.0

Fall &

Spring


Physics 4.0 Spring

14:155:201 Analysis I M 3.0 Fall

CHEB 204** Chem. Eng.

Thermodynamics2

3.0 Fall 14:155:208 Thermodynamics I M 3.0 Spring

14:155:307 Analysis II M 3.0 Fall MATH 351 Intro. To Numerical

Analysis3

3.0 Fall

01:750:227 Analytical Physics II 3.0 Fall PHYS 206** General Physics II4 3.0 Fall

01:750:229 Analytical Physics II Lab 1.0 Fall PHYS 104 General Physics Lab II5 1.0 Fall


Spring SOSC 321 Principles of Economics

6 3.0

Fall &

Spring


Spring MATH 110*** Calculus

7 3.0 Spring


Spring CHEB 206 Organic Chemistry I

8 3.0 Fall


Spring CHEB 207 Organic Chemistry II

9 3.0

Spring


Spring CHEB 211 Organic Chem. Lab

10 2.0

Spring

01:160:328 Physical Chemistry M 4.0 Spring CHEM 211 Physical Chemistry I11

3.0 Spring

14:155:309 Thermodynamics II M 3.0 Fall No equivalent course for 14:155:309, Thermodynamics II

14:155:303 Transport Phenomena I M 3.0 Fall CHEB417 Transport Phenomena I12

3.0 Fall

14:155:304 Transport Phenomena II M 3.0 Spring CHEB 418 Transport Phenomena II13

3.0 Spring


Mapping for The University Of Melbourne


* PHYC 30018 covers subjects relevant to 14:155:303, 14:155:304, and 01:160:311, Transport Phenomena I and II, and Physical Chemistry,

respectively. There is also a laboratory aspect of the course, consisting of 8, three hour laboratory sessions, including up to 30 minutes of pre-lab activity.

** CHEM 10003 and CHEM 10004, Chemistry 1 & 2, contain irrelevant material. Please read course description.

*** CHEN 90007, Advanced Thermo & Reactor Engineering is a graduate level course.

‡ A 12.50 credit University of Queensland course is equivalent to a 4.0 credit Rutgers University course. Students would need to take 3.0 University of Melbourne courses

(36.75 units) to achieve 12.00 Rutgers University credits.

Rutgers University Curriculum The University of Melbourne Equivalent Courses

Course Number Course Name Credits Term Course

Number Course Name


‡ Term


Spring MAST 20030 Differential Equations

1 12.50 Fall


Physics 4.0 Spring

14:155:201 Analysis I M 3.0 Fall

CHEN 20007 Chem. Process Analysis 12 12.50

Fall &

Spring

CHEN 20008 Chem. Process Analysis 23 12.50 Spring

14:155:307 Analysis II M 3.0 Fall MAST 30028 Numerical & Symbolic

Mathematics4

12.50 Fall

01:750:227 Analytical Physics II 3.0 Fall

PHYC 10002* Physics 2: Advanced5 12.50 Fall

01:750:229 Analytical Physics II Lab 1.0 Fall

14:155:324 Design Separ. Process M 4.0 Spring CHEN 20009 Transport Processes6 12.50 Fall

14:155:304 Transport Phenomena II M 3.0 Spring CHEN 30005 Heat & Mass Transport

Processes7

12.50 Spring


Spring No equivalent course for 01:220:102, Microeconomics


Spring MAST 20009 Vector Calculus

8 12.50

Fall &

Spring


Spring

CHEM 10003** Chemistry 19 12.50

Fall &

Spring

01:160:308 Organic Chemistry II M 4.0 CHEM 10004** Chemistry 2

10 12.50 Fall

01:160:311 Organic Chemistry Lab M 2.0

01:160:328 Physical Chemistry M 4.0 Spring PHYC 30018* Quantum Physics11

12.50 Spring

14:155:208 Thermodynamics I M 3.0 Spring

CHEN 90007*** Advanced Thermo &

Reactor Eng. 12

12.50 Fall

14:155:309 Thermodynamics II M 3.0 Fall

14:155:303 Transport Phenomena I M 3.0 Fall ENGR 30002 Fluid Mechanics13

12.50 Fall &

Spring


Mapping for The University Of Queensland


* PHYS 1002, Electromagnetism and Modern Physics contains a laboratory component. Additionally material relevant to 01:160:328, Physical Chemistry is taught.

** CHEM 2050 contains much material covering transition metals that is irrelevant to Chemical Engineering majors. This is the closest equivalent course, however.

*** Both PHYS 2041 and PHYS 3040, Quantum Physics contain a small laboratory component.

‡ A 2.0 credit University of Queensland course is equivalent to a 3.0 credit Rutgers University course. Students would need to take 4 University of Queensland

courses (8 units) to achieve 12 Rutgers University credits.

Rutgers University Curriculum The University of Queensland Equivalent

Courses

Course


Course

Number Course Name


‡ Term


Spring MATH 2100

Applied Mathematical

Analysis1

2.0 Fall

14:155:201 Analysis I M 3.0 Fall CHEE 2001 Process Principles2 2.0 Spring

14:155:307 Analysis II M 3.0 Fall COSC 2500 Numerical Methods in

Computational Science3

2.0 Fall

01:750:227 Analytical Physics II 3.0 Fall PHYS1002*

Electromagnetism & Modern

Physics4

2.0 Fall &

Spring 01:750:229 Analytical Physics II Lab 1.0

14:155:324 Design Separ. Process M 4.0 Spring CHEE 3020 Process System Analysis

5 2.0 Spring

CHEE 3004 Unit Operations6 2.0 Fall


Physics 4.0 Spring MATH 1052

Multi. Calc. & Ord. Diff.

Equat.7

2.0 Fall &

Spring 01:640:251 Multivariable Calculus 4.0

Fall &

Spring MATH 2000 Calculus & Linear Algebra II

8 2.0


Spring ECON 1010 Introductory Microeconomics

9 2.0

Fall &

Spring


Spring

CHEM 1200 Chemistry 210

2.0 Fall

CHEM 2050** Organic & Inorganic

Chem.11

2.0 Spring


Spring No equivalent course for 01:160:308, Organic Chemistry II



01:160:328 Physical Chemistry M 4.0 Spring PHYS 2041*** Quantum Physics

12 2.0 Fall

PHYS 3040*** Quantum Physics13

2.0 Spring

14:155:208 Thermodynamics I M 3.0 Spring ENGG 1500 Eng. Thermodynamics14

2.0 Fall &

Spring

14:155:309 Thermodynamics II M 3.0 Fall CHEE 3003 Chem. Thermodynamics15

2.0 Spring

14:155:303 Transport Phenomena I M 3.0 Fall CHEE 2003 Fluid & Particle Mechanics16

2.0 Fall

14:155:304 Transport Phenomena II M 3.0 Spring CHEE 3002 Heat & Mass Transfer17

2.0 Spring

v


Mapping for The University Of Auckland

Bachelor of Science Program

Chemical Engineering

* These courses possess laboratory components.

** MATHS 253, Advanced Mathematics 3 contains material relevant to 01:640:421, Advanced Calc. for Engineers.

‡ A 15.00 credit University of Auckland course is equivalent to a 3.0 credit Rutgers University course. Students would need

to take 4.0 University of Auckland courses (60 units) to achieve 12.00 Rutgers University credits. The University of

Auckland semester is fifteen weeks.

Rutgers University Curriculum The University of Auckland Equivalent Courses

Course


Course

Number Course Name


‡ Term


Spring MATHS 361* Partial Diff. Equat.

1 15.0 Spring

14:155:201 Analysis I M 3.0 Fall CHEMMAT

211* Intro to Process Eng.

2 15.0 Spring

14:155:307 Analysis II M 3.0 Fall MATHS 270* Numerical Computation3 15.0

Fall &

Spring

01:750:227 Analytical Physics II 3.0 Fall PHYSICS 325 Electromagnetism4 15.0 Spring

01:750:229 Analytical Physics II Lab 1.0 Fall PHYSICS 390 Experimental Physics 15 15.0

Fall &

Spring

14:155:324 Design Separ. Process M 4.0 Spring CHEMMAT 312* Transfer Processes 26 15.0 Spring


Physics 4.0 Spring MATHS 260* Differential Equations

7 15.0

Fall &

Spring


Spring ECON 101 Microeconomics

8 15.0

Fall &

Spring


Spring MATHS 253** Advanced Math 3

9 15.0

Fall &

Spring


Spring CHEM 10101 Introductory Chemistry

10 30.0 Fall


Spring CHEM 92F* Foundation Chem. 2

11 15.0 Fall



01:160:328 Physical Chemistry M 4.0 Spring PHYSICS 350 Quantum Mechanics &

Atomic Physics12

15.0 Spring

14:155:208 Thermodynamics I M 3.0 Spring CHEMMAT 212* Energy & Processing

13 15.0 Fall

14:155:309 Thermodynamics II M 3.0 Fall

14:155:303 Transport Phenomena I M 3.0 Fall

CHEMMAT 213* Transfer Processes 114

15.0 Fall

14:155:304 Transport Phenomena II M 3.0 Spring

Course Descriptions

University of Manchester

Link to Course Catalog 1 Vector Calculus: Scalar and Vector Fields. Reminder of scalar and vector products of vectors. The operators

gradient, divergence and curl. Differential Vector Calculus identities. Physical interpretation. Complex numbers:

Definition. Argand Diagram. Arithmetic Operations. Rectangular, Polar and Exponential Forms. Second order

Ordinary Differential Equations: Concept of 2nd

order ODE, role of initial and boundary conditions. Solution of

second-order constant-coefficient homogeneous (zero RHS) differential equations with and without boundary

conditions. Solution of equations with RHS being polynomial, exponential or trigonometrical. Fourier

Series/Transforms: Definition of Fourier series. Examples of sine/cosine series and complex exponential series.

Introduction to Fourier transform and its inverse. Laplace Transforms: Definition of Laplace Transforms.

Transforms and inverse Transforms of functions (including use of partial fractions for inverse transforms). Laplace

transforms of derivatives. The Dirac delta function and its Laplace Transform. The unit step function. First and

second shift theorems. Solution of ODEs by Laplace Transforms. Application to systems where flows etc. are

switched on and off.

2 Units, unit conversions, composition units, gas law, partial pressures and Dalton's Law. Introductory concepts of

material balances. Material balances for single stage, non-reacting processes. Reactions, combustion, stoichiometry,

conversion, limiting reactant, percentage excess, yield, and selectivity. Material balances for reactive, single stage

processes. Material balances for multiple stage processes, atomic balances and species balances. Processes with

recycle. Condensation and vapor/gas mixtures. Case studies: Chemical and bio-chemical syntheses.

3 Calculus: Brief review of differentiation (single variable). Integration (single variable): exact, numerical,

applications. Taylor series (single variable). Vectors algebra (includes scalar and vector products). Partial

differentiation: tangent planes, change of variables, stationary points. Complex numbers.

Statistics: Nature of errors. Summarizing data: Measures of central tendency – mean, median, mode. Measures of

dispersion – variance, standard deviation, median absolute deviation. Combination and propagation of errors.

Regression and correlation. Correlation coefficient. Least squares fitting.

4 Matrices, algebraic properties, matrix transpose, determinant and inverse. Linear equation systems. Gaussian

Elimination. Partial Pivoting. First-order scalar ordinary differential equations (ODEs). Solution by separation of

variables and by finding an integrating factor. Numerical solution of ODEs using forward Euler and implicit Euler

schemes. Nonlinear equations of single variable. Numerical solution using Bisection, Trapezium rule, Newton

Raphson and Runge-Kutta methods. Introduction to second order ODEs.

5 Introduction: Forces in nature; electric charge and its properties; vectors, fields, flux and circulation. Electric

Fields and Stationary Charges: Coulomb's law and superposition; electric field and potential; capacitance; electric

dipoles; energy in electric fields. Magnetic Fields and Steady Currents: Magnetic fields; Lorentz force; Biot-

Savart and Ampère's laws; magnetic dipoles. Electrodynamics: Electromotive force; electromagnetic induction;

Faraday and Lenz's laws; inductance; energy in magnetic fields. Maxwell's Equations: Maxwell's fix of Ampère's

law; Maxwell's equations in integral form.

6 Equilibrium stages: Conceptual characterization of separations. Batch distillation: Rayleigh distillation and

batch rectification for ideal mixtures. Continuous distillation: Revision of McCabe-Thiele construction, total and

partial reboilers and condensers, plate efficiencies. Non-ideal mixtures: material and enthalpy balances, Ponchon-

Savarit construction, operating characteristics, link with McCabe-Thiele construction. Column hydraulics:

Characteristics of plates and packings, flooding, flooding correlations and sizing of columns, column control

strategies.

7 The unit will cover first and second order ordinary differential equations including classification and standard

solution methods. Applications will be drawn from the field of classical mechanics, but no prior experience in

mechanics is expected or required. Matlab will be used to illustrate some of the ideas and methods.

http://www.manchester.ac.uk/study/undergraduate/courses/2015/

8 The subject matter of economics. Microeconomics and macroeconomics. Markets and the market economy. The

market forces of supply and demand. Demand curves and supply curves - graphical and algebraic treatment. Market

equilibrium. Elasticity of demand and supply. Government intervention in the market: Price controls and indirect

taxes. Demand. Derivation of the demand curve (single commodity case). Indifference Curve analysis: consumer

equilibrium, income consumption curves, price consumption curves. The costs of production. Perfect competition.

Profit maximization. The short run supply curve. Equilibrium of the competitive firm in the short run and the long

run. Adjustment to changes in demand. (short run and long run). Long run industry supply curve. Welfare and the

efficiency of markets: Consumer surplus and producer surplus. Maximizing the total (social surplus).

Pareto optimality and the problem of interpersonal comparison. Monopoly: Comparison with perfect competition.

Welfare costs of monopoly - the deadweight loss.

9 Introduces the basic ideas of complex numbers relating them to the standard rational and transcendental functions

of calculus. The core concepts of limits, differentiation and integration are revised. Techniques for applying the

calculus are developed and strongly reinforced. Vectors in two and three dimensions are introduced and this leads on

to the calculus of functions of more than one variable, vector calculus, integration in the plane, Green's theorem,

Stokes' theorem and Gauss' theorem.

10

Three lectures illustrating the place of 'Chemistry in the Modern World. The invention of the Periodic Table

Lavoisier to Mendeleyev. Sub-atomic structure Thompson to Schrodinger. The quantum mechanical description of

multi-electron atoms. Bonding and diatomic molecules. Common simplifications to describe bonding in polyatomic

molecules. Alkanes and cycloalkanes, conformation. Stereoisomerism. Mechanisms of reactions, electron movement

and distribution. Curly arrows. Polarization, inductive and resonance effects. Acidity, pKa; stability of anions.

Haloalkanes, synthesis and uses; substitution and elimination reactions. Ethers, alcohols and amines. Alkenes,

electrophilic addition; stability of carbocations. Alkynes; comparison with nitriles. Aldehydes and ketones,

carboxylic acids; interconversion between alcohols, aldehydes. Ketones and carboxylic acids by oxidation and

reduction; carboxylic acid derivatives: esters and amides. Spectroscopy, the basics. Beer-Lambert law. Rotational

spectroscopy. Vibrational spectroscopy. Harmonic and anharmonic oscillator. Electronic spectroscopy. Fluorescence

and phosphorescence. Lasers. NMR spectroscopy. Magnetic resonance imaging. The gas laws. Boltzmann

distribution of speeds. Non-ideal behaviour of gases. Solid structures.

11

Structure of the carbonyl group and review of nucleophilic additions to aldehydes and ketones. Hydration and

hemiacetal formation. Substitution at carbonyl groups leaving groups and use of pKa as a guide to the breakdown of

tetrahedral intermediates. Substitution reactions of acid chlorides. IR spectroscopy as a guide to the reactivity of

carboxylic acid derivatives conjugation delocalization of amides. Interconversion of carboxylic acids, esters, acid

chlorides and amides. Synthesis of alcohols and ketones from carboxylic acid derivatives - reactions with

organometallics. Acid and base catalysis. Substitution in which carbonyl oxygen is lost formation and hydrolysis of

acetals and imines, protecting groups, reductive amination, the Wittig reaction, conjugate addition and substitution.

Some simple enol and enolate chemistry. SN2 reactions nature of the transition state, relative reactivity of different

substrates and reagents. Hard and soft acids (electrophiles) and bases (nucleophiles). Reactivities of different leaving

groups halides and p-toluenesulfonates. SN1 reactions structure and stability of carbocations, relative reactivity of

different substrates. Stereochemical aspects of SN1 and SN2 reactions. E1 and E2 reactions kinetics, substrate

structure dependence, base and leaving group. Competing substitution and elimination. Addition of bromine to

alkenes bromonium ions, regioselectivity of opening, effect of nucleophilic solvents. Epoxides and epoxide opening.

Other oxidations of alkenes. Markovnikov and anti-Markovnikov hydration of alkenes. Hydrogenation of alkenes to

give alkanes. Reduction of alkynes. Structural features and reactivity of benzene (and other aromatics). Nitration,

sulfonation, halogenation and FriedelCrafts reactions of benzene. Direction and activation in substituted benzenes.

Diazotization. Nucleophilic aromatic substitution.

12

Rates of reaction; stoichiometry, mechanism and elementary reactions, molecularity. Experimental methods of

measuring reaction rates, rate laws, order of reaction. Determination of order. First, second and zeroth orders; half-

life. Parallel and consecutive reactions; rate determining step, steady state approximation. Temperature dependence

of reaction rates; Arrhenius equation, pre-exponential factor, activation energy, Arrhenius plot. Transition state,

reaction coordinate, steric factor. Fast reactions in solution; stopped flow, flash photolysis and relaxation methods.

Recapitulation of the 1st Law and of Thermochemistry. Exchange of Heat and Work in a Heat Engine; The Carnot

Process. The 2nd Law: Entropy and Spontaneous Processes. The 2nd Law: The Gibbs Energy (Free Enthalpy). The

Chemical Potential. Phase Diagrams. Thermodynamic Description of Chemical Equilibria; with Examples.

Electrochemical Equilibria: The Nernst Equation. Heisenberg uncertainty principle. de Broglie equation.

Schrodinger Equation. Photoelectric Effect. Interaction of molecules with light. Particle in a box model. Particle on

a ring model. Particle on a sphere model. Harmonic oscillator model. Rigid rotor model. Solutions for hydrogenic

atoms.

13

The first law: Internal energy, enthalpy, and heat capacity. Enthalpy of formation and reaction. Control volume

and steady flow energy equations. Phase diagrams: the phase rule, and PT diagrams for pure substances. Phase

equilibria for mixtures: Raoult’s law, gas solubilities - Henry's law. SLE. The second law of thermodynamics,

entropy and free energy. The Gibbs equation and the Maxwell relations. Conditions for phase and chemical

equilibria. Chemical equilibria - the influence of pressure, temperature and reactant ratio. Thermodynamics of steady

state systems. Analysis of simple heat and refrigeration cycles.

14

Introduction to intermolecular forces and their relevance to bulk properties. Phase behavior for binary and ternary

systems: V-L, L-L, S-L and V-L-L equilibria. Conditions for phase and chemical equilibrium: the Gibbs-Duhem

equation, activity coefficient models, quantitative prediction of phase behavior. Equations of state: fugacities and

fugacity coefficient evaluation, residual properties. Chemical equilibria for real mixtures.

15

Introductory concepts of fluids, units & dimensions, hydrostatics. Flow, flow regimes, conservation of mass &

energy, Bernoulli's equation, flow measurement. Conservation of momentum, force-momentum balances, forces on

pipework. Thermophysical properties of materials (esp. water). Temperature-enthalpy diagrams. Mechanisms of

heat transfer: conduction, convection, radiation. Concept of rate = driving force/resistance, analogy with electrical

circuits. Derivation and application of conduction heat transfer equations.

16

Dimensional Analysis; Rayleigh's Method. Flow around objects: Drag. Viscosity & friction in pipe flows.

Newton’s law of viscosity. Friction & loss factors, The Moody chart. Laminar flow, Hagen-Poiseuille equation and

flow between flat plates. Rating & design of pipelines. Pumps: Types, selection, characteristic curves and Net

Positive Suction Head (NSPH). Heat transfer by convection. Boundary Layer Theory. Correlations for predicting

convection heat transfer coefficients. Boiling & Condensation. Applications of heat transfer in process engineering:

heat losses, insulation, transient heating and cooling. Introduction to heat exchanger design.

University of Birmingham

Link to Course Catalog

1 Semester 1: This module uses real and complex analysis to develop the theory of Fourier transform up to the

inversion formula for piecewise smooth functions. The properties of the Lebesgue integral that are needed are stated

as facts at the beginning of the course and it is used throughout. The properties of the Laplace transform are deduced

as a special case of the Fourier transform.

Semester 2: This module introduces students to the techniques and analysis of numerical methods in linear algebra,

specifically to the numerical solution of linear equations and the numerical determination of eigenvalues and

eigenvectors. The theory is further illustrated by applications using current software packages like eg., Maple or

Matlab.

2 The aim of the module is to enhance the students' mathematical knowledge and confidence in preparation for the

demanding applications of the final stage modules, and a possible research career involving engineering science.

They will develop an understanding of the numerical techniques used within modern Finite Element Analysis

computer packages and develop an understanding of the mathematical basis of many of the advanced systems of

equations governing engineering problems.

Syllabus:

Number systems, errors and mathematical preliminaries, Taylor series

Non-linear equations - Newton's method

Interpolation and Approximation - Lagrange, cubic spline, least squares

Numerical Differentiation and Integration - Euler's method, Trapezoidal and Simpson's rule, Gauss Quadrature.

Systems of linear and non-linear equations

Ordinary Differential Equations - Euler's and Runge Kutta method

Vector differential calculus

Vector integral calculus

Stokes theorem and Gauss divergence theorems

Three-dimensional cylindrical and spherical co-ordinates Classification of partial differential equations

Solution of a range of differential equations of engineering importance

3 By the end of the module the student should be able to: Apply the laws of Gauss, Faraday and Ampère to problems

involving charges and magnetic fields; Have a firm grounding of Maxwell's equations and their origins; Apply and

solve Maxwell's equations to electromagnetic problems; Show that electric and magnetic fields can travel as waves

in free space and media; Calculate the major laws of optics using electromagnetic theory; Apply Maxwell's

equations in order to derive the conductivity of conductors and plasmas; Use Poynting's vector to calculate the

power in an electromagnetic wave. 4 Students spend 6 hours per week in the Year 2 Laboratory during semester 1. One purpose of the lab is to allow

students to investigate a variety of physical phenomena relevant to the second year module, and to understand their

applications. In some cases, the lab experiments investigate material already presented in lectures; in other cases, the

physics is introduced first in the lab. A second purpose of the lab is to introduce students to a range of techniques in

experimental physics, and to develop experimental skills that will be helpful in future work, for example the Year 2

project.

5 This two semester module (part A in Semester 1, Part B in semester 2) introduces the methodologies for the

synthesis of a new process and discusses the factors governing process selection. Process Integration and Unit

Operations Part A first introduces problem-solving approaches reflecting current trends in process integration

(efficient material and energy usage and emissions reduction). Pinch technology is introduced and used to develop

heat exchanger networks, with software demonstrations. The following topics concern equilibrium stagewise

process design, and starting with the unit operations of absorption, distillation and liquid-liquid extraction, students

will be introduced to the concepts of stage to stage calculations and diagrammatic problem solving techniques. They

are also introduced to novel processing routes, including a case study on supercritical fluids. Year 1 Chemical and

Biochemical Processes is a prerequisite module, because that is where the concept that a process is an integrated

whole and not just an assembly of unit operations has been introduced.

http://cis67.bham.ac.uk:7782/webhandbooks/WebHandbooks-control-servlet?Action=getModuleSearchList&pgDspAllOpts=N

http://cis67.bham.ac.uk:7782/webhandbooks/WebHandbooks-control-servlet?Action=getModuleSearchList&pgDspAllOpts=N

6 When mathematical modelling is used to describe physical, biological, chemical or other phenomena, one of the

most common results is either a differential equation or a system of differential equations, which, together with

appropriate boundary and/or initial conditions, describe the situation. These differential equations can be either

ordinary (ODEs) or partial (PDEs) and finding and interpreting their solution lies at the heart of applied

mathematics. This module develops the theory of differential equations with a particular focus on techniques of

solving both linear and nonlinear ODEs. Fourier series, which arise in the representation of periodic functions, and

special functions, which arise in the solution of PDEs such as Laplace’s equation that models the flow of potential,

are also introduced. A number of the classical equations of mathematical physics are solved.

7 By the end of this module the student will be able to: define Opportunity Costs, demonstrate how they affect

economic decisions, and identify these costs in a given economic decision, explain and apply the concepts of

Marginal Benefits and Marginal Costs to determine optimal economic decisions for both consumers and firms,

understand how producers and consumers interact in a competitive market.

8 The materials that will be covered are: (i) an introduction to General Equilibrium; (ii) externalities and Public

Goods; (iii) monopoly; (iv) oligopoly; (v) markets with asymmetric information (vi) an introduction to game theory.

9 Most models of real world situations depend on more than one variable and the techniques of calculus can be

extended to solve problems arising in such situations. Typically these are problems whose solutions are functions of

position, describing, for example, heat distribution or velocity potential, and involve the partial differentiation or

multiple integration of functions of more than one variable. The theory and classification of stationary points of

functions of two or more variables is developed allowing maxima and minima, including those subject to

constraints, to be identified. The differential operators divergence, gradient, curl and the Laplacian are introduced.

These are used in particular in the integral theorems (the Divergence theorem and the theorems of Green and Stokes)

that relate line, surface and volume integrals and are used in the mathematical formulation of physical conservation

laws. This module develops fundamental ideas that are used both in applied mathematics and in the development of

analysis.

10

This module introduces some of the most conceptually and practically important reactions in Organic chemistry.

A mechanistic approach is adopted; that is, the behavior of organic molecules is explained by referring to simple

molecular orbital descriptions of bonding and concepts such as electronegativity and polarization. A relatively

narrow range of principles can then be used to rationalize a diverse array of transformations. In practical terms, the

module shows how organic molecules can be constructed from simple starting materials or building blocks and how

functional groups can be added or manipulated accurately and with control.

By the end of the module the student should be able to: Understand the basic concepts of structure and reactivity in

carbon-based systems; Understand the basic mechanisms of reaction at sp3, sp2 and sp carbon centres; Use the

knowledge of reactions and mechanisms to devise simple synthetic reaction sequences; Use the knowledge of

reactions and mechanisms to rationalize observations given; To undertake simple synthetic organic reactions in the

laboratory, in order to develop basic manipulations and techniques.

11

This module provides an introduction to Aromatic Chemistry (the concept of aromaticity, electrophilic aromatic

substitution, substituent effects and, briefly, heteroaromatic compounds) and an introduction to Reactive

Intermediates (carbocations, carbanions, arynes, radicals, carbenes and nitrenes). The associated Laboratory

component allows techniques and manipulations associated with synthetic organic chemistry to be further developed

and, in some instances, reinforces the lecture material.

By the end of the module students should be able to: Demonstrate an understanding of aromaticity and to identify

whether a compound can be considered as aromatic Demonstrate an understanding of electrophilic aromatic

substitution and be able to draw arrow-pushing mechanisms for the reaction of aromatic compounds with a range of

electrophiles. Students should also be able to predict and account for substituent effects in electrophilic aromatic

substitution reactions. Demonstrate an understanding of the structure, bonding and reactivity of carbocations,

carbanions, arynes, radicals, carbenes and nitrenes. Demonstrate the ability to perform synthesis in organic

chemistry, characterise products obtained and present the results obtained in a coherent manner.

12

This module develops further the chemistry of carbon-based compounds, and builds upon the principles and

concepts introduced in the co-requisite module (Synthesis and Mechanism I). Two distinct areas are covered in the

module: The Chemistry of Carbonyl Compounds (enolate chemistry; enamines; aldol reactions; Claisen

condensation) and Physical Organic Chemistry which looks at how physical methods are used to probe the reactivity

of organic molecules. The associated Laboratory component allows techniques and manipulations associated with

synthetic organic chemistry to be further developed and, in some instances, reinforces the lecture material.

By the end of the module students should be able to:

Demonstrate an understanding of enolate chemistry, including enamines, the aldol reaction and the Claisen

condensation. Demonstrate an understanding of how physical methods can be used to probe the reactivity of organic

molecules and be able to interpret the results of physical experiments in terms of organic reaction mechanisms.

Demonstrate the ability to perform synthesis in organic chemistry, characterise products obtained and present the

results obtained in a coherent manner.

13

Quantum Mechanics:

Experimental observations of atoms and their interactions with radiation provided the driving force for the invention

of Quantum Theory. Quantum Mechanics offers the only model we have that explains the properties for atomic

systems. Evidence will be reviewed that leads us to the need and use of Quantum Mechanics. We will see how

Schrodinger's wave mechanics and Heisenberg's uncertainty principle can help us to understand atoms. This module

concentrates on the concepts and avoids a full mathematical treatment.

Optics and Waves: The study of wave motion underpins our understanding of basic physics. We discuss the properties of waves, often

taking as an example transverse waves in strings but also illustrating how the results are applicable not only to sound

and light but also to quantum mechanics. The study of optics builds directly on our wave concepts. Applications and

links to other branches of physics are emphasized.

By the end of the module the student should be able to:

Quantum Mechanics:

Appreciate the limitations of classical mechanics and the need for a theory at the microscopic level; Understand the

implications of the wave-like behavior of matter and electromagnetic radiation; Understand various atomic models

and the experimental evidence provided by optical and X-ray spectra, and methods for their production and study;

Apply the wave-like behavior of matter to electrons and the consequences for bound states.

Optics and Waves: Describe the basic concepts of wave motion and describe both travelling and standing waves;

Describe the interference and diffraction of waves and the importance of spatial and temporal coherence; Use

phasors in order to calculate interference patterns produced by sets of regular very narrow slits and also the

diffraction pattern produced by a slit of finite width; Describe the laws of reflection and refraction and apply them to

mirrors and lenses; Describe how modern light sources and detectors operate; Link the concepts developed in the

module and use them to solve a wide range of problems.

14

Quantum Mechanics describes the behavior of matter on sub-microscopic scales and, together with relativity, is

one of the two foundations of modern physics. Quantum systems are often described as having both wave-like and

particle-like aspects to their behavior, and are famous for producing results that defy common-sense intuition based

on observations at everyday scales. In this module we will introduce Schrödinger's wave equation and use it to

investigate the behavior of simple quantum systems, from a free particle through to single-electron atoms. We will

discuss the wavefunction, which describes the state of a system, how to interpret it, and how making a measurement

changes the wavefunction. We will illustrate some of the non-intuitive behavior of quantum systems, show how it

arises, and how, in the limit of large energies, it tends towards classical behavior. We will discuss how mathematical

operators are used to represent physical quantities, and see where the Uncertainty Principle comes from. We will

introduce the quantum treatment of angular momentum and show how an additional property of the electron (spin) is

required to describe atomic states. We will consider the special properties of quantum states consisting of more than

one electron, and show how the existence of complex chemistry depends on these.


Perform approximate calculations using the de Broglie relation and the Heisenberg Uncertainty Principle; Normalize

a wavefunction; Use wavefunctions to calculate expectation values and the probabilities of different outcomes of

measurements; Show how measurement changes the wavefunction; Be familiar with the use of Hermitian operators

to represent physical quantities in quantum mechanics and the properties of their eigenvalues and eigenfunctions;

Explain the physical significance of each element of an eigenvalue equation; Be familiar with the time-dependent

and time-independent Schrödinger equations; Solve the time-independent Schrödinger equation for simple 1-D and

3-D potential problems; Describe the main features of the solutions for a range of problems; Evaluate the

commutator of two operators and explain its physical significance; Be aware of how the Pauli exclusion principle

arises and be able to apply it to multi-electron systems; Describe the properties of angular momentum in quantum

mechanics; Relate the quantum numbers of atomic electrons to physical variables and know how their different

values are related; Explain why the concept of electron spin is required to explain experimental observations.

15

The aim of this module is to give a thorough grounding in the principles of quantum mechanics. It builds on the

wave mechanics studied in Years one and two where the wave nature of matter was introduced as described by the

Schrodinger equation. In this module we begin with the fundamental postulates underlying quantum mechanics.

We will introduce Dirac's notation for doing quantum mechanics which will allow us to study quantum properties

like "spin" which have no counterparts in classical physics. This is vital for applications of quantum mechanics such

as quantum computing. We will also see how the Schrodinger equation originates. The module will cover

fundamental aspects - such as the connection between symmetry and conservation laws - as well as applications and

approximate, yet powerful, tools like perturbation theory for handling situations where exact results are not possible.


Describe the main postulates of quantum mechanics; Compute the probabilities of observables and expectation

values given a sequence of measurements of a quantum system; Use Dirac notation; Use operator commutation

relations to compute the time-dependence of expectation values and uncertainty relations; Separate the Schrodinger

equation to address issues like the degeneracy of states in quantum systems in two or three dimensions and the time-

dependence of a wavefunction from stationary states; Use angular momentum and spin operators: for example, to

discuss the Stern-Gerlach experiment; identify and construct non-interacting wavefunctions suitable for

indistinguishable fermions and bosons; (Advanced students) Use time-independent perturbation to first order and the

variational method to approximate solutions to quantum problems.

16

Fluid Flow:

Introduction to fluid flow phenomena in engineering. Hydrostatics: Pressure variation with position in a static fluid,

manometers, hydrostatic forces on submerged surfaces, forces on unconstrained bodies, surface tension and

capillarity, methods of surface tension measurement. Hydrodynamics: classification of flows in terms of variation of

flow parameters in time and space, the concepts of streamline and stream tube, the principles of continuity, energy

and momentum, turbulent flow. Applications of principles to engineering problems, including flow measurement by

orifice, Venturi, Pitot tube, rotameter & weirs. Forces on pipe bends, nozzles and plates. Steady flow problems

concerning head loss and pressure drop due to friction in pipe flows (Bernoulli), non-circular ducts, friction factors,

Moody diagram and friction losses in fittings. Physical fluid properties, their dimensions and units, SI System,

dimensional analysis.

Thermodynamics: The scope of thermodynamics. The basic quantities and their SI units. The fundamental concepts: force, pressure,

temperature, intensive and extensive properties, the system and its surroundings, closed and open systems, state and

processes, phases and components, phase changes and equilibrium, and the different forms of energy. First Law. The

energy balance equation and its applications to closed and open systems. The continuity equation. Work and heat in

processes. Reversible and irreversible processes. Heat engines. Carnot cycle and some other theoretical cycles

including refrigeration. Second Law: Entropy and irreversible processes, spontaneous processes. The preparation

and the use of thermodynamic tables and diagrams (including using entropy to calculate work in adiabatic

processes).

Heat Transfer:

Conduction: (one-dimensional steady state) Fourier’s Law, conduction with multiple layers, simple geometries,

resistance in series. Convection and Boundary Layers: Heat transfer coefficients for natural and forced convection.

Practical problems involving forced convection, resistances in series, overall heat transfer coefficients, Design of

simple heat exchangers, log-mean temperature differences. Basics of radiation: (Stefan-Boltzmann equation),

emmissivity, absorptivity, transmissivity and reflectivity, net exchange of radiation between surfaces .

17 This module looks to develop the required skills for any graduate chemical engineering in the area of chemical

thermodynamics, with particular emphasis on how this information is used in practice.

The type of material covered will be.

(i) Introduction; refresh of fundamentals (zeroth, 1st, 2nd, 3rd laws, free energies)

(ii) Equations of state

(iii) Vapor-liquid equilibria and other phase equilibria

(iv) Chemical Potential and use in single and multicomponent systems

(v) Concept of fugacity and it links to Chemical Potential

(vi) Activity Coefficients

(vii) Phase Separation

(viii) Chemical Reaction Equilibria

University College London

Link to Course Catalog 1 This course is a continuation of Mathematical Methods 3 (MATH2401) and aims to introduce further tools

required to solve the partial differential equations which arise in applied mathematics.

It first looks at the application of the separation of variables method in cylindrical and spherical coordinates. This

necessitates a study of Bessel's and Legendre's equations and their solutions. This is done via a combination of the

Frobenius method of series solution of ODE's together with generating functions.

The course then moves on to study transform methods of solving PDEs, complementing the method of separation of

variables and concentrating on the Fourier and Laplace transforms. The necessary techniques of integration in the

complex plane will be reviewed.

2 Topics covered include:

Introduction. Types of flowsheet. Process variables and their units. Composition relationships. Ideal gases. Dalton's

Law. Mass balances. Tie substance. Flowsheet analysis. Problems involving reaction and recycle streams. Phase

equilibrium. Binary mixtures. Raoult's Law. Phase diagrams for simple binary mixtures. Mass balance problems

involving change of phase. Heat capacity. Heat of formation. Enthalpy and its estimation. Enthalpy-composition

charts. Energy balances: reaction and non-reaction applications. Problems involving combined mass and energy

balances. Introduction to chemical reactors. Heat exchangers: types and construction, log-mean temperature

difference. Pipe flow: friction factors, fittings. Pumps, power for pumping. Introduction to distillation.

3 This course offers an introduction to numerical analysis, the theory underlying the numerical methods that are

frequently used to solve a wide range of practical problems.

Methods covered in this course should include: estimating solutions of ordinary differential equations (including

systems with initial or boundary conditions); finding real roots of equations; interpolation and fitting of functions to

prescribed data points; fast Fourier transforms; advection schemes.

Basic programming skills are required for the project component, and students taking this course should have some

experience with e.g. FORTRAN or Mathematica or C/C++, or be willing to learn such skills themselves.

4 Syllabus:

Milestones in electromagnetism [1 Week]

Coulomb's torsion balance and the inverse square law of electric charges. Biot-Savart law

governing the force between a straight conductor and a magnetic pole. Introduction of the

concept of field by Faraday. Maxwell's equations. Hertz's oscillating dipole experiment.

Marconi's and Morse' invention of wireless communication.

Electrostatics [6 Weeks]

Coulomb's law; electric field; Gauss' law; superposition principle; electric field for a continuous

charge distributions and electrostatics in simple geometries (spherical, cylindrical and planar

distribution of charges). Gauss' law in differential form. Electric potential; electric field as

gradient of the potential; electric potential for a point charge; electric potential for a discrete

charge distribution; electric dipole; potential of acontinuous charge distribution. Electrostatic

energy; energy for a collection of discrete charges, and for a continuous charge distribution.

Conductors [3 Weeks]

Electric field and electric potential in the cavity of a conductor; fields outside charged

conductors; method of images. Vacuum capacitors: definition of capacitance; parallel plates,

spherical and cylindrical capacitors; capacitors in series and parallel; energy stored in a capacitor.

Dielectrics [1 Weeks]

Dielectrics: definition and examples. Energy of a dipole in an electric field. Dielectrics in

capacitors: induced charge, forces on dielectrics in non-uniform fields.

DC circuits [3 Weeks]

http://www.ucl.ac.uk/prospective-students/study-abroad-guide/application-study/subjects/search/subjects

Current and resistance; Ohm's law; electrical energy and power. DC circuits: emf, Kirchoff's

rules. Examples.

Magnetostatics [5 Weeks ]

Magnetic field, motion of a charged particle in a magnetic field and Lorentz force. Velocity

selector, mass spectrometer, Hall effect. Ampere's law and Biot-Savart law. Magnetic field due

to a straight wire, a solenoid, a toroid and a current sheet. Magnetic force between current

carrying wires. Energy of a magnetic dipole in a uniform field.

Electromagnetic induction [4 Weeks]

Magnetic flux. Gauss' law for magnetism. Ampère-Maxwell law. Faraday's law of

electromagnetic induction. Examples of emf generated by translating and rotating bars. Lenz's

law of electromagnetic induction; electric generators; self inductance and mutual inductance;

self inductance of a solenoid; back emf; eddy currents. Faraday's law in differential form.

Transients in RLC circuits. Energy in the magnetic field.

AC circuits [3 Weeks]

AC generators and transformers; circuit elements (R,C,L); impedance, complex exponential

method for LCR circuits: the RC circuit, the RL circuit and the RLC circuit. Resonances, energy

and power in the RLC circuit.

Maxwell's equations [1 Weeks]

Maxwell's equations in vacuo and plane wave solution

5 Scope of process flowsheeting, topology analysis, sequential and simultaneous solution methods, mass transfer unit

simulation, capital cost estimation. Mass transfer driving forces, rate equations, local and overall transfer

coefficients, Henry's Law, Film Theory. Methods of two-phase contacting for the purpose of mass transfer.

Stagewise contacting. The Ideal Stage. Absorption and stripping towers: design procedures. The Transfer Unit.

Estimation of physical and thermodynamic properties; ideal and non-ideal vapour-liquid equilibrium. Flash

distillation. Differential distillation. Rectification. Theoretical plates, plate efficiencies, transfer units. Use of

graphical methods for the analysis of continuous rectification processes. Multicomponent distillation. Tray

Hydraulics. Column design. Liquid-liquid extraction processes: The Lever Rule, theories of multiple contact, co-

current and counter-current extraction with both immiscible and partially miscible solvents. Extraction equipment.

6 Syllabus:

Linear ordinary differential equations

Non-linear ordinary differential equations

Asymptotic behaviour of integrals

7

Intended as an introductory course for students who have no background in Economics and are interested in

pursuing studies mainly in other subjects, this course introduces students to the central principles of

microeconomics. By the end of the course, students should be entirely familiar with the most commonly used

concepts from theoretical models of supply and demand; be aware of the applicability and limitations of theory;

combine concepts with data, and give explanations to current phenomena based on solid analytical models;

understand debates over consumer, firm behaviour, and prices; current policies and their effect on consumers and

firms.

8 This course introduces all the techniques necessary for an understanding of the theorems of Green and Stokes.

These theorems are important in the theory of electrostatic potential and Laplace's Equation. This equation is often

solved by the 'separation of variables' technique and for this reason Fourier series are also studied.

Syllabus: Partial differentiation. Chain rule. (Taylor series).

Line integrals. Potential energy. Gradient.

Integration over plane areas. Volumes. Change of variables. Jacobians.

Integration over volumes. Flux, Gauss' theorem, Green's theorem, Stokes' theorem, divergence, curl, standard

identities and manipulations, summation convention.

Fourier series: periodic functions, approximating series, formulae for coefficiants.

Series solution of ordinary differential equations about regular points.

9 An introduction to organic chemistry. The course involves lectures, tutorials and laboratory work.

A flavour of the material covered in this course is presented below:

Alkanes and Cycloalkanes. Conformation and dynamics of ethane, butane, and cyclohexane and their simple

substituted derivatives. Free radical chlorination and radical chain mechanisms. Alcohols, Ethers and Epoxides.

Relationship to water. Structure and hydrogen bonding in alcohols. Acidity of alcohols; alkoxide ions, Williamson

ether synthesis. Basicity of alcohols; substitution and elimination reactions on protonated alcohols. Substitution and

addition reactions with alcohol as nucleophile. Oxidation of alcohols. Inertness of ethers apart from autoxidation and

strong-acid cleavage, but contrasting reactivity of epoxides. Use as solvents; crown ethers Aldehydes and Ketones.

10

The course involves lectures, tutorials and laboratory work. Content includes synthesis, reactivity, structure

determination and mechanism in organic chemistry and biologically important molecules. CHEM1201 (or

equivalent) is a prerequisite.

Section A: Organic Synthesis I Reactivity And Synthetic Methods: Basic carbonyl chemistry, enolate chemistry.

Retrosynthetic Analysis I: Concepts. Retrosynthetic Analysis II: 1, 3-Functionalised Compounds and Their

Disconnections. Retrosynthetic Analysis III: 1,5-Functionalised compounds and their disconnections.

Section B: Spectroscopy: 1H, 13C, 19F, 31P NMR Spectroscopy, Mass Spectrometry, Structure elucidation using

IR, NMR, MS.

Section C : Organic Synthesis II: Nitrogen, sulfur, Boron, Silicon and Oxygen. Difunctionalised Compounds 1,2

Difunctionalised compounds and their disconnections, Umpolung methods, advanced disconnections Diels-Alder

Reactions.

Section D: Aromatic and Heteroaromatic Compounds: Substitution and Addition reactions.

11

This course aims to develop an understanding of the principles of quantum mechanics and their implications to the

solution of physical problems.

Topics include:

The failure of classical physics. Steps towards wave mechanics. One-dimensional time-independent problems. The

formal basis of quantum mechanics. Angular Momentum in quantum mechanics. The hydrogen atom - qualitative

treatment. Magnetic moments and electron spin. Correspondence principle and Expansion Postulate. Ehrenfest's

theorem. Introduction to atomic structure. Review of one electron atoms. Many-electron atoms including the Pauli

Principle and spin. Atoms and radiation. Atoms in static electric and magnetic fields. Molecular Structure and

bonding. Molecular Spectra. Harmonic oscillator.

12

Syllabus:

Review of one electron atoms. [2 Lecture]

One electron atoms. Correspondence Principle. Reduced mass. Atomic units and

wavenumbers. Review of quantum angular momentum and spherical harmonics. Review of

hydrogen atoms and spectra. Lyman, Balmer and Paschen series. Electron spin and

antiparticles.

Many electron atoms [10 Lecture]

Independent particle and central field approximations. Alkali atoms and quantum defect

theory. Indistinguishable particles, Pauli Principle. Helium atom and exchange.

Configurations and terms. Spin-Orbit interaction. Levels and Spectroscopic notation.

Overview of forces on isolated atom. Atoms in radiation: dipole allowed and forbidden

transitions. Einstein coefficients. Metastable levels. Laser operation. Laser cooling. X rays

and inner shell transitions.

Molecular Structure and spectra [9 Lecture]

The Born-Oppenheimer approximation. Electronic spectra : H2+ and H2. Effects of symmetry

and exchange. Bonding and anti-bonding orbitals. Nuclear motion: rotation and vibrational

spectra for ideal molecules (rigid rotation, harmonic vibrations). Covalent and ionic bonds.

Selection rules.

Atoms and Electromagnetic Fields [4 Lecture]

Atoms in static external fields: atoms in magnetic fields. Normal and anomalous Zeeman

effect. Hyperfine splitting. The Stern-Gerlach experiment. NMR and ESR. Atoms in electric

fields: Linear and Quadratic Stark effect.

Brief introduction to scattering [2 Lecture]

Total cross section. Differential cross section. Examples of electron-, positron- and

positronium- total cross-sections: dominant interactions. Quantum scattering

13

Topics include:

Fundamentals: origins and scope, basic definitions. Work: reversible and irreversible. First Law: internal energy,

enthalpy and heat capacity. Equations of state: ideal and real gases. Applications of first law to gaseous systems:

adiabatic expansion of ideal gas, poly-tropic expansion. Joule-Thomson effect. Second Law: Carnot theorem, Kelvin

temperature scale. Entropy: change in reversible cycles, T-S diagrams, availability, energy, lost work, Maxwell’s

relations, Clausius entropy principle, calculation of entropy changes. Criteria for spontaneous change and

equilibrium: Gibbs function changes in pure phases, Clausius-Clapeyron equation. Partial properties: Gibbs Duhem

equation, phase equilibrium between mixtures, phase rule, fugacity. Thermodynamics of Machines: reciprocating

compressors: single and multi-stage compression with intermediate cooling. Refrigeration systems: ideal Carnot,

vapour compression and absorption. Gas liquefaction: Linde process. Power cycles: Rankine, reheat and

regenerative feed-water heating. Chemical Thermodynamics: laws of Hess and Kirchoff, partial molal quantities,

chemical potential. Equilibrium constants and their temperature dependence. Activity and fugacity coefficients.

14

Topics include:

Nature of transport processes and fluids. Laminar and turbulent flow. Fluid statics: pressure variation in a static

fluid, pressure measurement and buoyancy. Dimensional analysis and similarity: Buckingham's pi theorem. Pilot

plants and the use of models. Conservation of mass, momentum and energy equations. Bernoulli's equation and its

application to flow measurement devices. Transport in solids and in laminar flow: steady state conduction of heat in

various geometries; plane Couette flow, laminar flow in pipes; mass transfer by diffusion. Transport in turbulent

flow: characteristics of turbulent flow. Momentum, heat and mass transfer coefficients. Frictional losses due to

roughness and fittings. Whitman two-film theory for mass transfer. Simple momentum, heat and mass transfer

analogies.

15

Modes of heat transfer: conduction, convection, radiation; Fourier's law; conduction in cylindrical and spherical

shells (critical thickness of insulation for tubes); derivation of heat conduction equations for transient and

multidimensional cases; boundary and initial conditions; methods for solving 1-D transient heat conduction equation

(slab, sphere and cylindrical geometries); thermally thin bodies, lumped heat transfer coefficient. Convective heat

transfer. Dimensional analysis; forced convection; natural convection; correlations for heat transfer coefficient.

Thermal radiation; electromagnetic spectrum; the black surface; real surfaces; shape factors; radiation transfer

through gases. Solar energy. Two phase flows; flow regimes; homogeneous flow; separated flow; drift-flux model;

bubbly flow; slug flow; annular flow. Condensation, evaporation and boiling; film condensation; film evaporation;

pool boiling; forced convection boiling and condensation; heat pipes. Heat exchangers; logarithmic mean

temperature difference; pressure drop; pressure drop in a tube for a compressible gas; counterflow double-pipe heat

exchangers; shell and tube exchangers; condensers; kettle reboilers; thermosyphon reboilers; multiple effect

evaporators. Direct contact gas-solid exchangers; cyclic batch operation - fixed beds.

16

Prediction of transport properties.

Continuity and Navier-Stokes equations: application to simple flow systems. Boundary layer theory: exact solution

for laminar boundary layer, momentum integral equation, analogies for heat and mass transfer. Turbulent flow:

turbulence measurement, statistical and mixing length theories, heat and mass transfer in turbulent flow. Momentum

transfer: single phase laminar and turbulent flow phenomena. The film and penetration models of mass transfer and

their application to gas-liquid reactions. Mixing. Transport phenomena in stirred tanks. Power consumption

(including non-Newtonian fluids): particle suspension and transport: gas dispersion, flooding and power

consumption. Heat transfer: prediction of heat transfer coefficients. Mass transfer: mixing time, mixing and

chemical reaction. Static mixers. Non-Newtonian fluid behaviour. Fluid-particle interactions.Viscoelasticity: models

and test methods, linear and non-linear behaviour, Weissenberg effect, die swell. Pipe flow: viscoelastic fluids, solid

suspensions and slurries. Heat transfer correlations.

University College Dublin

Link to Course Catalog 1 This module module introduces students to advanced techniques in multivariable calculus with an emphasis on

applications in Engineering and the Physical Sciences. Topics covered will include: Vector fields and potentials,

Gradieny, Divergence and Curl; Transformations between rectilinear, cylindrical and spherical co-ordinates; Line

integral, work integrals; Double integrals and Green's Theorem; Stokes' Theorem and the Divergence Theorem;

Laplace's/Poisson's equation; The heat equation, the wave/string equation; Fourier Transform and Fourier Series.

2 This module will introduce students to principles and techniques that are used in the analysis of chemical and

biochemical engineering processes. Steady state and un-steady state mass and energy balances are fundamental tools

for the assessment of such process. The use of balances in, for example, the development sustainable process will be

introduced. Students’ analytical abilities and problem solving skills will be developed through regular homework

assignments. Their technical reporting and communication skills are developed in the preparation and delivery of a

presentation on a technical topic making use of internet and library resources. The module will include a number of

site visits.

3 Students will learn to apply selected numerical methods in the solution of chemical engineering based problems

using Matlab and Excel. The module content will cover selected topics from the following,

1. Algorithms, Precision & Errors

2. Solutions of Non-Linear Equations

3. Solution of Systems of Non-Linear Algebraic Equations

4. Iterative Solutions of Systems of Linear Equations

5. Polynomial Interpolation

6. Cubic Spline Interpolation

7. Linear Regression

8. Data Smoothing & Differentiating

9. Non-Linear Regression

10. Numerical Integration

11. Numerical Solution of Ordinary Differential Equations

12. Partial Differential Equations

4 This module presents the field theory of electromagnetism. Gauss's Law, Ampere's Law, Biot-Savart's Law and

Faraday's Law are examined from the perspective of Maxwell's Equations. The physical significance of these

equations is emphasized. Solutions to Maxwell's Equations in the form of electromagnetic waves are presented.

Their behavior in vacuum, dielectrics, conductors, wave-guides, and at the interface between media is described.

Electromagnetism as a relativistic phenomenon is discussed and the nature of light is investigated. The source of

electromagnetic radiation is identified.

5 On completion of this module, students should be able to:

1. Demonstrate an understanding of the analysis of a range of separation processes in terms of equilibrium stages as

applied to chemical, oil & gas & bioprocessing systems.

2. Design and analyze batch and continuous distillation systems for binary systems, to achieve a specified degree of

separation.

3. Apply the Fenske-Underwood Gilliland method to the preliminary design of multi-component distillation

systems.

4. Specify appropriate system configurations for drying and multiple-effect evaporation processes.

5. Design absorption/scrubbing systems, based on the height and number of transfer units and on the generalised

pressure drop correlation.

6. Develop and apply the fundamental equations required for the design of cascades, with particular reference to

liquid-liquid extraction systems.

7. Specify the configuration and operating conditions of a selected range of solid-liquid and solid-gas separation

systems.

8. Use selected simulation tools for the preliminary analysis of a range of unit operations.

http://www.ucd.ie/students/course_search.htm

6 This course introduces students to the theory of differential equations and dynamical systems and to their many

applications as mathematical models. The topics covered prepare the student for more advanced subjects in ordinary

differential equations, dynamical systems theory, numerical methods and partial differential equations.

Course Outline: A) Review of the theory of 1st-order ODEs

B) 2nd-order ODEs: Definitions, linear vs. nonlinear, dimensional analysis, examples

C) Theory of 2nd-order linear ODEs: Superposition principle, Wronskians and linear independence, method of

undetermined coefficients, Abel's formula, method of variation of parameters.

Examples: forced and damped systems, Riccati equation, mechanical oscillations, resonances, etc.

D) Systems of 2 coupled ODEs: Linear and nonlinear, phase plane analysis, critical points and classifications in

terms of eigendirections and eigenvalues, Jacobi last multiplier method (integrating factor), non-autonomous

systems and chaos.

Examples: population models, the tragedy of the commons, epidemic models, etc.

E) Numerical methods: Numerical Root Finding: Newton method and other iteration methods, link with critical

points of systems of ODEs, convergence and stability of the iteration methods, Euler method for time evolution of

coupled ODEs.

Examples: Solving transcendental equations in classical and quantum mechanics, finding the critical points of highly

non-linear ODE systems, integrating numerically ODE systems such as the chaotic Lorentz model or the integrable

prey-predator system

7 This module provides a basic analytical framework for understanding the functioning of markets. The module

begins by examining gains from trade and exchange, demand, supply and price determination in individual markets

and the effect of taxes in those markets. The module also examines market failure and regulation and the

justification and nature of government intervention in markets. The module also examines the economics of firms in

different types of market structures (competition, monopoly, and oligopoly), strategic interaction between economic

agents (elementary game theory) and basic issues in the economics of labor markets.

8 The module is an introduction to organic chemistry, the chemistry of carbon. It covers the common organic

molecules (alkenes, alcohols, amines, carbonyls etc.) and emphasises their recognition, naming, reactions and

relevance to everyday life and health. Specific topics include 3D aspects of chemistry, what exactly happens in a

chemical reaction and how it is done in practice. A significant proportion of the module is devoted to the larger

molecules of life (proteins, carbohydrates, fats) and shows how these can be understood in terms of the simpler

molecules.

9 This module advances the concepts of the chemical reactivity of carbonyl and aromatic compounds with a specific

emphasis placed on gaining an understanding of their different modes of reaction. It includes numerous examples of

the application of the described chemistry to the making of complex chemical entities. The laboratory sessions

complement the material covered in lectures.

10

This module has two parts. The first part presents the key principles and techniques of quantum theory along with

applications of the theory to relevant model systems. This knowledge is then employed to make a comprehensive

description of (i) the internal structures of hydrogen-like and many-electron atoms, (ii) how atoms interact with

light, and (iii) why atomic properties exhibit periodic trends. The second part of this module deals with the

rotational, vibrational and electronic spectroscopy of molecules examining how changes in the energy, structure and

motion of molecules affect their spectroscopic properties. Conversely, careful analysis of molecular spectra is

demonstrated to be an important way by which one may obtain critical information about the nature of molecules

such as their electronic structure, the strengths, lengths and angles of their bonds, and their dipole moments.

11

On completion of this module students should be able:

1. to provide a molecular-level interpretation of key thermodynamic variables such as internal energy (U), Entropy

(S) and Gibbs Free Energy (G)

2. to solve chemical engineering problems amenable to analysis by chemical thermodynamics, in particular those

relating to first and second law principles (U, S, G)

3. to synthesize and solve rate-law expressions for both homogenous and non-homogenous chemical reacting and

equilibrium systems

4. to analyze heat cycles in terms of achievable efficiencies and propose techniques to maximize heat-cycle

efficiency

12

On completion of this module students should be able to: Estimate solubility of gases and solids in liquids;

Construct binary phase equilibrium diagrams for a range of solvents using non-ideal thermodynamics; Analyze

liquid-liquid equilibrium systems; Analyze reaction schemes to determine equilibrium constants and reaction

conversions; Use thermodynamic software tools and conduct simulations of flash operations available in commercial

software packages. Demonstrate an understanding of the role of thermodynamics in safe and effective process

design.

13

On completion of this module students should have acquired:

1. A familiarity with the modes of heat transfer and their relevance in practical engineering systems.

2. The ability to calculate rates of heat transfer for steady-state, mixed-mode exchange in chemical engineering

configurations.

3. An understanding of the basic elements of heat exchanger operation and design.

4. An understanding of the fundamental principles of molecular diffusion and the physical basis of the underlying

phenomena.

5. The ability to determine steady-state concentration profiles and diffusional fluxes in simple geometries.

6. The ability to determine overall mass transfer coefficients for inter-phase mass transfer and to determine the rate-

limiting step.

7. An ability to estimate losses in pipe flows.

8. An ability to apply the Engineering Bernoulli equation to practical flow configurations.

14

On completion of this module students should be able to:

1. Model steady and unsteady heat exchange systems involving conduction and /or convection.

2. Explain the origin and significance of selected dimensionless groups and apply dimensionless correlations to a

variety of heat exchange configurations.

3. Specify and design simple heat exchangers having due regard for the safety and environmental implications of

design decisions.

4. Apply the macrobalances of mass, momentum and energy to typical process flows including piping networks,

packed-bed and fluidized-bed reactors, pumped circuits, agitated reactors etc.

5. Analyze and quantify the effects of non-Newtonian behavior upon fluid flow in piping and reactor configurations.

6. Select and specify such items as pumps, valves and agitator impellers for a variety of process applications.

Hong Kong University of Science & Technology

Link to Course Catalog 1 Derivatives of the Laplace equations, the wave equations and diffusion equation; Methods to solve equations:

separation of variables, Fourier series and integrals and characteristics; maximum principles, Green's functions.

2 Processes and process variables, engineering data. The conservation principle. Material and energy balances on

non-reactive and reactive process units and systems, recycle and purge. Unsteady state processes.

3 Computer arithmetric, matrix computation, interpolation and approximation, numerical integration, solution of

nonlinear equations.

4 This course employs a calculus‐based approach. Key topics include Coulomb’s law, electric field and potential,

Gauss’ law, capacitance, circuits, magnetic force and field, Ampere’s law, electromagnetic induction, AC circuit,

Maxwell’s equations, electromagnetic waves, geometric optics, interference and diffraction.

5 Laboratory accompanying PHYS 1413.

6 Phase equilibria. Ideal and nonideal mixtures. Thermodynamic properties and VLE from equations of state.

Liquid-liquid and liquid-solid systems. Stage process, short-cut and rigorous calculations in absorption, distillation

or extraction. Continuous contacting processes. Separation sequences. Simulation and design.

7 First law of thermodynamics for closed and open systems, enthalpy and the energy equation. PVT data and

thermodynamic properties, methods for their estimation, phase equilibria. Second and third laws of thermodynamics,

entropy and the Carnot engine. Power cycles, refrigeration and liquefaction. Process examples.

8 First order equation, linear second order equations, Laplace transform, Euler and Runge-Kutta methods,

introduction to partial differential equations, matrix, systems of linear equations, eigenvalue and eigenvector,

systems of differential equations, orthogonal projection.

9 Theory of firm in a free enterprise system; theory of consumer demand; market structures and resource allocation;

efficiency of competitive markets; selected topics on government regulation. Students with non-local qualifications

should seek department’s or school’s approval for enrollment in the course.

10

Sequences, series, gradients, chain rule. Extrema, Lagrange multipliers, line integrals, multiple integrals. Green's

theorem, Stroke's theorem, divergence theorem, change of variables.

11 Structure and bonding; regio-, geometric, and stereoisomerism; polar and radical reactions of alkenes and alkynes;

substitution and elimination reactions; and an introduction to NMR, IR, and mass spectrometry.

12 Dienes, resonance and aromaticity; electrophilic aromatic substitution and nucleophilic aromatic substitution;

benzylic and allylic reactivity; the chemistry of carbonyl compounds and carboxylic acid derivatives; the chemistry

of amines; pericyclic reactions.

13 Experimental techniques of organic chemistry; preparation, separation and characterization of organic compounds

and natural products

14 Basic quantum theory, atomic and molecular structure, equilibrium statistical thermodynamics.

15 Applications of fluid mechanics in chemical engineering. Fluid properties; energy equations and applications in

process systems; flow in pipes and channels, around submerged objects. Laminar and turbulent flow, flow

measurements.

16 Steady-state conductive, forced and free convective, radiative heat transfer in simple and complex process

environments. Analysis and design of heat exchangers, fouling. Basic mass transfer concepts. Continuous contacting

process and traditional design methodologies. Numerical solutions and simulations of unconventional examples.

http://publish.ust.hk/prog_crs/ugcourse/

Pohang University of Science & Technology

Link to Course Catalog 1 The study of differential equations, which are the equations containing derivatives of functions, is one of the most

beautiful and important applications of calculus to our everyday lives. It is remarkable and inspiring that the

fundamental principles that govern many phenomena (in the fields of not only Sciences and Engineering, but also

Economics and Social sciences) could be expressed in the language of differential equations.

In this course we aim to learn the following:

1. The 1st- and 2nd

order ODEs

2. System of ODEs

3. Series solutions of ODEs

4. Laplace transforms

5. Fourier series

6. PDEs (Wave equation, Heat equation, Laplace equation), etc.

2 Lecture Plan:

1. Thermodynamic system, heat and work

2. Mass and energy balance

3. Entropy balance

4. Heart engines, power cycles, machieries

5. Evaluation of thermodynamic propertiesa with partial derivatiess, equatin of states and engineering concepts

3 Lecture Plan:

1. Roundoff Errors and Computer Arithmetic

2. Algorithms and Convergence

3. The Bisection Method

4. Fixed-Point Iteration

5. Newton's Method

6. Error Analysis

7. Zeros of Polynomials

8. The Lagrange Polynomials

9. Divided Differences

10. Hermite Interpolation

11. Cubic Spline

12. Parametric Curves

13. Numerical Differentiation

14. Richardson's Extrapolation

15. Numerical Integration

16. Composite Numerical Integration

17. Romberg Integration

18. Adaptive Quadrature

19. Gaussian Quadrature

10. Multiple Integrals

11. Linear System of Equations

12. Pivoting Strategies

13. Linear Algebra and Matrix inversion

14. The Determinant of a Matrix

15. Matrix Factorization

16. Special Types of Matrices

17. Norms of Vectors and Matrices

18. Eigenvalues and Eigenvectors

19. Iterative Technique for Solving Linear Systems

20. Iterative Technique for Solving Linear Systems

21. Error Bounds

http://lms.postech.ac.kr/Main.do?cmd=viewHelpMain&mainMenuId=menu_00053&subMenuId=&menuType=menu

4 General Physics II covers electromagnetism and optics, including electric field and potential concepts, electric

current and magnetic field, induction law, dielectrics and magnets, electromagnetic wave, and optics. Fundamental

concepts of quantum physics are also introduced briefly.

Course Plan: Chapter 20 Electric charge, Force, and Field

Chapter 21 Gauss’s Law

Chapter 22 Electric Potential

Chapter 23 Electrostatic Energy and Capacitors

Chapter 24 Electric Current

Chapter 25 Electric Circuits

Chapter 26 Magnetism: Force and Field

Chapter 27 Electromagnetic Induction

Chapter 28 Alternating-Current Circuits

Chapter 29 Maxwell’s Equations and Electromagnetic Waves

Chapter 30 Reflection and Refraction

Chapter 32 Interference and Diffraction

Chapter 33 Relativity

5 Experimental laboratory course to supplement PHY 102, through which students confirm and understand the

fundamental principles of physics.

6 Course Plan:

1. Economic principles

2. Economic thinking

3. Comparative Advantages

4. Supply and Demand

5. Elasticity

6. Supply, Demand, and Policy

7. Consumer/Producer Surplus

8,12.* Taxes, Tax Systems

9.International Trade

10, 11. Externalities, Public Goods

21. The Theory of Consumer Choice

13. Cost of Production

14. Competitive markets

15. Monopoly

16. Monopolistic competition

17. Oligopoly

23, 24. Measuring National Income

25. Long-term growth: Productivity

27. Financial system, Finance

29, 30. Monetary System, Money growth, and Inflation

31. Open economy

7 Calculus is a one-semester course of fourteen weeks, each consisting of two 75-minute Lectures, one 50-minute

lecture and two 50-minute exercise sessions (not including one week each for the midterm and final exams), which

covers concepts and techniques from both single-variables and multi-variable calculus.

Course Outline:

Week 1-2: Basic Terminologies, Limits and Continuity

Week 2-3: Differentiation and Integration

Week 3: Infinite Sequences and Series

Week 4: Tests of Series Convergence

Week 5: Power Series and Taylor Series

Week 6: Vectors

Week 6-7: Vector-Valued Functions and Partial Derivatives

Week 8: Midterm Exam

Week 9: Gradients, Directional Derivatives, and Level Sets

Week 10: Taylor Series for Two Variables

Week 11: Multiple Integrals in Rectangular Coordinates

Week 12-13: Multiple Integrals in Other Coordinates

Week 13-14: Line Integrals of Vector Fields

Week 14-15: Stokes’ Theorem

Week 15: The Divergence Theorem

Week 16 : Final Exam

8 Lecture Plan:

1. Structure and Bonding

2. Polar Covalent Bonds; Acids, and Bases

3. Organic compounds: Alkanes and Their Stereochemistry

4. Organic compounds: Cycloalkanes and Their Stereochemistry

5. An overview of Organic Reactions

6. Alkenes: Structure and Reactivity

7. Alkenes: Reactions and Synthesis

8. Alkynes: An Introduction to Organic Synthesis

9. Stereochemistry

10. Organohalides

11. Reactions of Alkyl halides: Nucleophilic Substitutions and Eliminations

12. Structure Determination: Mass Spectrometry and IR Spectroscopy

13. Structure Determination: Nuclear Magnetic Resonance Spectroscopy

9 Lecture Plan (Continued from Organic Chemistry I CHEB 206)

14. Conjugated Dienes and Ultraviolet Spectroscopy

15. Benzene and Aromaticity

16. Chemistry of Benzene

17. Alcohols and Phenols.

18. Ethers and Epoxides

19. Aldehydes and Ketones.

20. Carboxylic Acids and Nitriles

21. Carboxylic Acid Derivitives and Nucelophilic Addition Reactions.

22. Carbonyl Alpha- Substitution Reactions.

23. Carbonyl Condensation Reactions

24. Amines

25. Special Topics in Biomolecules

26. Special Topics in Macromolecules

10 Lecture Plan:

1. Introduction & Orientation - Extraction, Crystallization, and m.p.(Tech. 3,5)

2. TLC & Column Chromatography.(Exp.4, Tech.4,10,11)

3. Distilation & Gas Chromatography.(Tech.7,12)

4. Grignard Reaction & IR Analysis(Exp. 31)

5. Reduction ofd, 1 Camphor(Exp. 21)

6. Adol Condensation(Exp. 47)

7. Witting Reaction(Hand - out)

8. Final Exam & Check out

11

Lecture Plan:

1. Classical vs. quantum mechanics, Schrödinger equation

2. Quantum mechanical postulates

3. Particle in a box, tunneling through a square potential barrier

4. Operators and commutation

5. Particle in a sphere and others

6. Vibration and rotation of molecules

7. Hydrogen atom

8. Many-electron atoms, Spin & orbital angular momentum

9. Chemical bonding in diatomic molecules

10. Molecular structure and energy levels for polyatomic molecules

11. Electronic spectroscopy, Lasers

12. Molecular symmetry, Group theory, and Nuclear magnetic resonance spectroscopy

12 Course Objective:

We learn the basic principles of momentum transfer related to fluid motion. Important conepts are taught along wit

h the derivation of fundamental equations that govern fluid flows. Such concepts include material volume, linear m

omentum principle, kinematics, stress tensor, dimensional analysis, etc. Several appliaction problems are also cover

ed for better understanding of governing principles.

Lecture Plan:

1. Introduction to transport phenomena & fluid mechanics

2. Vector tensor analysis

3. Basic concepts (material volume, linear momentum principle)

4. Kinematics (description of motion)

5. Stress in a fluid (cause of motion)

6. The Navier-Stokes equation

7. Dimensional analysis & Reynolds number

8. 1D laminar flow

9. Low Reynolds number flow & Stokes flow

10. Electrokinetic flow (electrical double layer, electroosmotic flow, electrophoresis)

11. Turbulence

13

Course Objective:

The principles of heat and mass transfer are studied along with application problems. In heat transfer, the three fund

amental mechanisms, conduction, convection, and radiation are studied in detail. Then we will go on to the mass

transfer part to study molecular diffusion and convection problems. During the last part of the course, we will touch

the transport problems related to the electrolyte solutions to meet the cutting edge technologies such as biomedical

engineering, micro/nanofluidics, and lithium battery problems. During the last week, students' perspectives will be

extended by touching the analogies between the physical transport phenomena and financial transport phenomena in

economics.

Lecture Plan:

1. Heat conduction (Fourier's law)

2. Heat Convection (Forced convection, Natural convection)

3. Radiation (Black body radiation, non-Black body, Shape factor)

4. Molecular diffusion (Fick's law) - Stokes-Einstein diffusivity

5. Convection

6. Electrokinectics (Planck-Nernst-Poisson Equation)

- Electroosmosis in micro/nano channels (nano pores)

- Transport phenomena in a lithium battery

7. Analogy to financial transport phenomena

- Convective transport equation and Black-Scholes model in financial engineering

University of Melbourne

Link to Course Catalog 1 Differential equations arise as common models in the physical, mathematical, biological and engineering sciences.

This subject covers linear differential equations, both ordinary and partial, using concepts from linear algebra to

provide the general structure of solutions for ordinary differential equations and linear systems. The differences

between initial value problems and boundary value problems are discussed and eigenvalue problems arising from

common classes of partial differential equations are introduced. Laplace transform methods are used to solve

dynamical models with discontinuous inputs and the separation of variables method is applied to simple second

order partial differential equations. Fourier series are derived and used to represent the solutions of the heat and

wave equation and Fourier transforms are introduced. The subject balances basic theory with concrete applications.

2 This subject is an introduction to chemical engineering flowsheet calculations, including materials balances, unit

systems, and the prediction of real gas behavior. The concept of conversion of mass is developed as the basis for

determining mass flows in chemical processing systems. Students will be introduced to flowsheeting packages and

chemical engineering simulation software. The subject will include exercises in process optimization and the

solution of ill-defined process problems. The teaching of process safety is critical to any undergraduate chemical

engineering program. Students need to understand their responsibilities to themselves, their work colleagues and the

wider community. They need to be aware of safe practices and also the consequences that may arise when those safe

practices are not followed. This subject introduces students to concepts of process safety and the consequences when

safety management systems fail.

3 Energy balances: The concepts of energy, work and heat, the units of energy, internal energy, enthalpy, heat

capacity, latent heat, evaluation of enthalpy changes. The general energy balance equation, enthalpy balances,

system boundaries. Enthalpies of pure components and selection of enthalpy data conditions.

Energy balances and chemical reactions: Heat of reaction, definitions of standard heat of reaction, standard heat of

formation, standard heat of combustion. Hess' Law of adding stoichiometric equations. Adiabatic reaction

temperature. Heats of solutions and dilution, and use of enthalpy-concentration charts. Simultaneous material and

energy balances.

HYSIS: Training in the use of the process simulations package HYSIS. Performing simple material and energy

balances using the package.

4 Computer packages, such as MATLAB, Maple and Mathematica, are indispensable tools for many scientists and

engineers in simulating complex systems or studying analytically intractable or computationally intensive problems.

This subject introduces such numerical and symbolic techniques with an emphasis on the development and

implementation of mathematical algorithms including aspects of their efficiency, accuracy and stability. The

different strategies and style of programming methodologies required when tackling problems either numerically or

symbolically are highlighted. Examples used to illustrate numerical mathematics include the direct solution of linear

systems and time-stepping methods for initial value problems. Symbolic methods will be demonstrated with a wide

range of examples, such as applications to chaos theory and perturbative solutions to differential equations.

Learning Outcomes:

On completion of this subject, students should:

Understand the significance and role of both roundoff error and truncation error in some standard problems in

scientific computing;

Be able to write simple numerical programs that utilize a numerical Problem-Solving Environment such as Matlab;

Learn how to use a symbolic software system such as Mathematica to tackle certain mathematical problems exactly;

Be able to use both numerical and symbolic techniques, with the appropriate programming idioms, as required when

undertaking a mathematical or modeling investigation.

https://handbook.unimelb.edu.au/faces/htdocs/user/search/SimpleSearch.jsp

5 This subject is designed for students with a strong interest and background in physics, and aims to provide a deep

understanding of a broad range of physics principles and applications. Topics include:

Fluids: water and air pressure, breathing, hydraulics, flight (pressure in fluids, buoyancy, fluid flow, viscosity,

surface tension).

Thermal physics: heating and cooling, energy balance in environments, engines, refrigerators (temperature and

thermal energy, kinetic theory, phase changes, heat transfer mechanisms, first law of thermodynamics, diffusion).

Electricity and magnetism: electrical devices, lightning, household electricity and electrical safety, electric motors,

power generation and transmission, Earth’s magnetic field, particle accelerators, communications (electric charge

and field, conductors and insulators, electric potential, capacitance, resistance, electric circuits, magnetic field,

Faraday’s law of induction, Maxwell’s equations, electromagnetic waves).

Quantum and atomic physics: spectroscopy, lasers (photon, blackbody radiation, matter waves, quantisation in

atoms, interaction of light with matter, x-rays).

Nuclear physics and radiation: nuclear energy, radiation safety, formation of atoms in stars, carbon dating (the

atomic nucleus, radioactive decay, half-life, ionising radiation, nuclear fission and fusion).

6 This subject covers fundamental concepts of diffusion and conservation within momentum, heat and mass

transport. Use of these concepts is integral to the profession of Chemical Engineering. For example, heat exchangers

are used throughout Chemical Engineering processes to transfer thermal energy from one stream to another.

Knowledge of heat transport and momentum transport (ie fluid flow) is required to design a heat exchanger, other

key pieces of Chemical Engineering process equipment, including distillation columns. Similarly, knowledge of

mass transport is required to design other key Chemical Engineering processes, such as distillation.

7 This subject aims to extend the fundamental concepts of heat transfer from that covered in CHEN20009 Transport

Processes to include natural and forced convection and two phase systems. Mass transfer concepts are extended to

unsteady state mass transfer and Fick's Second Law, prediction of diffusivity and of mass transfer coefficients.

These fundamental concepts are then applied to the design of processes and equipment including shell and tube, air-

cooled and plate heat exchangers, evaporator systems, membrane devices, binary distillation systems, gas absorbers

and cooling towers. Experience in the use of appropriate simulation packages such as HYSYS for exchanger and

distillation column design are included. This simulation work builds on the skills developed in CHEN20009

Chemical Process Analysis 2.

Indicative Content:

Forced Convection: Use of heat transfer correlations to predict coefficients;

Heat Exchange: concept of an overall heat transfer coefficient, fouling factors; determination of the area required for

a given heat duty, Heat exchanger design. Use of simulation packages such as HYSYS and ASPEN.

Free convection: discussion and application of Grashof Number and other dimensionless groups.

Condensation and Boiling: Fundamentals. Evaporation: various evaporator types and their advantages and

disadvantages (forced circulation, film types); multiple and single effects; backward and forward feed; boiling point

elevation; mechanical recompression; evaporator energy balances.

Mass Transfer: Unsteady state mass transfer and Fick's Second Law; prediction of diffusivity; dimensional analysis

and equations of change for mass transfer.

Distillation: single-stage separations, equilibrium flash, differential distillation; multistage separations, operating

lines, reflux; binary distillation, varying reflux ratio, minimum reflux, total reflux, optimum reflux, feed plate

location, side streams, open steam; tray efficiency via overall and Murphree efficiencies. Use of simulation packages

such as HYSYS.

Gas absorption: basic mass transfer mechanism; material balances, co-current and countercurrent flow, limiting L/G

ratio; multistage absorption and the absorption factor method; continuous contact, transfer units, height of a transfer

unit, calculation of number of transfer units. Humidification and cooling tower height calculation.

Membrane Systems: Microfiltration, ultrafiltration, nanofiltration and reverse osmosis. Gas separation systems.

Robeson’s bound. Electrodialysis and pervaporation. Membrane selection.

8 This subject studies the fundamental concepts of functions of several variables and vector calculus. It develops the

manipulation of partial derivatives and vector differential operators. The gradient vector is used to obtain

constrained extrema of functions of several variables. Line, surface and volume integrals are evaluated and related

by various integral theorems. Vector differential operators are also studied using curvilinear coordinates.

Functions of several variables topics include limits, continuity, differentiability, the chain rule, Jacobian, Taylor

polynomials and Lagrange multipliers. Vector calculus topics include vector fields, flow lines, curvature, torsion,

gradient, divergence, curl and Laplacian. Integrals over paths and surfaces topics include line, surface and volume

integrals; change of variables; applications including averages, moments of inertia, centre of mass; Green's theorem,

Divergence theorem in the plane, Gauss' divergence theorem, Stokes' theorem; and curvilinear coordinates.

9 The subject provides an introduction to stoichiometry; gases; energy and thermochemistry; chemical equilibrium;

acid-base chemistry; properties of solutions, aspects of main group chemistry: structure and bonding in elements and

compounds of groups 14-18; solutions and pH equilibria; physical properties of solution. intermolecular forces and

extended solid state structures; structure and bonding of alkanes, alkenes and alkynes; benzene and its derivatives;

functional groups; and spectroscopy and determination of structure.

10

The subject provides an introduction to organic acids and bases; nucleophilic substitution reactions; elimination

reactions; addition reactions; electrophilic aromatic substitution reactions; nucleophilic addition reactions; organic

redox reactions; chemical kinetics; elementary quantum mechanics, atomic spectra and atomic structure; redox

reactions and electrochemistry; and transition metal and coordination chemistry.

11

Quantum mechanics plays a central role in our understanding of fundamental phenomena, primarily in the

microscopic domain. It lays the foundation for an understanding of atomic, molecular, condensed matter, nuclear

and particle physics.

Topics covered include: The basic principles of quantum mechanics (probability interpretation; Schrödinger

equation; Hermitian operators, eigenstates and observables; symmetrization, antisymmetrization and the Pauli

exclusion principle; entanglement), wave packets, Fourier transforms and momentum space, eigenvalue spectra and

delta-function normalization, Heisenberg uncertainty principle, matrix theory of spin, the Hilbert space or state,

vector formation using Dirac bra-ket notation, the harmonic oscillator, the quantization of angular momentum and

the central force problem including the hydrogen atom, approximation techniques including perturbation theory and,

the variational method, applications to atomic and other systems.

12

This subject is divided into advanced thermodynamics (approximately 9 weeks) and advanced reactor engineering

(approximately 3 weeks).

The laws of thermodynamics, which govern energy and the direction of energy flow, are amongst the most

important fundamentals of chemical engineering that students learn during their course. This subject revises and

expands the students’ understanding of the conservation of energy, learnt through subjects such as Chemical Process

Analysis and Fluid Mechanics. In addition the students learn about the concepts of entropy and equilibrium, which

form the basis for the topics of phase equilibrium, mixture properties, mixture equilibrium, reaction equilibrium and

interfacial equilibrium – topics that stretch across the entire chemical engineering curriculum.

The reactor engineering component of the course focuses on heterogeneous reactions and the influence of mass

transfer on chemical reactions and reaction design. The topics are solid-catalysed reactions, fluid-fluid reactions and

fluid-solid reactions. During the subject, students learn about the effect of mass transfer on the overall rate of

reaction and how to account for heterogeneous systems in reactor design.

The concepts covered by this subject provide the fundamental basis for chemical and process engineering and are

utilised throughout all sectors of industry by engineers. This subject provides students with the ability to perform

detailed calculations of complex systems to predict the performance and thus design process unit operations.

Indicative Content:

The advanced thermodynamics component focuses on the definitions and applications of the laws of

thermodynamics, especially the implications of entropy and equilibrium on phases, mixtures, chemical reactions and

interfaces:

1st Law of Thermodynamics: Closed and open systems, Unit operations, Thermodynamic cycles

2nd Law of Thermodynamics: Entropy, Reversibility and Spontaneity, Gibb’s Equations, Thermodynamic Identities

and Maxwell Relations

Phase Equilibria of Pure Substances: Equilibrium Criteria, Fugacity

Mixtures and Phase Equilibria of Mixtures: Partial Molar Properties, Gibbs-Duhem equation, Chemical Potential,

Species Fugacity, Activity Coefficients, Vapour-Liquid equilibrium, Colligative Properties, Liquid-Liquid

equilibrium

Chemical Reactions and Reaction Equilibria: Equilibrium Constant, Species Activity

Interfacial Thermodynamics: Surface Tension, Adsorption Isotherms

The advanced reactor engineering component focuses on mass-transfer limitations in multi-phase chemical reactions

and reactor design:

Non-ideal flow in reactors

Rate controlling mechanisms (film resistance control, chemical reaction control, surface and pore diffusion control,

ash layer diffusion, shrinking core mechanisms, effectiveness factors and Thiele modulus)

Kinetic regimes for fluid-fluid and gas-fluid reactions

Fluid-particle reaction design

Catalytic reactor systems

13

Topics covered include - Fluid statics, manometry, derivation of the continuity equation, mechanical energy

balance, friction losses in a straight pipe, Newton’s law of viscosity, Fanning friction factor, treatment of roughness,

valves and fittings; simple network problems; principles of open channel flow; compressible flow, propagation of

pressure wave, isothermal and adiabatic flow equations in a pipe, choked flow. Pumps – pump characteristics,

centrifugal pumps, derivation of theoretical head, head losses leading to the actual pump head curve, calculating

system head, determining the operating point of a pumping system, throttling for flow control, cavitation and NPSH,

affinity laws and pump scale-up, introduction to positive displacement pumps; stirred tanks- radial, axial and

tangential flow, type of agitators, vortex elimination, the standard tank configuration, power number and power

curve, dynamic and geometric similarity in scale-up; Newtonian and non-Newtonian fluids, Multi-dimensional fluid

flow-momentum flux, development of multi-dimensional equations of continuity and for momentum transfer,

Navier-Stokes equations, application to tube flow, Couette flow, Stokes flow.

University of Queensland

Link to Course Catalog 1 MATH2100 will cover the following 4 topics. ( Also for a general outline of the course, read About MATH2100.)

Topic 1. Systems of Ordinary Differential Equations (Kreyszig Chapter 4). Solutions to Homogeneous Linear

Systems of ODE's with constant coefficients using matrices. The Phase Plane for 2-Dimensional linear and some

nonlinear systems. Critical Points, linearization and the stability properties of critical points. Nonhomogeneous

Linear Systems.

Topic 2. Laplace Transforms (Kreyszig Chapter 6).The Laplace Transform and its Inverse Transform. Linearity,

Shifting, Convolution and the use of Partial Fractions. Transforms of Derivatives and Integrals. Use of Laplace

Transforms to solve Linear Differential Equations including those involving discontinuous functions such as the

Step Function and the Dirac Delta function.

Topic 3. Fourier Series (Brown and Churchill Chapters 1 and 2, Kreyszig Chapter 11). The idea of Fourier analysis,

and of orthogonal periodic functions. Formulas for Fourier coefficients. When a Fourier expansion works. Even and

odd functions and their expansions. Half-range sine and cosine series. Differentiation of Fourier series. Application

of Fourier series to a forced oscillator.

Topic 4. Partial Differential Equations (Brown and Churchill Chapters 3 to 6, Kreyszig Chapter 12). Concepts of

scalar and vector fields. The operator del; grad, div and curl. Flux of a vector field. Idea of a flux integral. Gauss'

divergence theorem. Conservation laws. The Laplacian operator. The heat, wave and Laplace's equation in 1, 2, and

3 dimensions. Nature of solutions of PDEs. Superposition principle for PDEs. General solution of wave equation

and d'Alembert's solution of the IVP. Examples. Fourier's method for wave equation. Green's function for the 1-d

heat equation. Solution of IVP on whole line. Example. The error function and other examples. Heat conduction and

diffusion. Temperature waves in the Earth. Kelvin's estimation of the Earth's age. Fourier's method for 1-d heat

equation with source term. Short-cut when source is time-independent. Revisit 1-d wave equation with forcing.

Fourier's method and Laplace's equation in a 2-dimensional rectangular region. Continuation: other BCs. Idea of

conjugate harmonic functions. Heat stream function. Point source for Laplace's equation in 2-d. Images for point

sources/sinks. Other applications of Laplace's equation: Fluid flow, electrostatics. Potentials and stream functions.

2

On completing this course students will be able to: Analyze any process as a system including defining sensible

system boundaries and identifying all input and output streams, formulate and solve mass and energy balances for

process systems with and without reaction, produce a clearly written engineering communication and effectively sell

a case through oral presentation, have improved their ability to manage their own study and their ability to work

effectively in an engineering team.

3 Module 1: (Weeks 2 & 3)

Finite precision and discretisation Finite precision arithmetic and error, arithmetic on computers, evalualating functions and sums

Fundamentals of numerical analysis, numerical differentiation and integration

Module 2: (Weeks 4 & 5)

Solving equations

Solving equations (root-finding)

Interpolation and curve-fitting.


Systems of equations

Systems of linear equations.

Iterative methods, nonlinear equations.


Differential equations 1

Ordinary differential equations (ODEs)

Initial value problems


http://www.uq.edu.au/study/

Differential equations 2

Boundary value problems

Finite element and finite difference methods


High-dimensional problems

Partial differential equations (PDEs) - DEs with more than 1 independent variable

Monte Carlo methods for high-dimensional integration and other problems

4 Module 1:

Electricity

Coulomb's Law, superposition.

Electric field, electric field due to continuous charge distributions.

Electric flux, Gauss's Law.

Electrostatic potential.

Potential and Fields.

Module 2: Magnetism and Waves

Current.

Magnetic field, magnetic force on current.

Electromagnetic induction.

Electromagnetic fields. Maxwell's equations.

Module 3:

Waves - superposition, standing waves, interference.

Wave optics - concept of light as a wave, interference and diffraction.

Module 4:

Modern Physics

Special Relativity

Reference frames.

Time Dilation.

Length Contraction.

Lorentz transformations.

Quantum Physics

The end of classical physics.

Quantization.

Wavefunctions and uncertainty.

One dimensional Quantum Mechanics.

5 The course introduces a systems approach to understanding and analysing the structure and behaviour of industrial

processes. The context and needs that give rise to process systems are examined along with the concepts of unit

operations & unit processes. Understanding the nature of individual units and complex flowsheets is done through

analysis of degrees of freedom & solvability issues. Techniques for the decomposition of large, complex systems to

smaller problems are developed. Application of computer-aided flowsheeting tools facilitate process analysis, which

includes economic & environmental impacts.

6 The aim of this course is to integrate concepts from fluid and particle mechanics, thermodynamics and heat and

mass transfer such that students are able to use these concepts to make holistic decisions about selection and

specification of equipment suited to specific objectives, as well as to analyse and troubleshoot problems. With an

understanding of these concepts as well as new modelling techniques to be introduced in the course, students will be

able to critically and professionally approach authentic cases. In this way the course looks back at the principles

learnt and their application but also looks forward towards capstone courses which foreground a broader design

approach.

On completing this course students will:

Be able to apply theory to real world situations and problems.

Gain an understanding of the fundamental concepts in each of the technologies to be studied, including

thermodynamics, equipment design, operation and simulation issues.

Have learned how to specify and select process hardware best suited to various problems and objectives.

Have used case histories to analyse the most effective problem solving and trouble-shooting methods.

Have learned how to tailor his or her approach to specific design, analysis and troubleshooting problems.

7 After successfully completing this course you should be able to:

1. Sketch, interpret and manipulate functions of two or more variables.

2. Calculate tangent planes and use them as approximations to functions.

3. Find the maxima and minima of functions of two variables.

4. Apply the method of Lagrange multipliers to optimisation problems.

5. Solve and analyse certain families of first and second order ODEs.

6. Model a problem with ODEs and either analytically or numerically solve the differential equation and interpret

the output.

7. Work fluently with parametric forms of curves, and derive parametric forms.

8. Understand fields and determine conservative fields and path integrals.

9. Model and solve problems with some real-world complexity using analytical methods and/or numerical methods

via Matlab programs.

8 Lecture Plan:

1. Solve a variety of first order ODEs

2. Use the methods of undetermined coefficients and variation of parameters to solve non-homogenous 2nd order

lin102 College Avenue New Brunswick, NJ 08901-8543ear ordinary differential equations

3. Derive properties of the hyperbolic functions and apply them in various mathematical contexts.

4. Evaluate multiple integrals, and change the order of integration

5. Apply your knowledge of multiple integrals to solve problems of volume, area, centre of mass and moments of

inertia.

6. Evaluate integrals in cylindrical and spherical polar coordinates

7. Know when to effectively use polar, cylindrical and spherical coordinate systems in problems involving multiple

integrals.

8. Understand the notion of a vector field, use the operators "grad", "div" and "curl" effectively and understand their

significance.

9. Understand and apply Green's theorem

10. Parameterize surfaces and be able to evaluate and apply surface and flux integrals, and be able to use the

theorems of Gauss and Stokes appropriately.

11. Find the LU or PLU decomposition of a given matrix and use it to solve a corresponding system of linear

equations.

12. Use eigenvalues and eigenvectors to (orthogonally) diagonalize certain matrices and use these techniques in a

variety of applications.

13. Understand and apply the power method.

14. Identify unitary and Hermitian matrices.

15. Model and solve problems with real-world application using mathematical techniques covered in this course.

16. Present clear and concise mathematical arguments in assignments and exams

9 Provides students with a practical understanding of the core economic principles that explain why individuals,

companies and governments make the decisions they do, and how their decision-making might be improved to make

best use of available resources.

10

This course builds on concepts that have been introduced in CHEM1100 (Chemistry 1) thereby developing the

knowledge and understanding across inorganic, physical and organic chemistry necessary for advancement to the

higher levels of study in chemistry, biochemistry and engineering courses. Core topics include: reaction profiles and

kinetics, structure, reactivity and mechanisms, organic functional group chemistry, structural determination, acid and

base chemistry and transition metal chemistry.

11

This course contains all of the theory for both inorganic & organic chemistry that a student will need to advance

to third level chemistry. Topics covered will include: Synthesis & mechanism in organic chemistry; Transition

Metal Chemistry; Bonding and Molecular Orbital Theory; Molecular Modelling; Stereochemistry; Modern

spectroscopic techniques for Structural Analysis; Strategies for complex syntheses.

12

The aim of this course is to introduce students to the theory and concepts of quantum physics. Important

experiments in the development of quantum physics will also be discussed. We will introduce students to the main

ideas of quantum physics and teach the basic mathematical methods and techniques used in the fields of advanced

quantum physics, atomic physics, laser physics, nanotechnology, quantum chemistry, and theoretical mathematics.

Some of the key problems of quantum physics are also described, concentrating on the background derivation,

techniques, results and interpretations. We will not finish a complete exploration of all the predictions of quantum

physics, but it is hoped that the predictions and problems explored here will provide a useful starting point for those

interested in learning more. The intention is to explore problems which have been the most influential on the

development of quantum physics and formulation of what we now call modern quantum physics.

13

Through studying PHYS3040 students will:

Develop an understanding of the basic features and laws of quantum physics

Develop an understanding of the key concepts in quantum physics such as quantum probabilities, superposition

states, quantization, wave-particle duality, simultaneous measurement, symmetry and conservation laws, density

operator, Heisenberg and Schrodinger pictures, particle identity.

Develop an understanding of and ability to apply the Dirac mathematical formalism of quantum mechanics.

Develop an understanding of and an ability to apply techniques such as matrix mechanics, wave mechanics,

perturbation theory to quantum physics situations.

Develop an understanding of the quantum behaviour of important physical systems in fields such as atomic physics,

molecular physics, solid state physics, quantum optics via the application of quantum physics methods.

Develop an ability to apply the methods of quantum physics to new physical systems and obtain analytical and

numerical results describing the behaviour.

14

Basic concepts in thermodynamics, forms of energy; properties of pure substances, phase diagrams & phase

transitions; first law of thermodynamics & applications - mass & energy balances in open & closed systems; entropy

& second law of thermodynamics, exergy; topical engineering case studies.

15

1st and 2

nd laws of thermodynamics for steady & unsteady systems. Exergy analysis. Equations of state. Gibbs

free energy, fugacity & activity. Phase equilibria, electrochemical equilibria. Pure components & solutions.

Chemical reaction equilibria.

16

Application of conservation laws, continuity, momentum & energy balances. Fluids statics, Bernoulli equation,

pipe flow. Experimental techniques, viscosity, flow measurement, pumps. Non-Newtonian behavior. Solids

characterization, drag, settling & flow. Packed bed & fluidization.

17

Fundamentals of heat & mass transfer. Concepts of heat exchange & heat exchanger selection. Differential &

stage-wise mass transfer processes. Case studies of equipment for heat & mass transfer unit operations.

University of Auckland

Link to Course Catalog 1 This is an introductory course in Partial Differential Equations (PDE’s). We cover Fourier series, Fourier integrals,

boundary value problems and separation of variables , with application to the solution of second order PDE’s in one,

two and three dimensions

1. Introduction [3 lectures]

PDE’s and boundary conditions. Modeling the diffusion (heat) equation. Introduction to separation of variables

2. Fourier Series [5 lectures]

Orthogonality of functions and sets of functions. Real trig series. Convergence and sketching Fourier series.

Complex Fourier series.

3. Sturm-Liouiville Problems [4 lectures]

Eigenvalues and eigenfunctions. Strum-Louville eigenvalue problems, existence and orthogonality of solutions,

eigenfunction expansions

4. Fourier Transforms [4 lectures]

Fourier representation of delta function. Convolution theorem. Application to PDEs.

5. Wave Equation [7 lectures]

Solution by Separation of Variables. Vibrating membrane. D’Alembert’s solution for the vibrating string. Using

Fourier and Laplace transforms.

6. Laplace Equation [6 lectures]

Heat flow in 2D. Laplace’s equation. Separation of Variables. Non-homogeneous boundary conditions. Laplace’s

equation in polar, cylindrical and spherical coordinates.

7. Laplace Transforms [3 lectures]

Introduction to transform methods. Calculation and properties of the transform. Solution of ODEs and PDEs

2 Materials and energy balancing with and without chemical reaction, materials and energy balances in multiphase

systems such as crystallization, evaporation, drying, humidification, dehumidification, absorption, distillation,

extraction and filtration. An introduction to the most important unit operations in the chemical industry, design

concept and safety as applied to processing.

3 Many mathematical models occurring in Science and Engineering cannot be solved exactly using algebra and

calculus. Students are introduced to computer-based methods that can be used to find approximate solutions to these

problems. The methods covered in the course are powerful yet simple to use. This is a core course for students who

wish to advance in Applied Mathematics.

Syllabus:

1. Review of Matlab

2. Iterative methods for linear algebraic equations - Jacobi, Gauss-Seidel (4 lectures)

3. Scalar non-linear equations – Linear models, iterative schemes, convergence, difficulties with methods (5

lectures)

4. Direct methods for linear algebraic equations - LU factoring, pivoting, conditioning (4 lectures)

5. Systems of non-linear equations – Newton’s method, finite differencing, continuation, use in unconstrained

optimization

6. Interpolation – Newton divided differences, uniqueness of the interpolant, interpolation error, Vandermonde

approach for general interpolation problems, Hermite cubic interpolation

7. Numerical differentiation, Quadrature - Newton-Cotes, error estimation, Gauss-Legendre, composite rules (6

lectures)

8. Ordinary differential equations - simple one-step and multi-step methods, behaviour of the error (6 lectures).

4 A systematic development of Maxwell's theory of electromagnetism and its applications to optics. Topics include:

electrostatics, dielectrics, polarisation, charge conservation, magnetostatics, scalar and vector potentials, magnetic

materials, Maxwell's equations, the wave equation. Propagation of electromagnetic waves in vacuum, dielectrics and

conducting media. Energy and momentum in electromagnetic waves.

http://www.student.guest.auckland.ac.nz/psp/ps/EMPLOYEE/HRMS/c/COMMUNITY_ACCESS.SSS_BROWSE_CATLG.GBL?&languageCd=ENG

5 Students may select experiments from a wide spectrum of physics that are appropriate to the lecture courses being

taken from PHYSICS 315--356.

6 Principles of continuous and staged processes. Mass transfer in various media, systems and phases. Interrelating

reactor design to mass transfer processes. Studies of selected separation processes such as absorption, solvent

extraction, and distillation. Heat transfer with phase change; nucleate and film boiling of liquids.

7 The study of differential equations is central to mathematical modeling of systems that change. Develops methods

for understanding the behavior of solutions to ordinary differential equations. Qualitative and elementary numerical

methods for obtaining information about solutions are discussed, as well as some analytical techniques for finding

exact solutions in certain cases. Some applications of differential equations to scientific modeling are discussed.

Lecture Plan:

1. First order differential equations [12 lectures]

Introduction to differential equations and modeling with differential equations. Introduction to the software

packages Matlab. Separable equations and linear equations. Slope fields. Numerical methods (introduction only).

The phase line, equilibria, and bifurcations.

2. First order systems of differential equations [16 lectures]

Phase plane and qualitative analysis. Linear systems, including classification of equilibria. Nonlinear systems,

including classification of equilibria.

3. Higher order differential equations [5 lectures].

8 Offers an introduction to the workings of market systems. This course deals with the economic behavior of

consumers and firms, covering analysis of demand and supply of goods, services and resources within an economy.

The framework developed is used to examine and evaluate the operation of the market mechanism for various

market structures and government policies

Syllabus:

1. Scarcity and Choice; Opportunity Cost; Supply and Demand Functions

2. Supply and Demand Functions and Applications

3. Consumer Behavior

4. Theory of the Firm: Production and Costs

5. Perfect Competition: Implications

6. Perfect Competition: Limitations of the Model

7. Introduction to Imperfect Markets and Market Failure

8. Monopoly and Monopolistic Competition

9. Oligopoly and Game Theory

10. Imperfect Information, Externalities and Public Goods

9 Covers topics in linear algebra and multi-variable calculus including linear transformations, quadratic forms,

double and triple integrals and constrained optimization. It is a preparation for a large number of Stage III courses in

mathematics and statistics, and for many advanced courses in physics and other applied sciences. All students

intending to advance in mathematics should take this course.

Lecture Plan:

1. Vector spaces over R and C and their subspaces.

2. Bases & dimension. The coordinate mapping.

3. Linear transformations and their matrices.

4. Change of basis matrices and their properties. Algebra of linear operators. Matrices of linear operators and change

of basis.

5. Eigenvectors and eigenvalues. Algebraic and geometric multiplicities of eigenvalues.

6. Invariant subspaces.

7. Diagonalisation of operators. Applications of diagonalisation.

8. Discrete time system evolution. Markov chains.

9. Projection formula. Gram-Schmidt orthogonalisation. Projection matrix.

10. Inner products and real inner product spaces. Orthogonality in inner product spaces and their orthogonal bases.

11. Orthogonal bases for vector space of polynomials and trigonometric polynomials.

12. Projections as best approximations. Polynomial and Fourier approximations.

13. Complex inner product. Eigenvalues of Hermitian operators.

14. Orthogonal matrices. Orthogonal diagonalisability.

15. Spectral decomposition and Cayley-Hamilton Theorem. Functions of matrices.

16. Quadratic forms, their matrices. Change of basis. Principal axes theorem.

17. Conics and Quadrics.

18. Positive definite quadratic forms. Sylvester’s criterion.

19. Congruent diagonalisation. Sufficiency of Sylvester’s criterion.

20. Functions of several variables. Limits and continuity.

21. Partial derivatives, higher order partial derivatives. Symmetry of the Hessian matrix.

22. Linear approximations, differentiability, tangent planes.

23. Differentials and the chain rule.

24. Gradient, directional derivatives, tangent planes.

25. Taylor series. Best approximations.

26. Maxima and minima. Critical points. Constrained and unconstrained optimisation.

27. Double integrals over rectangles.

28. Fubini’s theorem.

29. Double integrals over general domains.

30. Change of variables in double integrals.

31. Space curves. Geometric interpretation of the derivative.

32. Arc length parametrization.

33. Line integral of a vector function. Work as a line integral.

34. Fundamental theorem on line integrals.

35. Vector fields. Gradient vector fields. Potential functions.

36. A test for conservative vector field.

37. Green’s theorem

10

Three lectures illustrating the place of 'Chemistry in the Modern World. The invention of the Periodic Table

Lavoisier to Mendeleyev. Sub-atomic structure Thompson to Schrodinger. The quantum mechanical description of

multi-electron atoms. Bonding and diatomic molecules. Common simplifications to describe bonding in polyatomic

molecules. Alkanes and cycloalkanes, conformation. Stereoisomerism. Mechanisms of reactions, electron movement

and distribution. Curly arrows. Polarization, inductive and resonance effects. Acidity, pKa; stability of anions.

Haloalkanes, synthesis and uses; substitution and elimination reactions. Ethers, alcohols and amines. Alkenes,

electrophilic addition; stability of carbocations. Alkynes; comparison with nitriles. Aldehydes and ketones,

carboxylic acids; interconversion between alcohols, aldehydes. Ketones and carboxylic acids by oxidation and

reduction; carboxylic acid derivatives: esters and amides. Spectroscopy, the basics. Beer-Lambert law. Rotational

spectroscopy. Vibrational spectroscopy. Harmonic and anharmonic oscillator. Electronic spectroscopy. Fluorescence

and phosphorescence. Lasers. NMR spectroscopy. Magnetic resonance imaging. The gas laws. Boltzmann

distribution of speeds. Non-ideal behaviour of gases. Solid structures

11

Introduces further principles of chemistry. Physical chemistry and qualitative inorganic analysis, including

chemical kinetics and chemical equilibrium. Organic chemistry, including hydrocarbons, oxygen-containing

functional groups, isomerism and reaction classifications, acids, bases, buffer solutions and titrations. Laboratories

include reactions of hydrocarbon and oxygen-containing organic compounds, chromatography, testing for anions

and cations in solution, acid-base titrations.

12

Non-relativistic quantum mechanics will be developed using the three-dimensional Schrödinger equation, and will

be applied particularly to the physics of atoms and molecules. The interaction of like particles and the quantisation

of angular momentum will be studied.

13

Materials and energy balancing with and without chemical reaction, materials and energy balances in multiphase

systems such as crystallization, evaporation, drying, humidification, dehumidification, absorption, distillation,

extraction and filtration. An introduction to the most important unit operations in the chemical industry, design

concept and safety as applied to processing.

14

Fluid properties: specific gravity, viscosity, surface tension and types of flow. Fluid statics and manometry. Math

models of fluid motion: the Bernoulli equation. Dimensional analysis and similitude: Reynolds Number, Friction

factor and Prandtl number. Flow measurement, pumps/pumping and valves. Heat transfer via steady state

conduction, convection and radiation. Effect of geometry, force and natural convection. Dimensionless correlations

of heat transfer processes with flow processes. Film and overall heat transfer coefficients. Practical examples and

applications.

Documents

Study Abroad Curriculum Mapping with Selected Partner