INTERNATIONAL ISLAMIC UNIVERSITY MALAYSIA

COURSE OUTLINE

Kulliyyah / Institute Engineering

Department / Centre Science in Engineering

Programme All programmes

Name of Course / Mode Engineering Calculus I /Full time

Course Code MTH 1112

Name (s) of Academic staff /Instructor(s)

Dr Raihan Othman

Contact Hours 3

Rationale for the inclusion ofthe course / module in theprogramme

Required course for all Engineering Programmes

Semester and Year Offered Every Semester

Status CoreLevel 1Proposed Start Date

Batch of Student to be Affected

Total Student Learning Time(SLT)

Face to Face AssessmentsIn

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42 13 2 3 62 122Credit Value / Hours 3/122Pre-requisites (if any) NoneCo-requisites (if any) None

Course Objectives

The objectives of this course are to:1. Present and develop a clear understanding of definitions, concepts, rules,

theorems, techniques, and applications of differential and integralcalculus.

2. Encourage students to think visually and numerically by generating andinterpreting graphs, using calculators and computers whenever possible.

3. Strengthen the students’ number sense in order to be able to recognize anabsurd answer by encouraging them to make mental estimates, to appealto their intuition, and to work on problems both individually and ingroups.

Learning Outcomes

Upon completion of this course, students should be able to:1. Apply the concepts of limit and continuity in computing limit and

determining continuity of a function.2. Analyze the concept and computing techniques of derivatives with

applications in engineering problems.3. Analyze the concept and evaluating techniques of integration for solving

engineering problems.4. Evaluate series and its interval of convergence for various functions and

applications.

Transferable Skills:

Skills and how they are developed and assessed:Skills Development Assessment

Technical Lectures Written AssessmentTutorials

Teaching-Learning andassessment strategy

Lectures, Tutorials and Quizzes

Course SynopsisComplex numbers, limits, continuity, differentiation and integration withapplications, transcendental functions, techniques of integration, infinite andpower series.

Mode of Delivery Lecture and tutorial.

Assessment Methods andType/Course AssessmentState weightage of each type ofassessment.

LO Method %1-3 Quizzes 10

1-2Mid-term Examination (9 November 2014,Sunday, 10-12 am)

45

1-4 Final Examination 45

Mapping of course / module to the Programme Learning Outcomes

Learning Outcome of the course Programme Outcomes01 02 03 04 05 06 07 08 09 10 11 12

1. Apply the concepts of limit and continuity in computinglimit and determining continuity of a function.

2. Analyze the concept and computing techniques ofderivatives with applications in engineering problems.

3. Analyze the concept and evaluating techniques ofintegration for solving engineering problems.

4. Evaluate series and its interval of convergence forvarious functions and applications.

Content outline of the course / module and the SLT per topic

Weeks TopicsLearning

HoursTask/Reading

1Complex NumbersIntroduction, algebraic properties, modulus and conjugates, geometricpresentation, polar form and Euler’s formula, De Moivre’s Theorem.

2 Handout

2,3

Limits andLimit and ContinuityReview: Transcendental functions. Concept and evaluatingtechniques of limits and continuity for square-root and transcendentalfunctions, intermediate value theorem, limit involving infinity,asymptotes.

3.5Chapter

0,1

4,5

DifferentiationConcept of derivative, derivative and differential, differentiability andcontinuity, differentiation techniques for algebraic and transcendentalfunctions, implicit differentiation, Mean value theorem.

3.5 Chapter 2

6,7

Applications of DifferentiationLinear approximation, Newton’s method, indeterminate forms andL’Hopital’s rule, local and absolute extrema, increasing anddecreasing function, concavity and inflection points, transformationson curves, curve sketching, optimization, concept of derivative asslope and rates of change.

4Chapter 3

8,9

IntegrationAnti-derivatives, definite and indefinite integration, basic techniques,concept of definite integration as area and Riemann sum, fundamentaltheorems of calculus, integration by substitution.

4 Chapter 4

10

Applications of IntegrationArea between curves, volume of solid by slicing/disks/washers andcylindrical shells methods, arc length and surface area.

3.5Chapter 5

11,12Techniques of IntegrationIntegration by parts, Trigonometric techniques of integration,integration by partial fractions, improper

4 Chapter 6

13, 14

Infinite SeriesInfinite series and convergence, geometric series, harmonic series,tests for series of nonnegative terms: nth – term test for divergence,integral test and p-series, comparison test, alternating series:alternating series test, absolute and conditional convergence, ratiotest, root test, power series: radius of convergence, Taylor andMaclaurin series, application of Taylor series.

3.5 Chapter 8

Required references supporting the courseRobert, T.S. & Roland, B.M., (2006), Calculus (3rd ed.), McGraw Hill.

Recommended references supporting the courseAnton, H., Bivens, I. & Davis, S., (2002), Calculus (7th ed.), John Wiley.Edwards, C. H.& Penny, D.E., (2002), Calculus (6th ed.), Prentice Hall.Finney, R.L., Weir, M.D.L.F. & Thomas, G., (2001), Calculus (10th ed.), Addison-Wesley Publishing Company.Johnston, E. H. & Mathews, J.C., (2002), Calculus, Addison Wesley.Strauss, M.J., Bradley, G.L. & Smith, K.J.,(2002), Calculus (3rd ed.), Prentice Hall.

Programme Learning Outcome (PO)Students graduated from the Kulliyyah of Engineering programmes should have the ability to:

Programme Learning Outcome (PO) MQF Domain

1. Engineering Knowledge (T) -Apply knowledge of mathematics, sciences,engineering fundamentals and an engineering specialization to the solutionof complex engineering problems

Knowledge

2. Problem Analysis (T) – Identify, formulate, research relevant literature andanalyze complex engineering problems, and reaching substantiatedconclusions using first principles of mathematics, natural sciences andengineering sciences

Knowledge

3. Design/Development of Solutions (A) –Design solutions, exhibitinginnovativeness, for complex engineering problems and design systems,components or processes that meet specified needs with appropriateconsideration for public health and safety, cultural, societal, economical,ethical, environmental and sustainability issues.

Problem Solving and ScientificSkills

4. Investigation (D) Conduct investigation into complex problems, displayingcreativeness, using research-based knowledge, and research methodsincluding design of experiments, analysis and interpretation of data, andsynthesis of information to provide valid conclusions

Practical Skills

5. Modern Tool Usage (A & D) -Create, select and apply appropriatetechniques, resources, and modern engineering and IT tools, includingprediction and modelling, to complex engineering activities, with anunderstanding of the limitations

Problem Solving and ScientificSkills

Information Management andLifelong Learning Skills

6. The Engineer and Society (ESSE) -Apply reasoning based on contextualknowledge to assess societal, health, safety, legal, cultural, contemporaryissues, and the consequent responsibilities relevant to professionalengineering practices.

Social skills andResponsibilities

7. Environment and Sustainability (ESSE) -Understand the impact ofprofessional engineering solutions in societal, global, and environmentalcontexts and demonstrate knowledge of and need for sustainabledevelopment

Social skills andResponsibilities

8. Ethics (ESSE) –Apply professional ethics with Islamic values and committo responsibilities and norms of professional engineering code of practices.

Value, Attitudes andProfessionalism

9. Communication (S) -Communicate effectively on complex engineeringactivities with the engineering community and with society at large, such asbeing able to comprehend and write effective reports and designdocumentation, make effective presentations, and give and receive clearinstructions

Communication, Leadershipand Team Skills

10. Individual and Team Work (S) -Function effectively as an individual, andas a member or leader in diverse teams and in multi-disciplinary settings.

Communication, Leadershipand Team Skills

11. Life Long Learning (S) -Recognize the need for, and have the preparationand ability to engage in independent and life-long learning in the broadestcontext of technological change.

Information Management andLifelong Learning Skills

12. Project Management and Finance (S) -Demonstrate knowledge andunderstanding of engineering management and financial principles andapply these to one’s own work, as a member and/or leader in a team, tomanage projects in multidisciplinary settings, and identify opportunities ofentrepreneurship.

Managerial and EntrepreneurialSkills

The program learning outcomes are grouped into 5 general areas to identify the nature of the skills andcapability involved. These groups are:

1. Technical (T) – essential capabilities related to traditional scientific and engineering knowledge2. Analysis (A) – creatively working with available data and engineering tools and fundamental

knowledge to correctly solve basic problem3. Design (D) – being able to perceive the best solution for both small scale and large scale project by

involving all required basic problems4. Ethics, Safety, Society and Environment (ESSE) - giving appropriate consideration to matters

pertaining to professionalism and ethics, safety, local and global society and the environment5. Work skills (S) – being and effective communicator and effective member of a team and to

appreciate the need to continuously acquired skills and abilities.