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This is a live document. Do not print as it changes throughout the semester. We will be remote learning and testing for the rest of the semester.
Live streaming PDF of notes and video content April 30, 2020 (Last session of the semester) We live streamed the office hours today. The content we covered is not in addition to what has been assigned to you but is complementary to it. The recording of this session is available at https://us.bbcollab.com/collab/ui/session/playback/load/5c41c3c6b95a4405848b1b5643cc70cc April 28, 2020 We live streamed the office hours today. The content we covered is not in addition to what has been assigned to you but is complementary to it. The recording of this session is not available as it was mostly chat. I did make a video of the Q10 quadrature rule question of Test4 https://us.bbcollab.com/collab/ui/session/playback/load/7cceb57ade944b9c84b91259ed4a20b7 April 23, 2020 We live streamed the office hours today. The content we covered is not in addition to what has been assigned to you but is complementary to it.
• PDF file of notes is here • The video is here https://youtu.be/k6SWPYzTEJY
April 16, 2020 We live streamed the office hours today. The content we covered is not in addition to what has been assigned to you but is complementary to it.
• PDF file of notes is here • The video is here https://youtu.be/aLpzsqEcWVE • See you on Thursday, April 23, 2020 at 3:30 PM. I will put the link in the CANVAS chat
15 minutes before the class time and via email. April 9, 2020 We live streamed the office hours today. The content we covered is not in addition to what has been assigned to you but is complementary to it.
• PDF file of notes is here • The video is here https://youtu.be/Ir8uYs4_HfQ
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• See you on Thursday, April 16, 2020 at 3:30 PM. I will put the link in the CANVAS chat 15 minutes before the class time and via email.
April 7, 2020 We live streamed the office hours today. The content we covered is not in addition to what has been assigned to you but is complementary to it.
• PDF file of notes is here • The video is here https://youtu.be/Nz7NTBvLZwI • See you on Thursday, April 9, 2020 at 3:30 PM. I will put the link in the CANVAS chat 15
minutes before the class time. April 2, 2020 We live streamed the office hours today. The content we covered is not in addition to what has been assigned to you but is complementary to it.
• PDF file of notes is here • The video is here https://youtu.be/2nZsA6aRyyI • See you on Tuesday, April 7, 2020. I will put the link in the CANVAS chat 15 minutes
before the class time.
March 31, 2020 We live streamed the office hours today. The content we covered is not in addition to what has been assigned to you but is complementary to it.
• PDF file of notes is here • The video is here. Follow it along with the PDF notes above as sometimes the screen did
not cooperate. https://youtu.be/d6AujxVJDDo • See you on Thursday, April 2, 2020 at 3:30PM. I will put the link in the CANVAS chat 15
minutes before the class time as it seems that doing in advance messes it up.
Making a PDF of handwritten parts and about submitting soft copies of project This will be helpful for your tests and projects. It involves downloading an app on your iphone or android. https://www.youtube.com/watch?v=UkYlGa3y4tk&feature=emb_logo Another way is to insert images of handwritten work into a word doc. But check your file size. It can get too big for CANVAS to handle and your internet to upload. The limit may be 100MB. Try this before the project or test. I have made a graded assignment for you. It is under Modules -> Online Assignment. You do not want to be trying this just before the deadline. Do not email the files. You will be asked to upload them. I wrote a blog on this and it will help you with submitting your programming project https://autarkaw.org/2020/03/26/how-to-make-a-pdf-file/ .
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Tests and Final Exam Are Open Notes Both upcoming tests and final exam will be open notes including the formula sheet. Please print out the formula sheet as part of your notes as you will be restricted to one screen during the test. Do NOT develop a false sense of what you need to learn because the tests/exams are open notes. Go here to see instructions for test 3 and how to access the test https://usflearn.instructure.com/courses/1388974/pages/cumulative-test-3?module_item_id=14822527
Online Testing Needs Webcam Please make sure that you have a computer available that has a web camera (internal or external) as I will be using proctorio to proctor the test online. Webcams are inexpensive if you do not have one - try ebay or amazon. But get one now. https://www.usf.edu/innovative-education/resources/student-services/online-proctoring.aspx to conduct the tests to keep them fair to all by encouraging academic honesty. To get familiar with it, go to Modules>Module: Pre-Test Items. This is required and do this before March 31 at 3:30 PM. Then to check the webcam, Go to Quiz to Check Webcam: Go to Modules -> Quiz to Check Webcam and do this before Thu April 2 at 3:45 PM) https://usflearn.instructure.com/courses/1388974/modules/items/16118179
Use of Proctorio Students please note the following regarding the use of Proctorio for online exams for academic continuity. Online exams and quizzes within this course may require online proctoring. Therefore, students will be required to have a computer and possibly a webcam (USB or internal) with a microphone when taking an exam or quiz. If you do not have access to a computer or webcam you are required to notify your instructor. Students understand that this remote recording device is purchased and controlled by the student and that recordings from any private residence must be done with the permission of any person residing in the residence. To avoid any concerns in this regard, students should select private spaces for the testing. Students must ensure that any recordings do not invade any third party privacy rights and accept all responsibility and liability for violations of any third party privacy concerns. Students are strictly responsible for ensuring that they take all exams from a computer (mobile device not support) with a high speed internet connection and camera if required for the exam. Setup information will be provided prior to taking the online proctored exam.
Office Hours My office hours now are same as class time on Tuesday and Thursday: 3:30 PM - 4:45 PM. Dr. Kaw and Luis will hold Office Hours on CANVAS via Chat in CANVAS. Click on Chat on the left menu of CANVAS course during regular office hours. You can ask questions through Discussion Board on the content at any time. Ask questions about the project only via email to [email protected] or [email protected] and anything that is personal in nature only to [email protected]
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Outline for the Remote Learning that Started March 23 (For items before that date, click here) Below is the outline of remote learning work for the rest of the semester. Look at the description of the quizzes for content or just look at the pages of this document. Click for full timeline of the whole course for the full semester.
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Week of March 23-March 27 Adaptive: 06.XX: Regression: Nonlinear Models and Adequacy (Due March 24 2 PM) https://usflearn.instructure.com/courses/1388974/modules/items/14879185 Computer Project 1 Due March 26 3:30 PM https://usflearn.instructure.com/courses/1388974/modules/items/14822517 https://usflearn.instructure.com/courses/1388974/modules/items/16093153 Adaptive: 07.XX: Integration: Trapezoidal Rule and Discrete Data (Due March 31 2PM) https://usflearn.instructure.com/courses/1388974/modules/items/14879175
Getting used to online testing: Go to Modules -> Module: Pre-Test Items: This is required and do this before March 31, 2020 3:30PM.
Quiz to Check Wabcam: Go to Modules -> Quiz to Check Webcam (Due Thu April 2 3:45PM). https://usflearn.instructure.com/courses/1388974/modules/items/16118179
Week of March 30 – April 3 Look at previous week items to see if you have done them all.
LIVE lecture via YouTube Streaming: Tuesday, March 31, 2020, at 3:30 PM. I will send you the link separately in an email. All you have to do is go to the link. You will be able to ask questions as well. We will talk about the 07.05 chapter on Gauss Quadrature Rule and any other questions you may have. If some of you could log in at 3:15 PM, that would be great as I am doing this for the first time. I have tested it but it was just a local test.
Adaptive: 07.XX: Integration: Gauss Quadrature (Due April 7 2 PM) https://usflearn.instructure.com/courses/1388974/modules/items/14879177
Primer on Ordinary Differential Equations (Due April 7 at 2 PM) https://usflearn.instructure.com/courses/1388974/modules/items/14879209 Making a PDF file to upload handwritten pages (Due Apr 7 at 2 PM)
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https://usflearn.instructure.com/courses/1388974/modules/items/16176035
Week of April 6 – April 10 Chapter 08.02 Euler’s Method (Due April 14 at 2 PM) https://usflearn.instructure.com/courses/1388974/modules/items/14879211
Chapter 08.03 Runge Kutta 2nd order Method (April 14 at 2 PM) https://usflearn.instructure.com/courses/1388974/modules/items/14879215
Week of April 13- April 17 Test 3: Tuesday, April 14, See for details https://usflearn.instructure.com/courses/1388974/pages/cumulative-test-3?module_item_id=14822527 Computer Project 2 : Due Thursday April 16 3:30 PM https://usflearn.instructure.com/courses/1388974/modules/items/14822519 https://usflearn.instructure.com/courses/1388974/modules/items/16093329 Chapter 08.05 Higher Order/Coupled Ordinary Diferential Equations (Due April 21 at 2 PM) https://usflearn.instructure.com/courses/1388974/modules/items/14879217
Week of April 20 – April 24 Review for Test 4 Test 4: Friday April 24 11 AM-12:15 PM
Week of April 27 – May 1 Review for Final Exam
Week of May 4 – May 8 Final Exam: Thursday May 7 12:30 PM-2:30 PM
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Timeline Day Date Description Tuesday 01/14 Materials assigned from 01.01 Thursday 01/16 Materials assigned from 01.02; 01.03 Friday 01/17 Materials assigned from 01.04; Review of pre-requisite materials Tuesday 01/21 Materials assigned from 01.04, 01.05 Thursday 01/23 Materials assigned from 01.05, 01.07 Friday 01/24 Materials assigned from 01.07 and in-class exercises Tuesday 01/28 Materials assigned from 02.00 and 02.02 Thursday 01/30 Materials assigned from 02.02 and 02.03 Friday 01/31 Materials assigned from all of 02.02 Tuesday 02/04 Test#1 Thursday 02/06 Materials assigned from 03.03 Friday 02/07 Materials assigned from 03.04 Tuesday 02/11 In-class exercises from 03.XX Thursday 02/13 Materials assigned from 04.00A, 04.00G, 04.01 Friday 02/14 Materials assigned from 04.06 Tuesday 02/18 Materials assigned from 04.06 and 04.07 Thursday 02/20 Materials assigned from 04.07 and in-class exercises Friday 02/21 In-class exercises Tuesday 02/25 Materials assigned from 05.00A, 05.00G, 05.02, 05.05 Thursday 02/27 Materials assigned from 05.05, 05.10 Friday 02/28 Wrap up interpolation; In-class exercises Tuesday 03/03 Test#2 Thursday 03/05 Materials assigned from 06.00A, 06.00G, 06.01,06.02, 06.03 Friday 03/06 Materials assigned from 06.03, 06.04 Tuesday 03/10 Materials from 06.04 Thursday 03/12 Materials from 06.05 Friday 03/13 No class – enjoy spring break Tuesday 03/17 No class – spring break Thursday 03/19 No class – spring break Friday 03/20 No class – spring break Tuesday 03/24 Fourth check for adequacy of regression model (see material assigned for
06.05), optimum polynomial to use for regression (see materials assigned from 06.05)
Thursday 03/26 Materials assigned from 07.00A, 07.00F, 07.00G, Primer Integration Friday 03/27 Materials assigned from 07.02 Tuesday 03/31 Material assigned from 07.06 Thursday 04/02 Material assigned from 07.05 Friday 04/03 Wrap up exercises 07.XX Tuesday 04/07 Materials assigned 08.00A, 08.00G, Primer for ODE, 08.02 Thursday 04/09 Materials assigned from 08.02,08.03
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Friday 04/10 Materials assigned from 08.03,08.05 Tuesday 04/14 Test#3 Online Thursday 04/16 Materials assigned from 08.XX Friday 04/17 Mock concept test, concept mapping, concept test discussion (cancelled) Tuesday 04/21 Concept test (cancelled – everyone gets 100) Thursday 04/23 Wrap up exercises 08.XX Friday 04/24 Test#4 Online Tuesday 04/28 Review Course Thursday 04/30 Reading Day – no class Friday 05/01 Reading Day – no class Thursday 05/07 Final Exam Online
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Chapter 1: INTRODUCTION TO NUMERICAL METHODS (2 weeks)
Learning Objectives
Chapter 01.01 Introduction to Numerical Methods After finishing this chapter, you will be able to:
• enumerate reasons for the need for numerical methods, • give examples for the above reasons from real-life as well as previous courses, • go through the stages (mathematical modeling, solving and implementation) of solving a
particular physical problem, • enumerate the mathematical procedures for which we will use numerical methods.
Chapter 01.02 Measuring Errors • enumerate reasons why we need to measure errors • find the true and relative true error, • find the approximate and relative approximate error, • relate the absolute relative approximate error to the number of significant digits at least correct
in your answer, • identify how many significant digits a number has in decimal and scientific format.
Chapter 01.03 Sources of Error • know that there are two inherent sources of error in numerical methods – round-off and
truncation error, • recognize the sources of round-off and truncation error, and • know the difference between round-off and truncation error.
Chapter 01.04 Binary Representation of Numbers • convert a base-10 integer to a binary equivalent, • convert a binary integer to a base-10 equivalent, • convert a base-10 fractional part of a real number to a binary equivalent, • convert a fractional part of a binary number to a base-10 equivalent, • convert a base-10 real number to a binary equivalent, • convert a binary real number to a base-10 equivalent, • write a base-10 real number in fixed-point binary format, • calculate round-off error for a base-10 number being represented in binary format.
Chapter 01.05 Floating-Point Representation • convert a base-10 real number to a binary floating-point representation, • convert a binary floating-point number to its equivalent base-10 number, • write a binary floating number in floating-point format with an unbiased exponent, • write a binary floating number in floating-point format with a biased exponent, • calculate the machine epsilon of a floating-point format, • relate machine epsilon to the relative true error in the representation of base-10 numbers in
floating-point format.
Chapter 01.07 Taylor Series Revisited • recall the formula for Taylor’s theorem (pre-requisite) • express Taylor's theorem in plain language, (pre-requisite) • write transcendental and trigonometric functions as Taylor’s polynomial, (pre-requisite)
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• use Taylor’s theorem to find the values of a function at any point, given the values of the function and all its derivatives at a particular point, (pre-requisite)
• revisit with confidence the chapter whenever Taylor’s theorem is used to derive or explain numerical methods for various mathematical procedures.
Textbook (see important footnote) and Handouts • First Day of Class (PPT) • Chapter 01.01 Introduction to Numerical Methods - (Pages 1-6 from Customized Book1 or Pages
1-6 from Abridged Book) • Chapter 01.02 Measuring Errors - (Pages 11-17 from Customized Book or Pages 11-17 from
Abridged Book) • Chapter 01.03 Sources of Error - (Pages 22-27 from Customized Book or Pages 22-27 from
Abridged Book) • Chapter 01.04. Binary Representation: (Pages 34-40 from Customized Book, Pages 34-40 from
Abridged Book) • Chapter 01.05. Floating-point Representation: (Pages 44-top of page 50(Only up to end of
Example 4) from Customized Book, Pages 44-top of page 50(Only up to end of Example 4) from Abridged Book)
• Chapter 01.07. Taylor Series Revisited: (Pages 55-58 (Only up to end of Example 4) from Customized Book, pages 60-63 (Only up to end of Example 4) from Abridged Book
• Brief History of Numerical Systems (YouTube video) • Patriot Missile Fails to Intercept Iraqi Missile (text).
Assigned Exercises • Assigned and graded online quizzes on CANVAS • Programming review exercise handout • Friday Jan 24 in-class exercise set • Multiple-choice tests at the end of Chapter 01.01, Chapter 01.02, Chapter 01.03, Chapter 01.04,
Chapter 01.05, Chapter 01.07 (Skip Problem 5 and 6 from 01.07) in the textbook • Problem sets at the end of Chapter 01.01 (you can do these using MATLAB), Chapter 01.02,
Chapter 01.03, Chapter 01.04 and Chapter 01.05 in the textbook
1 To minimize costs, you can get a used textbook. There are two options – Either get the customized textbook (Numerical Methods with Applications: Customized for Mechanical Engineering of University of South Florida (USF)) http://www.lulu.com/shop/autar4-kaw-and-egwu-kalu/numerical-methods-with-applications-customized-for-mechanical-engineering-of-university-of-south-florida-usf/paperback/product-23481431.html OR the abridged textbook (Numerical Methods with Applications: Abridged) http://www.lulu.com/shop/autar4-kaw-and-egwu-eric-kalu/numerical-methods-with-applications-abridged/paperback/product-15098428.html I have put the page numbers down for both options.
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CHAPTER 2 NUMERICAL DIFFERENTIATION (1 week)
Learning Objectives
Chapter 02.02 Differentiation of Continuous Function • state the exact formula for the first derivative of a continuous function (pre-requisite) • derive formulas for approximating the first derivative of a function, • derive formulas for approximating first and second derivatives from Taylor series, • derive finite difference approximations for higher order derivatives, • use the developed formulas in examples to find derivatives of a function, • find the order of accuracy of first derivative formulas • relate order of accuracy of first derivative formulas to true error
Chapter 02.03 Differentiation of Discrete Functions • find approximate values of the first and second derivatives of functions that are given at discrete
data points, • use direct polynomial interpolation to find derivatives of discrete functions.
Textbook and Handouts • Chapter 02.00A - Physical Problem - General Engineering: (Pages 65-66 from Customized Book,
Pages 70-71 from Abridged Book) • Chapter 02.00B - Physical Problem - Chemical Engineering: (Pages 67-68 from Customized Book,
Pages 72-73 from Abridged Book) • Chapter 02.02. Differentiation of Continuous Functions: (Pages 77-89 from Customized Book,
Pages 94-106 from Abridged Book) • Chapter 02.03. Differentiation of Discrete Functions: (Pages 94-98 (Only up to the end of
Example 2) from Customized Book, Pages 111-115 (Only up to end of Example 2) from Abridged Book)
• Making sense of Big-O - the order of accuracy • A test problem using central divided difference error • A test problem video solution using the order of accuracy concepts • Class Handout: Forward Backward Central example 7x cubed.pdf
Assigned Exercises • Assigned and graded online quizzes on CANVAS • Multiple Choice Tests at the end of Chapter 02.01, Chapter 02.02, Chapter 02.03 in the textbook • Problem sets at the end of Chapter 02.02, Chapter 02.03 in the textbook • Practice Test • Friday class Exercise handout (02.02 and 02.03) • In-class exercise handout (02.03)
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Chapter 3 SOLUTION OF NONLINEAR EQUATIONS (1 week)
Learning Objectives
Chapter 03.03 Bisection Method
• identify when at least one root of an equation does and does not lie in an interval, • follow the algorithm of the bisection method of solving a nonlinear equation, • use the bisection method to find roots of a nonlinear equation, • enumerate the advantages and disadvantages of the bisection method.
Chapter 03.04 Newton Raphson Method
• find the tangent line to a curve (pre-requisite) • find where the tangent line crosses the x-axis (pre-requisite) • find the angle the tangent line to the curvev makes with the x-axis (pre-requisite) • derive the Newton-Raphson method formula from geometry and calculus, • develop the algorithm of the Newton-Raphson method, • use the Newton-Raphson method to solve a nonlinear equation, • derive Newton-Raphson method from Taylor series, • discuss the drawbacks of the Newton-Raphson method.
Textbook Content and Handouts • Handout used in class for an introduction to nonlinear equations • Chapter 03.00A - Physical Problem - General Engineering - (Pages 105-108 from Customized
Book, Pages 122-125 from Abridged Book) • Chapter 03.00G - Physical Problem - Mechanical Engineering - (Pages 115-118 from Customized
Book, Pages 147-150 from Abridged Book) • Chapter 03.03 Bisection Method - (Pages 126-134 from Customized Book, Pages 158-166 from
Abridged Book) • Chapter 03.04 Newton Raphson Method - (Pages 139-148 from Customized Book, Pages 171-
180 from Abridged Book) • Class Handout about why we need to solve nonlinear equations
Assigned Exercises • Assigned and graded adaptive lesson • In-class exercises • Multiple Choice Test at the end of Chapter 03.03, Chapter 03.04 in the textbook • Problem sets at the end of Chapter 03.03, Chapter 03.04 in the textbook
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Chapter 4 SIMULTANEOUS LINEAR EQUATIONS (2 weeks)
Learning Objectives
Chapter 04.01 Introduction to Matrix Algebra (pre-requisite) • define what a matrix is • identify the number of rows and columns in a matrix • identify and define row and column vectors • identify and define square matrices • identify and define identity matrices • identify and define upper and lower triangular matrices • add two matrices • subtract two matrices • multiply two matrices • find the inverse of a matrix • able to write algebraic equations in matrix form • relate the inverse of a matrix to solve a set of simultaneous linear equations
Chapter 04.06 Gaussian Elimination • write an algorithm for Naive Gaussian elimination method • solve a set of simultaneous linear equations using the Naive Gaussian elimination method • identify the pitfalls of the Naive Gaussian elimination method • illustrate the effect of round-off errors in solutions of simultaneous linear equations • write an algorithm for the Gaussian elimination with the partial pivoting method • solve a set of simultaneous linear equations using the Gaussian elimination with the
partial pivoting method • find the determinant of a square matrix using the forward elimination steps of Naive
Gaussian elimination method • relate the determinant to the invertibility of a square matrix.
Chapter 04.07 LU Decomposition • decompose a nonsingular matrix into LU, • solve a set of equations through the LU decomposition method, • identify when LU decomposition is numerically more efficient than Gaussian elimination, • calculate the computational time for LU decomposition and Gaussian elimination methods, • show how LU decomposition is used to find the inverse of a matrix.
Textbook Content and Handouts • Chapter 04.00A - Physical Problem - General Engineering - (Pages 153-155 from Customized
Book, Pages 194-196 from Abridged Book) • Chapter 04.00G - Physical Problem - Mechanical Engineering - (Pages 166-171 from Customized
Book, Pages 218-223 from Abridged Book) • Chapter 04.01 Introduction to Matrix Algebra(prerequisite) - (Pages 172-192 from Customized
Book, Pages 224-244 from Abridged Book) • Chapter 04.06 Gaussian Elimination - (Pages 199-216 from Customized Book, Pages 251-268
from Abridged Book) • Chapter 04.07 LU Decomposition Method - (Pages 222-231 from Customized Book, Pages 274-
284 from Abridged Book)
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• Applications SLE PPT • Naive Gauss Elimination Method PPT • Gaussian Elimination with Partial Pivoting Method PPT • LU Decomposition Method PPT • The computational time for the back substitution handout • Adequacy of Solution PPT • Determinant of matrix by cofactor method program (Not part of the syllabus; only for the
curious)
Assigned Exercises • Assigned and graded adaptive lesson • In-class exercises • Multiple Choice Tests at the end of Chapter 04.01, Chapter 04.06, Chapter 04.07 in the textbook • Problem sets at the end of Chapter 04.06, Chapter 04.07 in the textbook
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Chapter 5 INTERPOLATION (1 week)
Learning Objectives
Chapter 05.02 Direct Method of Interpolation • find the interpolant through the direct method, • choose the correct data points for interpolation, • solve problems using the direct method of interpolation, • use the direct method interpolants to find derivatives of discrete functions, • use the direct method interpolants to find integrals of discrete functions.
Chapter 05.05 Spline Interpolation • interpolate data using spline interpolation, • interpret why spline interpolation is important • use splines to find derivatives of discrete functions, • use splines to find integrals of discrete functions.
Chapter 05.10 • estimate the length of a curve • find the shortest smooth path through consecutive points, • compare lengths of different paths.
Textbook and Handouts • Chapter 05.00A - Physical Problem - General Engineering: (Pages 238-239 from Customized
Book, Pages 306-307 from Abridged Book) • Chapter 05.00G - Physical Problem - Mechanical Engineering: (Pages 250-253 from Customized
Book, Pages 323-326 from Abridged Book) • Chapter 05.02. Direct Method of Interpolation: (Pages 256-264 from Customized Book, Pages
329-337 from Abridged Book) • Chapter 05.05. Spline Method of Interpolation:(Pages 269-279 from Customized Book, Pages
357-367 from Abridged Book) • Chapter 05.10. Short-Path of a Robot: (Pages 295-299 from Customized Book, Pages 383-387
from Abridged Book • An exam problem solution for finding the length of a curve (download (not open) the file first
and then open with Acrobat Reader to listen to audio) • Interpolation PPT used in class
Assigned Exercises • Assigned and graded online quizzes on CANVAS • In-class Worksheet • Practice test 2 • Multiple Choice Tests at the end of Chapter 05.02, Chapter 05.05 in the textbook • Problem sets at the end of Chapter 05.02, Chapter 05.05 in the textbook
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Chapter 6 REGRESSION (2 weeks)
Learning Objectives
Chapter 06.01 & 06.02 Background for Regression • review the statistics background needed for learning regression, and • know a brief history of regression • know what regression analysis is, • know the effective use of regression, and • enumerate uses and abuses of regression
Chapter 06.03 Linear Regression • define regression, • use several criteria for minimizing residuals to choose the right criterion, • derive the constants of linear regression models based on the least-squares method criterion, • use in examples, the derived formulas for the constants of a linear regression model, and • prove that the constants of the linear regression model are unique and correspond to a
minimum.
Chapter 06.04 Nonlinear Regression • derive constants of nonlinear regression models, • use in examples, the derived formula for the constants of the nonlinear regression model, and • transform data to find constants of some nonlinear regression models
Chapter 06.05 Adequacy of Linear Regression • find whether a linear regression model is adequate through four criteria • apply the criterion of visual inspection of plot and data • check the criterion of the standard error of estimate • calculate the standard error of estimate • calculate scaled residuals • check the criterion of the coefficient of determination • calculate the coefficient of determination • calculate the correlation coefficient • relate slope of the regression line to the sign of the correlation coefficient • check if the assumption of random errors is met
Textbook and Handouts • Chapter 06.00A - Physical Problem - General Engineering - (Pages 300-303 from Customized
Book, Pages 388-391 from Abridged Book) • Chapter 06.00G - Physical Problem - Mechanical Engineering - (Pages 309-313 from Customized
Book, Pages 407-411 from Abridged Book) • Chapter 06.01 - Statistics background of regression analysis - (Pages 314-319 from Customized
Book, Pages 412-417 from Abridged Book) • Chapter 06.02 - Introduction of regression analysis - (Pages 322-327 from Customized Book,
Pages 418-423 from Abridged Book) • Chapter 06.03 - Linear Regression -(Pages 329-338 from Customized Book (skip pages 339-341),
Pages 427-436 from Abridged Book (skip pages 437-439))
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• Chapter 06.04 - Nonlinear Regression - (Pages 346-350, 352-359 from Customized Book, Pages 444-448, 450-457 from Abridged Book)
• Chapter 06.05 – Adequacy of Regression Models (Pages 374-387 from Customized Book, Pages 472-485 from Abridged Book)
• Linear Regression Simulation • Better off buying a big pizza - A nonlinear regression example - "People get a smaller pizza
because they either don't want to be wasteful or they don't want to be waistfull." - John Scott (optional example)
• Comparing exponential models with and without transforming data: Blog and Wolfram Demo • Applications of Regression PPT • Effect of significant digits problem • Exponential model with data transformation (COVID19) • Primer on minimum of a function (Same as in adaptive lesson) • Primer on partial derivatives (Same as in adaptive lesson) • Adequacy of Regression PPT (Same as in adaptive lesson)
Videos Assigned Beyond The Class or Adaptive Lesson
• Dangers of mixing causality with correlation - throw away your participation trophies YOUTUBE • Adequacy of Regression Models : Check Four: Assumption of Random Errors [YOUTUBE
6:32] [TRANSCRIPT]
Assigned Exercises • Assigned and graded adaptive lesson • Multiple Choice Tests at the end of Chapter 06.03, Chapter 06.04 in the textbook • Problem sets at the end of Chapter 06.03, Chapter 06.04, Chapter 06.05 in the textbook
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Chapter 7 NUMERICAL INTEGRATION (2 weeks)
Learning Objectives
Chapter 07.02 Trapezoidal rule of integration • derive the trapezoidal rule of integration • use the trapezoidal rule of integration to estimate integrals of continuous functions • derive multiple segment trapezoidal rule of integration • use the multiple-segment trapezoidal rule of integration to estimate integrals of continuous
functions • derive the relationship between the true error in the multiple-segment trapezoidal rule to the
number of segments • use the relationship between the true error in the multiple-segment trapezoidal rule to the
number of segments to find more accurate values of integrals
Chapter 07.06 Discrete data integration • derive the trapezoidal rule of integration with unequal segments • use the trapezoidal rule of integration with unequal segments to estimate integrals of discrete
functions • revisit how spline interpolation is used for integrating discrete data functions • revisit how polynomial interpolation is used for integrating discrete data functions
Chapter 07.05 Gauss quadrature rule of integration • derive the trapezoidal rule of integration using the method of undetermined coefficients • derive 2-point Gauss quadrature rule using the method of undetermined coefficients • apply 2-point Gauss quadrature rule to estimate integrals • derive 1-point Gauss quadrature rule using the method of undetermined coefficients • convert integrals with [a,b] limits to [-1,1] limits • apply n-point Gauss quadrature rule to estimate integrals via changing their limits to [-1,1] • determine the highest order of polynomial for which n-point Gauss quadrature rule is exact, and
vice-versa. • derive special quadrature rules
Textbook and Handouts • Page 1-6 of Primer on Integration
https://nm.mathforcollege.com/mws/gen/07int/mws_gen_int_bck_primer.pdf • Chapter 07.00A Physical Problem for General Engineering - (Pages 388-390 from Customized
Book, Pages 486-88 from Abridged Book) • Chapter 07.00F Physical Problem for Industrial Engineering - (Pages 391-394 from Customized
Book, Pages 514-517 from Abridged Book) • Chapter 07.00G Physical Problem for Mechanical Engineering - (Pages 395-398 from Customized
Book, Pages 518-521 from Abridged Book) • Chapter 07.02 Trapezoidal rule of integration - (Pages 404-419 from Customized Book, Pages
527-542 from Abridged Book) • Chapter 07.06 Discrete data integration - (Pages 444-451 from Customized Book, Pages 583-590
from Abridged Book)
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• Chapter 07.05 Gauss quadrature rule of integration - (Pages 425-438 from Customized Book, Pages 564-577 from Abridged Book)
• PPT for Introduction to Numerical Integration Videos Assigned Beyond the Adaptive Lesson and Class
• Trapezoidal Rule Multiple Segment Rule: Error Derivation [YOUTUBE 8:46] [TRANSCRIPT] • Trapezoidal Rule Multiple Segment Rule: Error Example [YOUTUBE 8:52] [TRANSCRIPT] • Method of Undetermined Coefficients: Trapezoidal Rule Derivation [YOUTUBE 10:00]
[TRANSCRIPT] • Integrating Discrete Functions by Average Method [YOUTUBE 8:29] [TRANSCRIPT] • Integrating Discrete Functions via Polynomial Interpolation [YOUTUBE
9:32][TRANSCRIPT] • Integrating Discrete Functions via Spline Interpolation [YOUTUBE 5:32] [TRANSCRIPT] • Integrating Discrete Functions via Regression Method[YOUTUBE 8:23] [TRANSCRIPT] • n-pt Gaussian Quadrature Rule: Discussion [YOUTUBE 8:52] [TRANSCRIPT] • Converting Limits of Integration [YOUTUBE 7:13] [TRANSCRIPT] • Gaussian Quadrature Rule: Example [ YOUTUBE 8:55] [TRANSCRIPT] • 1-pt Gaussian Quadrature Rule: Derivation [YOUTUBE 8:36] [TRANSCRIPT] • Complete Derivation of Two Point Gaussian Quadrature Rule: Part 1 of 3 [ YOUTUBE
9:46] [TRANSCRIPT] • Complete Derivation of Two Point Gaussian Quadrature Rule: Part 2 of 3 [ YOUTUBE
3:31] [TRANSCRIPT] • Complete Derivation of Two Point Gaussian Quadrature Rule: Part 3 of 3 [ YOUTUBE
9:58] [TRANSCRIPT]
Assigned Exercises • Assigned and graded adaptive lesson • Multiple Choice Tests at the end of Chapter 07.02, Chapter 07.05, Chapter 07.06 in the textbook • Problem sets at the end of Chapter 07.02, Chapter 07.05, Chapter 07.06 in the textbook
Page 20 of 21
Chapter 8 ORDINARY DIFFERENTIAL EQUATIONS (2 weeks)
Learning Objectives
Chapter 08.02 Euler's method • develop Euler’s Method for solving ordinary differential equations, • determine how the step size affects the accuracy of a solution, • derive Euler’s formula from Taylor series, and • use Euler’s method to find approximate values of integrals.
Chapter 08.03 Runge-Kutta 2nd order method • derive Runge-Kutta 2nd order Method for solving ordinary differential equations • relate Runge-Kutta 2nd order Method to Taylor series, and • use Runge-Kutta 2nd order Method to find approximate values of integrals.
Chapter 08.05 Higher-order and coupled ordinary differential equations • take real-life problem and model it as coupled ordinary differential equations • reduce higher-order and coupled ordinary differential equations to simultaneous first-order
ordinary differential equations • use Euler's method to solve higher-order and coupled ordinary differential equations • use Runge-Kutta 2nd order method to solve higher-order and coupled ordinary differential
equations • write simultaneous first-order ordinary differential equations in state variable form
Videos Assigned PRIMER ON ODE (CHAPTER 08.01)
Exact Solution of 1st order ODE [YOUTUBE 6:48] Exact Solution of 1st order ODE: Another Example [YOUTUBE 7:37] Exact Solution of 1st order ODE: Polynomial Forcing Function[YOUTUBE 9:12] Exact Solution of 2nd order ODE: Distinct Roots of Characteristic Equation [YOUTUBE 8:50] Exact Solution of 2nd order ODE: Repeated Roots of Characteristic Equation [YOUTUBE 8:41] Exact Solution of 2nd order ODE: Complex Roots of Characteristic Equation [YOUTUBE 9:34]
EULER'S METHOD (CHAPTER 08.02)
Euler's Method of Solving ODEs: Derivation [YOUTUBE 9:53] Euler's Method of Solving ODEs: Example [YOUTUBE 10:57] Euler's Method of Estimating Integrals: Theory [YOUTUBE 7:11] Euler's Method of Estimating Integrals: Example [YOUTUBE 8:58]
RUNGE-KUTTA 2ND ORDER METHOD (CHAPTER 08.03)
Runge-Kutta 2nd Order Method: Background [YOUTUBE 9:46] Runge-Kutta 2nd Order Method: Formulas [YOUTUBE 10:57] Runge-Kutta 2nd Order Method: Heun's Method [YOUTUBE 9:27]
Page 21 of 21
HIGHER ORDER/COUPLED DIFFERENTIAL EQUATIONS (CHAPTER 08.05)
Higher Order Differential Equations: Background [YOUTUBE 6:47] Coupled Differential Equations: Background: Part 1 of 2 [YOUTUBE 5:44] Coupled Differential Equations: Background: Part 2 of 2 [YOUTUBE 6:44] Higher Order Differential Equations: Euler's Method: Part 1 of 2 [YOUTUBE 9:50] Higher Order Differential Equations: Euler's Method: Part 2 of 2 [YOUTUBE 4:24] Writing a Higher Order Differential Equation in State Variable Form [YOUTUBE]
Textbook and Handouts • Chapter 08.00A - Physical Problem General Engineering - (Pages 467-470 from Customized Book,
Pages 606-609 from Abridged Book) • Chapter 08.00G - Physical Problem Mechanical Engineering - (Pages 475-480 from Customized
Book, Pages 629-634 from Abridged Book) • Primer on ODEs (videos and do the MC test) • Chapter 08.02 Euler's method - (Pages 485-492 from Customized Book, Pages 639-646 from
Abridged Book) • Example of the order of global truncation error in Euler's method • Chapter 08.03 Runge-Kutta 2nd order method - (Pages 501-509 from Customized Book, Pages
655-663 from Abridged Book) • Chapter 08.05 Higher-order and coupled ordinary differential equations - (Pages 519-527 from
Customized Book, Pages 687-695 from Abridged Book) • Writing a higher order differential equation in state variable form • Writing coupled ordinary differential equations in state variable form (simple example) • Writing coupled ordinary differential equations in state variable form (Applied Example: Bus-
suspension system example) Mfiles for second-order ODE higher_order_ODE.m and highersys.m
• Practice Test 3 • Practice Test 4
Assigned Exercises • Assigned and graded online quizzes on CANVAS • Multiple Choice Tests at the end of Chapter 08.02, Chapter 08.03, Chapter 08.05 in the textbook • Problem sets at the end of Chapter 08.02, Chapter 08.03, Chapter 08.05 in the textbook
