ME 203 Ordinary Differential Equations

Fall 2002 Course Outline and Notes

 

Instructor:      Pete Teertstra   E3-2133H         x5610               pmt@mhtl

                       

Office Hours:  2:30 – 4:00pm - Tuesday, Thursday

                       

TAs:                Josh Dyment     E3-3101            x2309               jdyment@lagavulin

                        Meishen Li        CPH-3372E      x6177               m6li@engmail

 

Course Goals:  This is an introductory level course on single-variable (ordinary) differential equations.  Differential equations are at the foundation of most mathematical models used in engineering.  In this course the student will be introduced to the standard analytical methods of solving ODE’s including the Laplace Transform method.  There may be some coverage of basic numerical techniques for computer solution of ODE’s, but this is covered in more detail in ME303.  Applications of ODE’s to mechanical engineering science will be introduced throughout. 

 

Textbook:       Fundamentals of Differential Equations and Boundary Value Problems, 5th ed.

R.K. Nagle, E.B. Saff and A.D. Snider.  Addison-Wesley Longman, 2000.

 

Web Site:        http://www.mhtlab.uwaterloo.ca/courses/me203/index.html

 

Tutorials:        Weekly tutorials will be held throughout the term in which the TAs will solve selected problems and will be available to answer questions on the lecture material and assignments. NOTE that the tutorials are held in small rooms that cannot accommodate the whole class, so please stick with your assigned lab section.

T01                  Monday            1:30-2:20           DWE 3522A    

T02                  Tuesday            1:30-2:20           RCH 309

 

Grades:           The course grades will be based on a course project, midterm and final exams using the following weighting scheme:

            Midterm Exam:          30%

            Course Project:          10%

            Final Exam:                 60%

Exams are closed book with equation sheet permitted – single page for midterm, double-sided for final exam. The course project will be given after the midterm exam.

 

Assignments:  Problem sets will be posted on the course website on a weekly basis.  Problem sets will be posted by Thursday morning and will cover the lecture material for that week.  In accordance with Department policy, these will not be marked for credit, but it is recommended that you complete each assignment prior to the following week’s tutorial. Experience has shown that solving assigned problems on a weekly basis is the best way to properly learn and consolidate the methods demonstrated in the lectures.  Solutions to the problem sets will be posted to the website after the tutorial on Tuesday.

 

Make-up Lectures:    Tuesday, Sep. 17           8:30 – 9:20AM              CPH 3388

                                    Thursday, Oct. 3           8:30 – 9:20AM              CPH 3388

                                    Tuesday, Oct. 29           8:30 – 9:20AM              CPH 3388

 

Important Dates:        Midterm                        Monday, Oct. 21

                                    Lectures End                Tuesday, Dec. 3

                                    Final Exam Period         Friday, Dec. 6 – Friday, Dec. 20           

                                    Thanksgiving Holiday     Monday, Oct. 14                      

 

 

Course Schedule

 WEEK            TOPICS                                                                                              TEXT        

1                Introduction  to ODEs                                                                            1.1 – 1.3

2                First Order ODEs                                                                                  2.1 – 2.5

                  - separable equations

                  - linear equations

                  - exact equations

                  - special integrating factors

3                First Order ODEs                                                                                  2.6

                  - substitutions and transformations

                  Mathematical Modelling                                                                         3.1 – 3.4

4                                 Mathematical Modelling
- Matlab demonstration
Second Order ODEs                                                                             4.1 – 4.2
- introduction

5                                 Second Order ODEs                                                                             4.2 – 4.5
- fundamental solutions of homogeneous equations
- homogeneous linear equations with constant coefficients

6                                 Second Order ODEs                                                                             4.6
- complex roots
Higher Order Linear ODEs                                                                    6.1 – 6.2

MIDTERM EXAM

7                                 Second Order ODEs                                                                             4.7 – 4.10
- non-homogeneous linear equations                                                       
- method of undetermined coefficients
- variation of parameters
- variable coefficient and nonlinear equations

8                                 Second Order ODEs                                                                             4.11 – 4.12
 - applications
Systems of Linear ODEs                                                                       5.3 – 5.4

9                                 Systems of Linear ODEs                                                                       5.3 – 5.4
Laplace Transform Methods                                                                  7.1 – 7.2

10                             Laplace Transform Methods                                                                  7.3 – 7.6

11                             Series Solutions                                                                                     8.1 – 8.3, 8.5

12                             Special Functions                                                                                   8.8