# Ordinary Differential Equations

MATH 310  Fall 2020

#### Instructor:

Lyudmyla Barannyk
317 Brink Hall
tel:  (208) 885-6719
fax: (208) 885-5843
barannyk@uidaho.edu

 Handouts and Lecture Notes Additional Help / Tutoring Exam Proctoring

## Course Description

This is an introductory differential equations course for undergraduate students of mathematics, science and engineering. Methods for solving ordinary differential equations are studied together with physical applications, Laplace transforms, numerical solutions, and series solutions.

## Textbook

Differential Equations and Boundary Value Problems: Computing and Modeling by C. Henry Edwards, David E. Penney and David Calvis, 5th Edition, Prentice Hall

## Homework and Matlab Projects

There will be assigned and suggested homework problems chosen from the textbook. A random selection of problems will be graded. Students are required to solve all homework problems  after each lecture in order to gain a better understanding of the course material and prepare for exams.

EO students should submit their homework assignments and Matlab projects in a pdf format (a single .pdf file for each assignment) by email barannyk@uidaho.edu  by the end of the due day. There is 3 business day grace period. Late homework after the grace period will not be accepted.

Matlab is available through VLAB at https://vlab.uidaho.edu/vpn/index.html

Phone: 208-885-4357 (HELP)
Email: helpdesk@uidaho.edu

Teaching Learning Center Room 128

ThinkTank Tutoring Center Schedule

Homework assignments:

Homework # 1: due September 4
Assigned homework
Section 1.1: # 1, 3, 11, 13, 23, 31, 35, 45
Section 1.2: # 3, 8, 15, 27, 35
Section 1.3: # 1, 5, 13, 21
Section 1.4: # 1, 3, 21, 29, 33, 35, 40, 43
Section 1.5: # 3, 5, 27, 36, 37

Suggested homework
Section 1.1: # 5, 8, 15,  17, 19, 27, 28, 29, 32, 34, 36, 47
Section 1.2: # 1, 5, 11, 18, 24, 25, 26, 30, 36
Section 1.3: #  2, 3, 11, 15-18,  26, 27, 28
Section 1.4: # 5, 7, 11, 19, 23, 24, 27, 31, 37, 39, 44, 49, 56
Section 1.5: # 1, 7, 17, 21, 33, 35

Matlab Project # 1: .pdf  due  September 4

Matlab dfield module to a folder. Start Matlab, go to the folder where dfield9.m is. Type dfield9 from the command line to launch the software. Note that dfield solftware should be saved to the same directory you are working in.

Java version of dfield is also available:

https://math.rice.edu/~dfield/dfpp.html

Homework # 2: due September 9
Assigned homework
Section 2.1: # 1, 7, 12, 23, 32
Section 2.2: # 7, 9, 24, 29
Section 2.3: # 2, 7, 11, 19

Suggested homework
Section 2.1: # 2-6, 8-10, 15, 17, 18, 21,  29, 30, 33
Section 2.2: # 3, 13, 19, 21
Section 2.3: # 1, 3, 5,  9,  13, 16, 27, 29

Homework # 3:  due September 16
Assigned homework
Section 2.4: # 1, 5
Section 2.5: # 1, 5
Section 2.6: # 1, 5
Section 3.1: # 3, 11, 20, 21, 33,  45
Section 3.2: # 1, 5, 7, 17, 21

Suggested homework
Section 2.4: # 2, 3, 5, 6, 7, 8, 9, 12, 13, 15, 16
Section 2.5: # 2, 4, 5, 7, 8, 9, 11, 12, 13, 14, 16
Section 2.6: # 2, 3, 4, 7, 8, 9, 12, 13, 15
Section 3.1: # 1, 13, 15, 17, 22, 23, 29, 35, 43, 47, 48
Section 3.2: # 2, 4, 3, 6, 8, 9, 10, 11, 13, 23, 30

Exam 1:  due by September 18.  Exam covers sections 1.1-1.5,  2.1-2.6, 3.1 and 3.2. Review classification of DEs: order, linear/nonlinear, homogeneous/non-homogeneous. Topics and practice problems
Review session: see
Lecture 16.

Matlab Project # 2: .pdf   due September 22

All necessary files together can be found here: programs_project2.zip.  If the links below to .m files do not work, please download these .m files from  programs_project2.zip.

1) Numerical methods (Euler, Modified Euler, Runge-Kutta) can be written in Matlab using functions that can be used for solving various 1st order IVPs without rewriting them each time for a specific equation is mind. Functions are .m files. The right hand side function f(x,y) is evaluated using a separate function f.m (see below). A different differential equation would require an update of function f.m.

Matlab ODE solvers: Euler, Improved/Modified Euler, Runge-Kutta

These solvers implement three methods: Euler, Modified Euler and 4th order Runge-Kutta.

Matlab function that defines the right hand side of a differential equation y'=f(x,y) f.m

In this example written as a program main.m all the above numerical methods are called to solve an IVP. The numerical results are compared with a known exact solution. This is the main program that calls ODE solvers, which in turn call function f.m to evaluate f(x,y) needed for ODE solvers.

Matlab function that computes exact solution of y'=f(x,y) at grid points: exact_sol.m that is derived here.

Please  note that when you need to solve an initial value problem for which exact solution is not available, you would need to comments lines where exact solution and errors are computed and plotted (lines 19-23, 28-32, 62-92).

For comparison:

2) Sample program implementing Euler method for y'=x+y, y(0)=1

In this example, the Euler method is implemented directly for solving IVP y'=x+y. If a differential equation changes, the program needs to be rewritten.

Homework # 4:  due September 30
Section 3.3: # 1, 7, 11, 21, 33, 39, 41, 43
Section 3.4: # 1, 3, 5, 13, 15, 17, 22
Section 3.5: # 3, 5, 7, 17, 19, 21, 23, 37, 53, 61
Section 3.6: # 1, 5, 7, 11, 15, 19, 24

Suggested homework
Section 3.3: # 3, 13, 18, 27, 29, 35, 38, 44, 45
Section 3.4: #  2, 4, 6,  14,  16, 18, 19, 20, 23, 24,  25, 26, 27
Section 3.5: # 1, 4, 13, 15, 16, 18, 25, 27, 28,  29, 35, 39, 41, 43, 44, 45, 46, 47, 50, 54, 59, 60
Section 3.6: # 3, 6, 8, 10, 14, 16, 18

Exam 2: due by October 16. Exam covers sections 3.1-3.6. Topics and practice problems
Review session: see Lecture 33.

Homework # 5:  due October 28
Section 3.7: # 1, 3, 4, 8, 13, 17, 21
Section 4.1: # 1, 3, 7, 9, 11, 17, 19, 23, 30, 32, 33
Section 4.2: # 1, 3, 7, 9, 23, 27, 31
Section 5.1: # 1, 4, 7, 13, 17, 21, 27, 31
Section 5.2: # 1, 3, 5,  8, 11, 17, 27
Section 5.3:  categorize the eigenvalues and eigenvectors and sketch the phase portrait for problems from Section 5.2: # 1, 6, 7, 9, 11, 16, then solve problems from Section 5.3: 18, 19, 20, 21

Suggested homework
Section 3.7: # 2, 5, 6, 7, 9, 11, 12, 14, 16, 18, 19, 20
Section 4.1: # 4, 15, 21, 25, 28, 34, 35
Section 4.2: # 5, 11, 13, 17, 24, 25, 29, 30, 32, 37, 39, 47
Section 5.1: # 3, 5, 11, 14, 16, 23, 29, 32
Section 5.2: # 2, 4, 6, 7, 9, 19, 29
Section 5.3: # 3, 8, 10, 13, 17, 22, 23, 24, 25

Exam 3: due by November 13. Exam covers sections 3.7, 4.1, 4.2, 5.1-5.3.  Topics and practice problems

Homework # 6
: due November 20
Assigned homework
Section 7.1: # 1, 4, 9, 11, 13, 15, 17,  21, 23, 25, 27, 29, 31
Section 7.2: # 1, 3, 5, 17, 21, 25, 28
Section 7.3: # 1, 3, 4, 5, 7, 8, 13, 21, 23, 27, 29
Section 7.4: # 2, 3, 7, 9, 13, 17, 21, 23, 29, 36

Suggested homework
Section 7.1: # 2, 3, 5, 6, 8, 10, 12, 16, 18, 19, 22, 24, 28, 32, 36
Section 7.2: # 4, 6, 7, 10, 11, 15, 19, 20, 24, 30, 31, 32
Section 7.3: # 2, 6, 9, 10, 11, 12, 14, 15, 16, 22, 24, 28, 30, 31, 34, 38
Section 7.4: # 1, 3, 8, 11, 14, 16, 18, 19, 20, 22, 30, 33, 37

Homework # 7:  due December 11
Assigned homework
Section 7.5: # 1, 4, 5, 11, 12, 15, 20, 25, 31
Section 7.6: # 1, 3, 5, 9, 11, 17
Section 8.1: # 3, 5, 13, 15, 19, 21
Section 8.2: # 1, 3, 7, 17, 19, 21, 23, 29

Suggested homework
Section 7.5: # 2, 3, 6, 8, 9, 10, 13, 14, 15, 19, 27, 28, 32, 33, 37, 39
Section 7.6: # 2, 4, 5, 10, 13, 18
Section 8.1: # 1, 4, 7, 8, 9, 11, 16, 17, 21, 23, 26
Section 8.2: # 5, 9, 11, 13, 16, 18, 22, 25

Final Exam:  due by Thursday, December 17

Final exam is cumulative. It covers previous sections and sections 7.1-7.6, 8.1, 8.2.  Topics and sample problems
Review session: Lecture 42 as well as Lecture 41 including some solved problems.

## Handouts

List of formulas to know (commit to memory) pdf
Newton's Law of cooling/heating pdf
Exact Equations and Integrating Factors pdf
Euler's method: example pdf
Improved Euler's method: example pdf
4th order Runge-Kutta example: pdf
Operator Identities pdf
Method of Undetermined Coefficients pdf
Laplace Transform Table .pdf

Video lectures are available through Engineering Outreach at https://eo.uidaho.edu/portal.

## Lecture Notes 2019 (please use 2015 notes)

Lecture 1: 1/09/2019
Lecture 2: 1/11/2019
Lecture 3: 1/14/2019
Lecture 4: 1/16/2019
Lecture 5: 1/18/2019

Lecture 40: 4/29/2019

Video lectures are available through Engineering Outreach at https://eo.uidaho.edu/portal.

## Lecture Notes 2015

Lecture 1: 8/24/2015                            Lecture 11: 9/18/2015                        Lecture 21: 10/14/2015                        Lecture 32: 11/09/2015
Lecture 2: 8/26/2015                            Lecture 12: 9/21/2015                        Lecture 22: 10/16/2015                        Lecture 33: 11/11/2015 (Review 2)
Lecture 2: 8/26/2015                            Lecture 12: 9/21/2015                        Lecture 23: 10/19/2015                        Lecture 34: 11/16/2015
Lecture 3: 8/28/2015                            Lecture 13: 9/23/2015                        Lecture 24: 10/21/2015                        Lecture 35: 11/18/2015
Lecture 4: 8/31/2015                            Lecture 14: 9/25/2015                        Lecture 25: 10/23/2015                        Lecture 36: 11/20/2015
Lecture 5: 9/02/2015                            Lecture 15: 9/28/2015                        Lecture 26: 10/26/2015                        Lecture 37: 11/30/2015
Lecture 6: 9/04/2015                            Lecture 16: 9/30/2015 (Review 1)     Lecture 27: 10/28/2015                        Lecture 38: 12/02/2015
Lecture 7: 9/09/2015                            Lecture 17: 10/05/2015                      Lecture 28: 10/30/2015                        Lecture 39: 12/04/2015
Lecture 8: 9/11/2015                            Lecture 18: 10/07/2015                      Lecture 29: 11/02/2015                        Lecture 40: 12/07/2015
Lecture 9: 9/14/2015                            Lecture 19: 10/09/2015                      Lecture 30: 11/04/2015                        Lecture 41: 12/09/2015 some solved problems
Lecture 10: 9/16/2015                          Lecture 20: 10/12/2015                      Lecture 31: 11/06/2015                        Lecture 42: 12/11/2015  (Duhamel's Principle and Final Review)

Wolframalpha:  symbolic computations online

## Exams

Exam 1: due by Friday, September 18.  Exam covers sections 1.1-1.5 and 2.1-2.6, 3.1 and 3.2. Topics and sample problems
Review session: see
Lecture 16.

Exam 2: due by Friday, October 16. Exam covers sections 3.3-3.7. Topics and sample problems
Review session: see Lecture 33.

Exam 3
: due by Friday, November 13.
Exam covers sections 3.7, 4.1, 4.2, 5.1-5.3.  Topics and practice problems

Final Exam : due by Thursday, December 17. Final exam is cumulative. It covers previous sections and sections 7.1-7.6, 8.1 and 8.2  Topics and sample problems
Review session: Lecture 42 as well as Lecture 41 including some solved problems.

Operator Identities .pdf
Laplace Transform Table .pdf

Tutoring sessions in Commons

as well as in ThinkTank

Exam 1: 15%
Exam 2: 20%
Exam 3: 25%
Homework and Matlab Projects: 10%
Final Exam: 30%

## Exam Proctoring

Please visit the proctor/exam information page on the website. https://eo.uidaho.edu/proctor

Students living outside of the United States will be required to use approved testing centers as their proctors. A testing center is a university, business, or military department with the primary purpose of proctoring tests and exams under direct observation. Students are required to provide a name of a person who will be the primary contact at the testing center. EO reserves the right to require students to take exams at specific pre-approved testing centers in locations outside of the United States.

You can view our proctor approved map to see if there is an approved testing center at the location you will be this summer.https://eo.uidaho.edu/map-international-proctors

If you know of a University Testing Center in the area you will be visiting that is not on our map you can submit that proctor to our office and we can begin the approval process before the semester starts: https://eo.uidaho.edu/proctorform