## Instructor: |
Lyudmyla Barannyk |

Handouts and Lecture Notes |
Additional Help / Tutoring | Exam Proctoring |

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

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

If you have problems with installing or running Matlab, please
contact the ITS Help Desk at

Email: helpdesk@uidaho.edu

ITS HELP DESK Physical Address:

Teaching Learning Center Room 128

ThinkTank Tutoring Center Schedule

Homework assignments:

Homework # 1: due June 19

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 June 22

Dowload 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.

https://www.mathworks.com/matlabcentral/answers/242199-dfield8-with-r2015b-on-mac-osx-issues

https://www.mathworks.com/matlabcentral/answers/267587-dfield6-errors-with-matlab-2015

Java version of dfield is also available:

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

Homework # 2: due June 25

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 July 2

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 July 2. 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 July 6

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 July 10

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 July 13. Exam covers sections 3.1-3.6. Topics and practice problems

Review session: see Lecture 33.

Homework # 5: due July 17

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 July 24. Exam covers sections 3.7, 4.1, 4.2, 5.1-5.3. Topics and practice problems

Homework # 6: due July 27

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 August 3

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, August 6

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.

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 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

Examples of functions of
exponential order

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

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

Exam 1: due by Friday, February
21. 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, March 20. Exam
covers sections 3.3-3.7. Topics and sample problems

Review
session: see Lecture 33.

: due by Friday, April 17.
Exam covers sections 3.7, 4.1, 4.2, 5.1-5.3. Topics and practice problems

Exam 3

Final Exam : due by
Thursday, May 7. 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 2: 20%

Exam 3: 25%

Homework and Matlab Projects: 10%

Final Exam: 30%

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

If
you have any further questions please contact theg office at eo-support@uidaho.edu.