Ordinary Differential Equations
MATH 310 Fall 2020
Section 10: Engineering Outreach
Instructor:
|
Lyudmyla Barannyk
317 Brink Hall
tel: (208) 885-6719
fax: (208) 885-5843
barannyk@uidaho.edu
|
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
Syllabus
Download syllabus: .pdf
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
If you have problems with installing or running Matlab, please
contact the ITS Help Desk at
Phone: 208-885-4357 (HELP)
Email: helpdesk@uidaho.edu
ITS HELP DESK Physical Address:
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
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
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
Examples of functions of
exponential order
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
Additional Help / Tutoring
Tutoring sessions in Commons
as well as in ThinkTank
Grading
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
If
you have any further questions please contact theg office at eo-support@uidaho.edu.