MATH 246H -- Honors Differential Equations

This course is an introduction to ordinary differential equations. The course introduces the basic techniques for solving and/or analyzing first and second order differential equations, both linear and nonlinear, and systems of differential equations. Emphasis is placed on qualitative and numerical methods, as well as on formula solutions. The use of mathematical software system is an integral and substantial part of the course. All sections of the course will use the software system MATLAB. Prerequisites for this course are: MATH141 and any one of the following: MATH240 or ENES102 or PHYS161 or PHYS171.

Here is some more basic information about MATH246H:

Time & Place:

TuTh 12:30-1:45 pm, PHYSICS 1204

Instructor:

Professor Richard A. Wentworth
Office: 3109 Mathematics Building
Phone: (301) 405-5130
Office Hours: TuTh 9-10am and by appointment
Email: raw@umd.edu
Web: www.math.umd.edu/~raw

Texts:

Elementary Differential Equations, William E. Boyce and Richard C. DiPrima, Ninth Edition J. Wiley and Sons, New York, 2009 ISBN: 978-0-470-03940-3.
Differential Equations with MATLAB, Brian R. Hunt, Ronald L. Lipsman, John E. Osborn, and Jonathan M. Rosenberg, Second Edition J. Wiley and Sons, New York, 2005 ISBN: 978-0-471-71812-3.

Homework and MATLAB:

There will be six MATLAB assignments. Click here for more on MATLAB. In addition, problems from the book are suggested below. These will not be graded. Nevertheless, you should work through all of them, since they are typical of the types of problems that will appear on quizzes and exams.

Quizzes:

There will be 10 quizzes. These will be at the end of class every Tuesday except exam days, the week of Thanksgiving, and the last week of classes.

Exams:

There will be three midterm exams on Sep 27, Nov 1, and Dec 6. These will be given during the normal lecture period in the usual room. There will be a comprehensive final exam on Dec 15, 1:30-3:30 pm. More information will be posted here: FINAL EXAM INFO.

Makeups:

There will be no makeups for quizzes or midterms. If you have compelling reasons for missing a quiz or an exam let me know as soon as possible.

Grading:

The final grade will depend on your performance on the exams, quizzes, and MATLAB assignments. The breakdown of the 750 possible points is as follows: three midterm exams = 300, final exam = 200, quizzes = 100, MATLAB = 150.

Help:

You can find information about tutoring and other useful resources here.

Academic Integrity :

You should be familiar with the University's policies on Academic Integrity, including the Honor Pledge.

Students with disabilities :

If you have some disability related to testing under the usual timed, in-class conditions, you may contact the office of Disabled Students Services (DSS) in Shoemaker. If they assess you as meriting private conditions and/or extra time, then you may arrange to take your tests at DSS, with extra time as they indicate. You must arrange this well in advance of a test. Click to Disability Support Services for further information.

Religious observances:

If your religion dictates that you cannot take an exam or hand in assigned work on a particular date, then contact me at the beginning of the semester to discuss alternatives. You are responsible for making these arrangements.

Detailed Syllabus:

Below is an outline of the material I hope to cover and when. This will undoubtedly change as the semester progresses, so check here often for updates. The reading selections and homework are from Boyce and DiPrima.

WEEK

DATE

TOPICS

READING

SUGGESTED PROBLEMS

1

Sep 1

Classification of ODE's. Integrating factors.
1.1-1.3, 2.1
1.1: # 1,7,16,18,20,26,29,31,33. 1.2: # 1,4. 1.3: # 1,7,15,29. 2.1: # 3,13,16,21,34.

2

Sep 6

First order equations. Separable equations.
2.2-2.4
2.2: #1,9,21,25,26. 2.3: # 1,2,7,8,14,15,25,26. 2.4:# 1,7,13, 27, 32.

3

Sep 13

 Modeling. Numerical methods.
2.5, 2.7, 8.1-8.3
2.5: # 1,3,5,7,9,12,13,20,23. 2.7:# 1,11. 8.1:# 7,9,12. 8.2:# 7,9,12. 8.3:# 7,9,12.

4

Sep 20

 Exact equations and integrating factors.
2.6
2.6: # 1,13,15,18,19.

5

Sep 27

 First midterm exam. Second order equations.
3.1-3.2
3.1: # 1, 9, 23. 3.2: # 1, 7,14,22,24.

6

Oct 4

 Characteristic equations. Reduction of order.
3.3, 4.1-4.2
3.3: # 1,7,17,23. 4.1:# 1,3,5,11,13. 4.2:#11,13,19,32.

7

Oct 11

 Non-homogeneous equations.
3.4-3.5, 4.3
3.4:#1,11,15,23. 3.5:# 1, 13, 19, 27. 4.3:# 1,3,5,7,11,15,17.

8

Oct 18

 Variation of parameters.
3.6, 4.4
3.6:# 1,5,13,21. 4.4:# 1,4,9.

9

Oct 25

 Mechanical and electric vibrations.
3.7-3.8
3.7:#1,5,9. 3.8:#1,5,15,21.

10

Nov 1

 Second midterm exam. Laplace transform.
6.1-6.2
6.1:# 7,11,15,21,26. 6.2:# 1,3,5,7,9,11,15,17,19,21,23.

11

Nov 8

 Step functions. Systems of ODE's.
6.3-6.4, 7.1-7.3
6.3: #1,3,5,7,9,11,13,15,17. 6.4:# 1,5,9,10,11,13. 7.1:# 1,8. 7.2:# 1,3,5,10. 7.3:# 1,7,13,26.

12

Nov 15

 Systems of ODE's (cont.)
7.4-7.6
7.4:# 6,7. 7.5:# 1,5,7,11,15,17,25,27,30. 7.6:# 1,3,5,9,10.

13

Nov 22

 Systems of ODE's (cont.)
7.7-7.8
7.7:# 1,3,5,7,9,11. 7.8:# 1,3,5,7,9.

14

Nov 29

 Qualitative theory. Phase portraits.
9.1-9.3
9.1:# 1, 13, 20,21. 9.2:# 1,5,17. 9.3:# 1,5, 19.

15

Dec 6

Third midterm exam. Predator-prey problems.

9.4-9.5
9.4:# 1,8. 9.5: # 1,7.

16

Dec 13

Review.

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Richard A. Wentworth