MATH 341 -- HONORS MULTIVARIABLE CALCULUS, LINEAR ALGEBRA,
AND DIFFERENTIAL EQUATIONS II

This course is a continuation of MATH 340. The honors sequence MATH 340-341 covers roughly the same material of MATH 240, 241, and 246, but in greater depth and rigor. This semeseter will begin with remaining material from Multivariable Calculus (MATH 241) on extrema of functions of several variables and Lagrange multipliers. The remainder of the semester, and the bulk of the course, is then devoted to the theory of Ordinary Differential Equations (MATH 246).

Here is some more basic information about Math 341:

Time & Place: TTH 2-3:45 pm, MATH 0106

Instructor:

Professor Richard A. Wentworth
Office: 3109 Mathematics Building
Phone: (301) 405-5130
Office Hours: TTh 9:30-11 and by appointment
Email: raw@umd.edu
Web: www.math.umd.edu/~raw
Texts:

Differential Equations and their Applications, 4th Edition, by Martin Braun. Published by Springer-Verlag. ISBN: 0387978941
Vector Calculus, by S. Colley. Published by Prentice Hall. ISBN: 0131858742
Recommended: Matrices and Linear Transformation, by C.G.Cullen. Published by Dover. ISBN: 0486663280
Homework: Suggested homework problems will be assigned every week. It is essential that you also try on your own as many similar problems from the book as possible. While homework from the book will not count towards your grade, the periodic quizzes in section will. Quizzes will consist of selected problems from the homework.
Quizzes:

There will be short quizzes periodically (approximately every other week). These will be given in lecture. The lowest quiz grade will be dropped from the average.

Exams: There will be two midterm exams on March 12 and April 23. These will be given during the regular lecture period in the regular classroom. In addition, there will be a comprehensive final exam on Monday, May 18, 10:30-12:30. Check the exam schedule for the room and any changes.
Makeups:

Attendance policy follows the university guidelines. The reason for any absence must be unavoidable, documented, and reported to me as early as possible.
Grading: The final grade will depend on your performance on the exams and quizzes, and completion of the MATLAB exercises. The relative weights I will use are: Midterm exams = 25% each, Final exam = 35%, Quizzes = 15%.
Expectations:

You are expected to come to class, do the homework, and be actively engaged in learning the material. Two tips for success: (1) Don't fall behind -- try to do a little homework every day; and (2) Make friends -- ask questions and help each other (especially after trying alone first).

Academic Integrity : You should be familiar with the University's policies on Academic Integrity, including the Honor Pledge.
Students with disabilities : If you have a 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 you cannot take an exam or quiz on a particular date due to religious observance, contact me at the beginning of the semester to discuss alternatives. You are responsible for making these arrangements at the beginning of the semester.
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 the texts above (C=Colley, B=Braun).

WEEK

DATE

TOPICS

READING

 HOMEWORK

1

Jan 27

Extrema of functions of several variables

C: 4.1-4.3

4.1: # 4, 10, 12, 18, 24, 29, 30, 32; 4.2: # 6, 10, 18, 22, 32, 38, 44; 4.3: # 6, 9, 18, 20, 22, 26, 28

2

Feb 3

Lagrange multipliers and applications; ODE's

C: 4.4; B: 1.1-2

4.4: # 1, 5, 8, 12, 14; 1.2: # 2, 4, 5, 6, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22

3

Feb 10

ODE's, examples

B: 1.3-1.5

1.3: # 2, 5, 7, 8; 1.4: # 1, 2, 4, 5, 6, 9, 10, 12; 1.5: # 2a, 3, 4, 6, 7, 9, 12

4

Feb 17

Further examples; existence and uniqueness

B: 1.9-10, 2.1

 1.9: # 3, 4, 6, 7, 8, 9, 11, 17; 1.10: # 1, 2, 5, 7, 11, 14, 19; 2.1: # 1, 3, 5

5

Feb 24

Second order equations

B: 2.2-3

 p. 140: # 1, 3, 7, 10, 11; p. 144: # 3, 5, 9; pp. 149-150: # 3, 7, 11, 13, 19; 2.3: # 2, 3, 4.
6
Mar 3

Variation of parameters; vibrations

B: 2.4-6

 2.4: # 1-10; 2.5: # 2, 4, 6, 14, 17; 2.6: # 1, 5, 6, 7.

7

Mar 10

Vibrations (cont.)

B: 2.6

 pp.172-3: # 1, 2, 5, 10, 13; p. 177: 1, 6, 7
   
SPRING BREAK
   

8

Mar 24

Series solutions

B: 2.8

 p. 197: # 1, 3, 5, 7, 9, 10, 11; p. 203: 1, 3, 5, 10

9

Mar 31

Laplace transform

B: 2.9-10

 2.9: # 3, 9, 17, 19, 20, 22, 23; 2.10: # 1, 2, 3, 5, 7a, 19, 20, 21

10

Apr 7

Dirac function; convolution

B: 2.12-3

 2.12: # 3, 5, 7, 8; 2.13: # 1, 5, 7, 9, 19, 20;

11

Apr 14

Systems of ODE's

B: 3.1, 3.4, 3.8

3.1: # 1, 3, 5, 7, 12, 13, 15; 3.4: # 1, 3, 7, 9, 13; 3.8: # 1, 3, 5, 9, 11, 15, 17.

12

Apr 21

Systems (cont.)

B: 3.9-11, 4.1-3
 3.9: # 1, 3, 5, 7, 9; 3.10: # 1, 3, 5, 11; 3.11: # 1, 3, 5, 9, 11.

13

Apr 28

Qualitative theory

B: 4.1-4.3

 4.1: # 1, 3, 5, 9, 11; 4.2: 1, 3, 5, 12, 14, 15; 4.3: 1, 3, 5, 7, 13.

14

May 5

Stability, phase portraits, Poincare-Bendixson.

B: 4.4, 4.7, 4.8

4.4: 3, 5, 7, 11; 4.7: 1, 3, 5, 7, 10, 11; 4.8: 5, 7, 9, 12, 13.
15
May 12
Preditor-prey; Review
B: 4.10
4.10: 3, 5.

Richard A. Wentworth