# Math 33B: General Course Outline

## Catalog Description

33B. Differential Equations. (4)Lecture, three hours; discussion, one hour. Requisite: course 31B with a grade of C- or better. Highly recommended: course 33A. First-order, linear differential equations; second-order, linear differential equations with constant coefficients; power series solutions; linear systems. P/NP or letter grading.

## Course Information:

In addition, two hour exams should be given. These exams are usually given in the fourth and eighth week; the exact time they are scheduled is up to the instructor. 24 of the 26 lectures are specified.

The course Math 33B has evolved over the years. At one time it was a course in infinite series, including power series solutions of differential equations. In the Fall of 1997 the infinite series course was renumbered as Math 31C, in hopes that students would take it earlier, but by the Fall of 1998 the course was back at the end of the calculus sequence with its original label Math 33B.

In 2004, the courses Math 33A and 33B were reorganized. The differential equations portion of Math 33A was moved to Math 33B, so that Math 33A is now a course in linear algebra and Math 33B is now a course in differential equations. The topics currently treated in Math 33B are as follows:

Introduction to first order differential equations

• second order linear differential equations with constant coefficients
• power series solutions of second order differential equations
• linear systems of differential equations

## Textbook

Polking, Differential Equations, 2nd Ed., Prentice Hall.

Footnotes

1. On page 22 of the Polking text the author has a section on a 'numerical solver". He writes "We assume that each of our readers has access to a computer." He also adds We assume that you have access to a solver [computer and software] that will draw direction fields, provide numerical solutions?, and plot solutions." The author goes into detail on the vibrating spring example, pages 137-140. You might wish to put this off until 4.4 when he returns to the topic.

3. Math 33B does not have math 33A, linear algebra, as a prerequisite. This was a concession to the Chemistry Department. You will have to give a short, fast explanation of eigenvalues and eigenvectors.

4. All eiganvalue possibilities are discussed in this section.

Outline update: 9/14

## Schedule of Lectures

Lecture Section Topics

1

2.11

Examples, Direction Fields

2

2.2

Separable equations

3

2.4

Linear Equations, x' (t) = a (t) x (t) + f (t)

4

2.5

Mixing Problems

5

2.6

Exact Differential Equations

6

2.6

Continuation of Previous Lecture

7

2.7

Existence and Uniqueness

8

2.9

Autonomous Equations and Stability

9

4.12

Existence and Uniqueness, Linear Dependence, The Wronskian

10

4.3

Second Order Constant Coefficient Equations

11

4.3

Continuation

12

4.4

Harmonic Motion -- Unforced

13

4.5

Undetermined Coefficients

14

4.6

Variation of Parameters

15

9.13

Linear Systems with Constant Coefficients

16

9.24

2 x 2 systems

17

9.2

Continuation

18

9.2

Continuation

19

9.3

Phase Plane Portraits

20

9.4

The Trace-Determinant Plane

21

9.5

Higher-Dimensional Systems

22

9.5

Continuation

23

9.6

The Exponential of a Matrix

24

9.6

Continuation