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.
Textbook
    Polking, Differential Equations, 2nd Ed., Prentice Hall.
    Gilbert, Maple Projects for Differential Equations, Prentice Hall. (free supplement given by publisher)
Comments
    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.
Schedule of Lectures

Lecture
Sections
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

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." Our students will have access to computers, equipped with Maple, which is fairly easy to use. In addition the publisher provides a free manual on Maple.

2. 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: 9/06
For more information, please contact Student Services, ugrad@math.ucla.edu.
 

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