Math 308.200 Syllabus

Week 1 [1/14-1/18] - Chapter 1.
Overview, What is a differential equation, Direction fields, Euler's method.

Due 1/24/02:

1.1 - 13,14,15,16,17 [Solutions]
1.2 - 3,6, 9,10,13,16,18,20,21,26,27 [Solutions]
1.3 - 3,4,5,7,17,18,19 [Solutions]
1.4 - 6,8,10,13,15, 17,20,21,22,23,24,25 [Solutions]

Week 2 [1/21-1/25] - Sections 2.1-2.3
First order differential equations - separable, linear equations.

Due 1/31/02:

1.5 - 4,5,7,11,12,13, 15,16 [Solutions]
2.1 - No homework
2.2 - 5,6,9,10,13,16, 19,22,29,34,37 [Solutions]

Week 3 [1/28-2/1] - Sections 3.1-3.4
Applications of first order equations.

Due 2/7/02:

2.3 - 6,9,10,17,22,30,31, 32,33,36 [Solutions]
3.1 - No homework
3.2 - 9, 11, 18, 19, 21, 22, 25, 26 [Solutions]

3.3 - 1, 2, 5, 12, 15 [Solutions]

Week 4 [2/4-2/8] - Sections [3.5,3.6] 4.1-4.3
Second order linear equations.

[Extra Credit] Improved Euler, Taylor, Runge-Kutta Numerical Methods:
Modify the Matlab file euler.m to create impeuler.m (improved euler), and rk.m (runge kutta). Solve the initial value problem y'=y, y(0)=1, with h=0.1, 0.01, and compare to exact solution y=ex

Due 2/14/02:

3.4 - 1, 9, 12, 18, 20, 24, 25 [Solutions]
4.1 - 1, 2, 4 [Solutions]
4.2 - 9, 11, 26, 27, 30, 31, 33, 36 [Solutions]
4.3 - 1, 2, 19, 20, 23, 27 [Solutions]

Week 5 [2/11-2/15] - Sections 4.4-4.6
More second order linear equations.

Due 2/21/02:

4.4 - 1, 3, 6, 9, 13, 14, 15 [Solutions]
4.5 - 7, 11, 20, 28, 34, 39, 46,47 [Solutions]
4.6 - 3, 4, 15, 28, 29, 36, 37 [Solutions]

Week 6 [2/18-2/22] - Sections 4.7-4.9
Undetermined coefficients. Variation of Parameters.

Due 2/28/02:

4.7 - 2, 4, 7, 13, 18 [Solutions]
4.8 - 17, 18, 24, 30, 33, 40, 45, 49, 55 [Solutions] and
57[the speed bump problem]
4.9 - 10, 13, 17, 21, 22, 26, 28 [Solutions]

Week 7 [2/25-3/1] - Sections 4.10-4.12
Applications of second order equations (vibrations).

Due 3/7/02:

4.10 - 4, 6, 11, 15, 16 [Solutions]
4.11 - 1, 3, 6, 14, 15 [Solutions]
4.12 - 3, 5, 7, 10 [Solutions]

Week 8 [3/4-3/8] - Sections 5.1-5.3

Due 3/21/02:

5.1 - No Homework
5.2 - 1, 5, 8, 18, 23, 26, 33, 36, 37 [Solutions]
5.3 - 9, 13, 18, 22, 35 [Solutions]


Introduction to systems and phase-plane .

[3/11-3/15]    SPRING BREAK!

Week 9 [3/18-3/22] - Sections 5.4-5.6

Due 4/4/02:

5.4 - 3, 8, 9 [Solutions] [Problem 8 - Maple Worksheet]
5.5 - 9, 10, 11 [Solutions]
5.6 - 4, 9, 12, 22, 27 [Solutions]
[Note: Use rkf4.m from Polking's site]


Applications of systems - coupled springs, circuits. Runge Kutta, reduction of a higher order differential equation to a system of first order odes so. Numerical algorithms.

Week 10 [3/25-3/29] - Sections 7.1-7.3

Due 4/11/02:

7.1 - No homework
7.2 - 4, 11, 18, 31 [Solutions]
7.3 - 1, 12, 13, 20, 22, 27 [Solutions]


Laplace Transforms.

Week 11 [4/1-4/5] - Sections 7.4-7.5

Due 4/18/02:

7.4 - 3, 7, 10, 15, 16, 22, 25, 30 [Solutions]
7.5 - 5, 8, 11, 17, 23, 25, 32 [Solutions]


Inverse Laplace transforms and applications to ODEs.

Week 12 [4/8-4/13] - Sections 9.1-9.3

Due 4/25/02:

9.1 - 6, 7, 8, 9, 12, 13 [Solutions]
9.2 - 3, 6, 10, 11, 14 [Solutions]
9.3 - 3, 6, 7, 16, 18, 24, 41, 42, 43 [Solutions]


Linear Systems of Equations

Week 13 [4/15-4/20] - Sections 9.4-9.6

9.4 - 9, 15, 16, 23, 26 [Solutions]
9.5 - 9, 10, 18, 20, 49 [Solutions]
9.6 - 3, 5, 13 [Solutions]

Linear Systems of Equations (cont'd)

Week 14 [4/22-4/29]
Chaos and Dynamical Systems