The following abbreviations will be used:
Book Ordinary Differential Equations by Polking,
Boggess & Arnold
Manual Ordinary Differential Equations using MATLAB by Arnold
& Polking
|
Week |
Topics |
Read |
Homework |
|
08/23-08/27 |
Introduction to ODE Solutions of ODE Plotting in MATLAB |
Book: Manual: |
Book (Sect. 2.1): 3, 11, 13, 18, 24 Manual ( Due Tuesday, 08/31 |
|
08/30-09/03 |
Solutions to Separable Equations Models of Motion |
Book: Sections
2.2, 2.3 Manual: Chapter
3 |
Book (Sect. 2.2): 5, 15, 27, 35 (Sect. 2.3): 4, 9, 11 Manual ( Due Tuesday, 09/07 |
|
09/06-09/10 |
Linear Equations Mixing Problems Existence and Uniqueness |
Book: Sections
2.4, 2.5, 2.7 Manual: Chapter
3 |
Book (Sect. 2.4): 4, 5, 16, 21 (Sect. 2.5): 1, 6, 12 (Sect. 2.7): 7, 9, 14 Due Tuesday, 09/14 |
|
09/13-09/17 |
Autonomous Equations Modeling Population Growth Personal Finance |
Book: Sections
2.9, 3.1, 3.2, 3.3 Manual: Chapter
3 |
Book (Sect. 2.9): 2, 9, 19, 25 (Sect. 3.1): 2, 12, 15 (Sect. 3.3): 4, 9, 15 Due Tuesday, 09/21 |
|
09/20-09/24 |
Second order equations Linear, homogeneous equations with constant coefficients |
Book: Sections
4.1, 4.3 |
Book (Sect. 4.1): 3, 11, 13 (Sect. 4.3): 4, 9, 13, 22, 28 Due Tuesday, 09/28 |
|
09/27-10/05 |
Inhomogeneous equations (method of undetermined coefficients) Harmonic motion |
Book: Sections
4.5, 4.4, 4.7 |
Book (Sect. 4.5): 1, 17, 21, 25, 37 (Sect. 4.4): 9, 11, 16 (use Matlab for plotting) (Sect. 4.7): 9, 19 Due Thursday, 10/07 |
|
10/07-10/14 |
Numerical Methods |
Book: Sections 6.1, 6.2, 6.3 Manual: Chapter
5 |
Book (Sect. 6.1): 5, 7 (Sect. 6.2): 5, 7 (Sect. 6.3): 9 Manual ( Due Tuesday, 10/19 |
|
10/18-10/21 |
Vectors and Matrices The Geometry of Linear Equations Solving Linear Systems |
Book: Sections 7.1, 7.2, 7.3 Manual: Chapter
11 |
Book (Sect. 7.1): 11, 35, 46, 53 (Sect. 7.2): 3, 7 (Sect. 7.3): 5, 13, 23, 24 Due Tuesday, 10/26 |
|
10/25-10/28 |
Properties of Solution Sets Subspaces |
Book: Sections 7.4, 7.5 Manual: Chapter
11 |
Book (Sect. 7.4): 11, 12, 21, 23, 31 (Sect. 7.5): 5, 14, 22, 31, 39 Manual ( Due Tuesday, 11/2 |
|
11/01-11/04 |
Determinants Introduction to Systems Geometric Interpretation of Solutions Qualitative Analysis |
Book: Sections 7.6, 8.1, 8.2, 8.3 Manual: Chapter
7 |
Book (Sect. 7.6): 9, 20, 27, 37, 50 (Sect. 8.1): 3, 11 (Sect. 8.2): 5, 23, 26 (use pplane6.m for #23 and #26) (Sect. 8.3): 3, 6, 7 Due Tuesday,
11/9 |
|
11/08-11/11 |
Linear Systems Eigenvalues and eigenvectors Planar (2x2) systems |
Book: Sections 8.4, 9.1, 9.2 |
Book (Sect. 8.4): 13, 31, 37 (Sect. 9.2): 5, 11, 27, 33, 39, 45 Due Thursday, 11/18 |
|
11/15-11/18 |
Phase plane portraits Higher dimensional systems |
Book: Sections 9.3, 9.4 Manual: Chaper 12 (pages 181-193) |
Book (Sect. 9.3): 12, 13, 15, 19, 23, 45 (Sect. 9.4): 7, 13, 23, 34 Due Tuesday, 11/23 |
|
11/23-12/03 |
The linearization of a nonlinear system Invariant Sets and nullclines Long-term behavior of solutions The exponential matrix |
Book: Sections 10.1, 10.2, 10.3, 10.4, 9.5 Manual: Chapter 13 |
Book (Sect. 10.1): 3, 6, 11, 14 (Sect. 10.2): 3, 7, 21 (Sect. 10.3): 1, 3, 9, 13 Due Thursday, 12/02 |