Differential Equations Schedule | ||||||

rev. 1/22/2008 | ||||||

week | topics… | read… | due in class | |||

1 | 22-Jan | Tu | What's a DE? What's a solution? Some Modeling. Separable Equations. |
1.1, pp. 1-8 1.2, pp. 10-28 |
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24-Jan | Th | More separable equations. Slope fields. Software tools. |
1.3, pp. 36-43 | 1.2 ## 2, 3, 6, 7, 10, 26 Also, "problem 1" |
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2 | 29-Jan | Tu | Euler's method for numerical
solutions. Existence and Uniqueness. |
1.4, 1.5 | ||

31-Jan | Th | More existence and uniqueness:
extending solutions; continuous dependence on initial conditions and
parameters. Autonomous equations. Equlibria, attracting or otherwise. Phase lines. |
1.6 | |||

3 | 5-Feb | Tu | First-order linear equations (formula handout). Homogeneous equations. | 1.8 | ||

7-Feb | Th | First-order linear equations:
linear model with general and particular solutions; exact equations and
integrating factors. More modeling (logistic model). |
1.9; rest of 1.1, 1.2 | |||

4 | 12-Feb | Tu | Systems of equations | 2.1 | ||

14-Feb | Th | Vector fields in the phase plane: sources, sinks, periodic solutions, attractors | 2.2 | |||

5 | 19-Feb | Tu | Analytic methods: Decoupled and partly decoupled systems, substitutions in systems, conserved or monotone quantities | 2.3 | ||

21-Feb | Th | Euler's method for systems | 2.4 | exam about now | ||

6 | 26-Feb | Tu | Linear systems. Geometry and eigenvalues. |
3.1-3.2 | ||

28-Feb | Th | Straight-line solutions. Geometry of systems with two eigenvalues. |
3.3 | |||

7 | 4-Mar | Tu | What if the eigenvalues are
complex? "Undetermined coefficients." Zero eigenvalues and repeated eigenvalues. |
3.4 | ||

6-Mar | Th | Higher-order linear equations (not sytems) with constant coefficients | 3.5, 3.6 | |||

Spring Break | ||||||

8 | 18-Mar | Tu | (Schedule from here on is
speculative) Traces and determinants again. Examples of linearization. |
3.6, 3.7, 3.8 | ||

20-Mar | Th | Higher-dimensional systems; first example from chapter 4 | ||||

9 | 25-Mar | Tu | Chapter 4: systems with forcing terms | 4.1 | ||

27-Mar | Th | More systems with forcing terms | 4.2 | exam about now | ||

10 | 1-Apr | Tu | Chapter 5? More likely, skip to Chapter 6, numerical methods | Ch. 6 | ||

3-Apr | Th | |||||

11 | 8-Apr | Tu | Laplace transforms: example of solving and equation; example involving convolutions | Part of Ch. 7 | ||

10-Apr | Th | |||||

12 | 15-Apr | Tu | Dynamic systems: bifurcations and all that | Ch. 8 and excursions | ||

17-Apr | Th | |||||

13 | 22-Apr | Tu | Auction examples? | |||

24-Apr | Th | Kepler orbits: solution of r''=r/(|r|^3) | ||||

14 | 29-Apr | Tu | ||||

1-May | Th | Party / picture | ||||

Final exam |