Differential Equations Schedule | ||||||

rev. 3/25/07 | ||||||

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

1 | 22-Jan | M | What's a DE? What's a solution? Modeling. | 1.1, pp. 1-8. | ||

24-Jan | W | Separable equations | 1.2, pp. 20-28. | 1.1 ## 10, 11, 12 | ||

26-Jan | F | Slope fields, software tools | 1.3, pp. 36-43 | mini-mini-exam 1.2 ## 2, 3, 35, 6, 7,10, 26, plus any of 5-32 |
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2 | 29-Jan | M | Euler's method for numerical solutions | 1.4 | 1.3 ## 1,2,3,5 (with HPGSolver), 15,16,17 (for class); print interesting slope field | |

31-Jan | W | Existence and Uniqueness. Extending solutions. Continuous dependence on initial conditions and parameters. | 1.5 | |||

2-Feb | F | Autonomous equations. Equlibria, attracting or otherwise. Phase lines. | 1.6 | mini-exam | ||

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

7-Feb | W | First-order linear equations: linear model with general and particular solutions; exact equations and integrating factors | 1.8, 1.9; rest of 1.1, 1.2 | |||

9-Feb | F | More modeling (logistic model) | All of 1.1 thru 1.8 | graded problem set | ||

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

14-Feb | W | More logistic equation, more systems | end of 1.1; 2.1 | graded problem set due | ||

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

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

21-Feb | W | Euler's method for systems | 2.4 | |||

23-Feb | F | Linear systems | Start chapter 3 (or Monday) | exam about now | ||

6 | 26-Feb | M | Geometry and eigenvalues | 3.1-3.2 | ||

28-Feb | W | Straight-line solutions | 3.2 | |||

2-Mar | F | More geometry of systems with two eigenvalues, hence straight-line solutions on two lines | 3.3 | |||

7 | 5-Mar | M | What if the eigenvalues are complex? | 3.4 | ||

7-Mar | W | More complex
eigenvalues "undetermined coefficients" zero and identical eigenvalues |
more 3.4 | |||

9-Mar | F | Higher-order linear equations (not sytems) with constant coefficients | 3.5, 3.6 | mini-mini-exam | ||

Spring Break | ||||||

8 | 19-Mar | M | Traces and determinants
again Substitution in the spiral case |
3.6, 3.7 | graded problem set | |

21-Mar | W | Examples of linearization | 3.7, 3.8 | mini-exam | ||

23-Mar | F | Higher-dimensional systems; first example from chapter 4 | graded problem set due | |||

9 | 26-Mar | M | Chapter 4: systems with forcing terms | 4.1 | Due: Sec. 3.8, ## 17, 18 (to turn in) | |

28-Mar | W | 4.2 | ||||

30-Mar | F | exam about now | ||||

10 | 2-Apr | M | ||||

4-Apr | W | Chapter 5? More likely, skip to Chapter 6, numerical methods | Ch. 6 | |||

6-Apr | F | |||||

11 | 9-Apr | M | ||||

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

13-Apr | F | |||||

12 | 16-Apr | M | Dynamic systems: bifurcations and all that | Ch. 8 and excursions | ||

18-Apr | W | |||||

20-Apr | F | |||||

13 | 23-Apr | M | ||||

25-Apr | W | Auction examples? | ||||

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

14 | 30-Apr | M | ||||

2-May | W | |||||

4-May | F | Party / picture | ||||

Final exam |