Date:March 10, 2002
| Lecture | Topics/Sections | Some Standard Examples/Concepts |
|---|---|---|
| Day 1
March 27 |
2.3, 2.5 | Modeling: decay, mixing, cooling, growth. Physical models and the differential equations which result. |
| Day 2
March 29 |
2.1, 2.2, 2.4 | Review derivation of solution to first order linear, and review separable equations. Mixing problems (equal rate in/out is separable; unequal rate is FOL) |
| Day 3
April 1 |
5.1, 5.2 | Review series, Taylor series, and the radius of convergence. Series solutions to first order linear or second order constant coefficient. Solve y''+y'=0 via series, and isolate fundamental solutions as S(x) and C(x). Observe that sin(x) and cos(x) are also solutions. How are S(x) and C(x) related to sin(x) and cos(x)? Leads to representation of functions by series. |
| Day 4
April 3 |
5.2 | Series solutions for the differential equations with nonconstant coefficients. Integral test for the positive series convergence and the p-series. |
| Day 5
April 5 |
5.3 | More series solutions at the ordinary point. Alternating series and error estimates. |
| Day 6
April 8 |
2.6 | Exact Differential Equations and integrating factors. |
| Day 7
April 10 |
3.1 - 3.2 | Review of second order differential equations with constant coefficient
(real roots).
|
| Day 8
April 12 |
3.3, 3.4 | Review of complex numbers, complex exponential and second order differential equations with constant coefficients (complex roots). |
| Day 9
April 15 |
3.5, 3.6 | Repeated roots, reduction of order. Method of undetermined coefficients |
| Day 10
April 17 |
3.6, 3.7 | Method of undetermined coefficients Variation of parameter |
| Day 11
April 19 |
3.8 | Applications |
| Day 12
April 22 |
4.1 | Higher order linear differentiqal equations |
| Day 13
April 24 |
4.2, 4.3 | |
| Day 14
April 26 |
4.3, 4.4 | |
| Day 15
April 29 |
7.1, 7.2, 7.3 | |
| Day 16
May 1 |
7.3, 7.4 | |
| Day 17
May 3 |
7.4, 7.5 | |
| Day 18
May 6 |
7.5 and 7.6 | |
| Day 19
May 8 |
7.6, 7.7 | |
| Day 20
May 10 |
7.7, 7.8 | |
| Day 21
May 13 |
7.8, 7.9 | |
| Day 22
May 15 |
7.9, summary | |
| Day 23
May 17 |
NO CLASS FRIDAY, WE WILL MEET IN THE X-HOUR on 5/23 |
|
| Day 24
May 20 |
10.1, 10.2 | |
| Day 25
May 22 |
10.3, 10.4 | |
| Day 26
May 24 |
||
| May 27 | Memorial Day | College Holiday |
| Day 27
May 29 |