This is a list of the lectures we had so far, with the homework set.
All section numbers are from Boyce and DiPrima, unless stated otherwise. The exercises marked by a star (*) are what I would call "interesting" (usually, but not always, more difficult than the average).
| N | Date | Homework exercises |
|---|---|---|
| 1 | Jan 18 | Read Chapter 1, Section 2.1 (p.24) 8, 11*; (p.10) 27, 31; (p.39) 7-12, 16-20, 38* |
| 2 | Jan 20 | Read Sections 2.2, 2.6 (p.47) 2, 4, 6, 8, 10, 12, 14, 16; (p.99) 2, 4, 6, 8, 14, 17, 18 |
| 3 | Jan 25 | 2.6: 23 Braun 1.3 1, 2, 7 |
| 4 | Jan 27 | read Braun 1.10, prove |a+b|<=|a|+|b| and same for integrals |
| 5 | Feb 1 | read Braun 1.10, prove properties of Lipschitz functions and uniqueness for DEs with Lipschitz right-hand side |
| 6 | Feb 8 | Braun 1.10: 5, 6, 7, 12, 16, 19 Ex.16c has a misprint. Should be 1/(2a), not (1/2)a. |
| 7 | Feb 10 | Braun 2.1: 9, 10*, 13, 16, 17 |
| 8 | Feb 15 | no homework -- prepare for the exam |
| 9 | Feb 17 | -- exam 1 -- |
| 10 | Feb 22 | BDi, p.190: 7, 9, 11, 12, 13, 15, 28-31 |
| 11 | Feb 24 | BDi, p.184: 7-18 |
| 12 | Mar 1 | BDi, p.204: 15, 19, 20, 26 BDi, p.214 6, 12, 13, 17 |
| 13 | Mar 3 | bonus problem:
for what value(s) of b will the solution of {x''+bx'+9x=0, x(0)=90, x'(0)=-810} remain positive for all t? |
| 14 | Mar 8 | 7.2 all |
| 15 | Mar 10 | 7.3 6-24 |
| 16 | Mar 22 | 7.4 6, 7, 8; 7.5 1,3,5,6,12 |
| 17 | Mar 24 | 7.5 24-27 |
| 18 | Mar 29 | 7.6 1-6, 13-20 |
| 19 | Mar 31 | exam 2 |
| 20 | Apr 5 | 7.7 3, 5, 7, 13, 15 |
| 21 | Apr 7 | 7.8 2, 5, 6; 7.9 1, 5, 14, 15, 16 |
| 22 | Apr 12 | 9.1 1-12abc, 17, 20, 21 |
| 23 | Apr 14 | 9.2 1-4, 5-10a (here is a nice plot of trajectories from question 19) |
| 24 | Apr 19 | 9.3 5-15abc, 17, 24, 25, 26 |
| 23 | Apr 21 | -- quiz 3 -- (here is a sketch of the phase plane) |
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