- Wednesday, Dec 8 Some review materials for the final exam are now posted under Handouts:
- A summary of the topics covered in Chapters 5 and 6 [PDF]
- A set of practice problems for the final exam [PDF] Short answers [PDF] Updated Dec 10 and 12: corrected errors in the solutions to Problems 2, 3 and 4.
Please note that, apart from pens/pencils, eraser and calculator, you may bring two letter-sized sheets (four pages) of notes into the exam. No formulas will be provided in the exam, so be sure to include in your notes the formulas/procedures that you find most difficult to remember.
- Friday, Dec 3
The final exam will take place on Tuesday, December 14, at 2pm in Barus & Holley 166.
The class on Wednesday, December 8 (1–1:50pm) will be a review session.
My office hours during reading period and exam period are as follows:
| Monday, December 6 | 1–2pm | Wilson 302 |
| Wednesday, December 8 | 2–3pm | Wilson 302 |
| Monday, December 13 | 12–2pm | Wilson 302 |
- Past announcements
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- Course outline & general information (Sep 1) [PDF]
- Classification of differential equations (§1.3, Sep 1) [PDF]
- Applications of first-order ODEs (§2.3, Sep 8) [PDF] Solution to Example 2 [PDF]; solution to Example 4(b) [PDF]
- Linear vs nonlinear & Bernoulli equations (§2.4, Sep 17) [PDF]
- Euler's method of numerical approximation (§2.7 and §8.1, Sep 24) [PDF]
- Numerical error and implicit methods: backward Euler and trapezoid (§8.1, Sep 27)
- Multistage methods: modified Euler (midpoint), improved Euler (Heun), Runge–Kutta (§8.2, §8.3, Sep 29)
- Multistep methods (§8.4, Oct 1) [PDF]
- Derivation of the 2nd- and 4th-order Adams–Bashforth and Adams–Moulton methods: derive-ab2_am2_ab4_am4.mw (Maple worksheet)
- 2nd-order Adams–Bashforth: ab2.m (Matlab) and ab2.mw (Maple)
- 4th-order Adams–Bashforth: ab4.m (Matlab) and ab4.mw (Maple)
- 2nd-order Adams–Moulton: am2.m (Matlab) and am2.mw (Maple)
- 2nd-order Adams predictor–corrector: pc2.m (Matlab) and pc2.mw (Maple)
- Fundamental solutions and the Wronskian (§3.2, Oct 15) [PDF] Solutions to §3.2 Problems 14 and 15 [PDF]
- Complex roots of the characteristic equation (§3.3, Oct 20) [PDF]
- Spring–mass systems: Free vibrations (§3.7, Oct 22) [PDF]
- Reduction of order (§3.4, Oct 25) [PDF]
- Euler equations (§3.3–3.4&5.4, Oct 27) [PDF]
- Method of undetermined coefficients (§3.5, Oct 29) [PDF]
- Variation of parameters (§3.6, Nov 1) [PDF]
- Spring–mass systems: Forced vibrations (§3.8, Nov 3) [PDF]
- Power series solutions about an ordinary point (§5.2, Nov 12) [PDF] Additional examples [PDF]
- Power series solutions about a regular singular point (§5.5, Nov 17) [PDF] Extra examples: §5.5 Problem 9 and Nov 17 class example—general formula for coefficients; (Nov 19) §5.5 Problem 5 and §5.7 Problem 5
- Laplace transform example in which partial fractions, completing the square and s-shifting are used: §6.2 Problem 22
- Laplace transform examples that involve t-shifting: solutions to selected problems from §6.3 and §6.4
- Laplace transform examples that involve convolution: solutions to selected problems from §6.6
Review materials
- Midterm 1:
- Some remarks about preparing for the exam [PDF]
- A summary of the topics in sections 2.1–2.7 and 8.1–8.3 [PDF]
- A set of practice problems [PDF] Short answers [PDF]
- The list of problems used for discussion in the review session [PDF] Short answers [PDF]
- Exam solutions [PDF]
- Midterm 2:
- A summary of the topics in Chapter 3 [PDF]
- A set of practice problems [PDF] Short answers [PDF]
- The list of problems used for discussion in the review session [PDF] Short answers [PDF]
- Exam solutions [PDF]
- Final:
- A summary of the topics covered in Chapters 5 and 6 [PDF]
- A set of practice problems for the final exam [PDF] Short answers [PDF] Updated Dec 10 and 12: corrected errors in the solutions to Problems 2, 3 and 4.
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Homework will be collected on Fridays of most weeks, except those weeks in which there is a midterm exam or Thanksgiving recess.
| Section | Problem numbers | Due dates and solutions |
|---|
| 1.3 | 1, 2, 4, 5, 6, 8, 9, 15, 22 | due Sep 10 |
| 2.1 | 5c, 6c, 14, 15, 22bc, 29a | due Sep 10 [Solutions (PDF); comments (PDF)] |
| 2.3 | 3, 16, 21a, 29 | due Sep 17 |
| 2.2 | 4, 14ac, 23 | due Sep 17 [Solutions (PDF)] |
| 2.6 | 1, 6, 14, 15 | due Sep 24 |
| 2.4 | 6, 12, 16, 30 | due Sep 24 [Solutions (PDF)] |
| 2.5 | 8, 9, 10 | due Oct 1 [Solution to Problem 28 (PDF)] |
| 2.7 | 7, 8, 10, 13, 17 | due Oct 1 |
| 8.1 | 10, 12, and use a computer program
to demonstrate the order of the error
for the backward Euler method | due Oct 1 [Solutions part 1, part 2 (PDF)] |
| 8.2 | 10, 12 | due Oct 15 |
| 8.3 | 10, 12 | due Oct 15 |
| 8.4 | 10ab, 12ab, 14, 15 | due Oct 15 [Solutions (PDF), derive-ab3_am3.mw] |
| 3.1 | 3, 10, 12, 15, 19 | due Oct 22 |
| 3.2 | 1, 5, 17, 25, 30 | due Oct 22 |
| 3.4 | 1, 11, 12, 34 | due Oct 22 [Solutions (PDF)] |
| 3.3 | 8, 17, 22 | due Oct 29 |
| 3.7 | 10, 11, 17 | due Oct 29 |
| 3.4 | 23, 26 | due Oct 29 [Solutions (PDF)] |
| 3.4 | 41, 43, 46 | due Nov 5 |
| 3.5 | 1, 4, 6, 17 | due Nov 5 |
| 3.6 | 7, 14, 17 | due Nov 5 [Solutions (PDF)] |
| 3.8 | 6, 8ab, 9 | due Nov 19 |
| 5.1 | 12, 21, 23, 24 | due Nov 19 |
| 5.2 | 11ab, 12ab, 15a | due Nov 19 |
| 5.2 | 3ab, 14ab | due Nov 19 [Solutions (PDF)] |
| 5.4 | 21 | due Dec 3 |
| 5.5 | 6, 3, 1, 2 | due Dec 3 |
| 6.1 | 5a, 6 | due Dec 3 |
| 6.2 | 1, 19 | due Dec 3 |
| 6.2 | 3, 11, 10, 16 | due Dec 3 [Solutions (PDF)] |
| 6.2 | 22 | not due [Solution] |
| 6.3 | 12, 14, 21, 22 | not due |
| 6.4 | 2, 4, 9, 13 | not due [Solutions to §6.3 and §6.4 problems] |
| 6.6 | 9, 15, 19 | not due [Solutions] |
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