The schedule below is tentative and will be updated
as the course progresses. Homework is due on Fridays
at the end of class. Unless otherwise indicated, the problem numbers are
the same for old and new editions of the book.
|
|
|
|
|
| Mon., Jan. 7 | 1.1, 1.2 | Introduction to differential equations and mathematical modeling,
integrals as general and particular solutions |
|
| Wed., Jan. 9 | 1.3 | Slope fields and solution curves, existence and uniqueness theorem | |
| Fri., Jan. 11 | 1.4 | Separable ODEs and applications | |
| Mon., Jan. 14 | 1.5 | Linear first-order ODEs | |
| Wed., Jan. 16 | 1.5, 1.6 | Applications of linear first order ODEs, substitution methods | |
| Fri., Jan. 18 | 1.6 | Substitution methods (cont'd) | HW#1 due:
1.1: 10, 21, 25, 42 1.2: 7, 16 1.3: 11, 18, 23*, 26* 1.4: 6, 15, 25, 44, 49 * Use this or similar programs to plot the slope fields |
| Mon., Jan. 21 | No class (MLK day) | ||
| Wed., Jan. 23 | 2.4 | Numerical approximation: Euler method | |
| Fri., Jan. 25 | 2.5, 2.6 | Modified Euler and Runge-Kutta methods | HW#2 due:
1.5: 10, 19, 24, 26, 37, 38 1.6: 4, 14, 16, 21, 29, 36, 56, 59, 60 |
| Mon., Jan. 28 | 3.1 | Second-order linear ODEs | |
| Wed., Jan. 30 | 3.1, 3.3 | Second-order linear ODEs (cont'd), complex roots | |
| Fri., Feb. 1 | 3.2 | Higher-order linear ODEs: general solution | HW#3 due:
2.4: 3, 7, 10 2.5: 3, 7, 10 2.6: 3, 7, 10 |
| Mon., Feb. 4 | 3.3 | Homogeneous equations with constant coefficients | |
| Wed., Feb. 6 | 3.4 | Mechanical vibrations | |
| Fri., Feb. 8 | Review | HW#4 due:
3.1: 10, 15, 34, 39, 51, 54 3.2: 4, 6, 37, 38, 44 3.3: 14, 26, 31, 32, 41 |
|
| Mon., Feb. 11 | Exam 1 (up to 3.3) | ||
| Wed., Feb. 13 | 3.5 | Nonhomogeneous equations: method of undetermined coefficients | |
| Fri., Feb. 15 | 3.5 | Undetermined coefficients (cont'd), variation of parameters | HW#5 due:
3.4: 15, 17, 21, 24, 26, 27, 29, 30, 32, 33 |
| Mon., Feb. 18 | 3.5 | Variation of parameters (cont'd) | |
| Wed., Feb. 20 | 3.6, 3.7 | Forced oscillations and resonance, analogy with electrical curcuits | |
| Fri., Feb. 22 | 4.1 | First-order systems and applications | HW#6 due:
3.5: 5, 7, 8, 11, 16, 20, 44, 50, 53, 55, 58, 61 |
| Mon., Feb. 25 | 5.1 | Matrices and linear systems | |
| Wed., Feb. 27 | 5.1 | Matrices and linear systems (cont'd) | |
| Fri., Feb. 29 | 5.2 | Eigenvalues and eigenvectors, distinct eigenvalues | HW#7 due:
3.6: 2, 5, 6, 11, 12, 16, 17, 25, 26, 27 4.1: 4, 8, 11, 12, 21 (use pplane to plot the direction field for problems 11 and 12) |
| Mon., Mar. 3 | 5.2, 5.4 | Complex and repeated eigenvalues | |
| Wed., Mar. 5 | 5.5 | Matrix exponentials and linear systems | |
| Fri., Mar. 7 | 5.6 | Nonhomogeneous linear systems | HW#8 due:
5.1: 5, 6, 7, 20, 28 solve the hwk problems in the supplementary notes 5.2: 4, 9, 16 (use pplane to plot the phase portraits), 18, 23 |
| Mar. 9-16 | No classes - spring break | ||
| Mon., Mar. 17 | 6.1 | Stability and phase plane analysis | |
| Wed., Mar. 19 | 6.2 | Linear and almost linear systems | |
| Fri., Mar. 21 | Review | HW#9 due:
5.4: 3, 4, 8, 10 5.5: 7, 10, 15, 31, 32 5.6: 10, 14, 25, 27, 31 |
|
| Mon., Mar. 24 | Exam 2 (3.4-5.6) | ||
| Wed., Mar. 26 | 6.3 | Predator-prey and competition models | |
| Fri., Mar. 28 | 7.1 | Laplace transform and its inverse | HW#10 due:
6.1: 14, 15, 24, 26 6.2: 3, 5, 7, 11, 13, 30, 32, 33, 35, 37, 38 Use pplane to plot the phase portraits where needed. |
| Mon., Mar. 31 | 7.2 | Solution of initial value problems via Laplace transform | |
| Wed., Apr. 2 | 7.3 | Partial fractions and translation | |
| Fri., Apr. 4 | 7.4 | Derivatives, integrals and products of transforms | HW#11 due:
6.3: 2, 8, 9, 10, 14, 15, 16, 17, 33 7.1: 5, 8, 10, 15, 19, 39, 40 |
| Mon., Apr. 7 | 7.5 | Periodic and piecewise continuous input functions | |
| Wed., Apr. 9 | 7.6 | Impulses and Delta functions | |
| Fri., Apr. 11 | 9.3 | Fourier sine and cosine series | HW#12 due:
7.2: 4, 7, 16, 28, 31, 36 7.3: 11, 16, 21, 27, 35 7.4: 13, 17, 22, 27, 31 |
| Mon., Apr. 14 | 9.5 | Heat conduction and separation of variables | |
| Wed., Apr. 16 | Review and catch up | ||
| Fri., Apr. 18 | Review, take-home Exam 3 given | HW#13 due:
7.5: 7, 12, 17, 26, 27, 32, 42 7.6: 2, 7, 12, 14, 15 9.5: 10, 11, 17, 20 |
|
| Friday, Apr. 25, 11 am | Take-home Exam 3 (covers 6.1-6.3, 7.1-7.6,
9.3, 9.5)
due in 611 Thackeray |