| Spring 2021 MAT 308: Differential Equations with Linear Algebra | ||
| Schedule | MW 4:25-5:45pm Javits 109 | |
| Instructor | Robert Hough | |
| Office hours | F 9-11am in Math Tower 4-118, W 6-7pm in Math Learning Center | |
| TA | Blythe Davis | |
| Recitations | Th 4:45-5:40pm in Engineering 145 | |
| Description | Linear algebra: determinants, eigenvalues and eigenvectors, diagonalization. Differential equations; existence and uniqueness of solutions. First- and second-order equations; linear versus nonlinear equations. Systems of linear equations. Laplace transform. Applications to physics. More theoretical and intensive than MAT 303, this course is primarily intended for math majors. Together with MAT 307, it forms a 2-semester sequence covering the same material as the 3-semester sequence of MAT 205, MAT 211 and MAT 305. May not be taken for credit in addition to MAT 303, MAT 305 or AMS 361. | |
| Prerequisites | MAT 307 or MAT 125 or 211 | |
| Textbook | Williamson and Trotter. Multivariable Mathematics. Pearson Education (2004). | |
| Homework | Weekly problem sets will be assigned, and collected in class on Monday. Late homework is not accepted, but under documented extenuating circumstances the grade may be dropped. Your lowest homework grade will be dropped at the end of the class. | |
| Grading | Homework: 20%, Midterm I: 20%, Midterm II: 20%, Final: 40%. | |
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Syllabus/schedule (subject to change)
| Week 1. | 1st order ODE, separation of variables, linear equations | 10.1-10.3 | HW 1. p.466 #1, 4, 8, 17, 18, p.478 #4, 6, 14, 26, p. 487 #6, 7, 18, 19 |
| Week 2. | Linear maps, Euclidean spaces, vector spaces, linear maps | 3.1-3.3 | HW 2. p.111 #17, 18, 20, 33, p.118 #14, 15, 22, 33, 34, p. 125 #7, 8, 34 |
| Week 3. | Image, null space, coordinates, dimension | 3.4-3.6 | HW 3. p.130 #7, 8, 19, 20, 22, p.137 #15, 17, 18, 32, 41, p.142 #2, 3, 9, p.148 #11, 13, 14, p.154 #6, 7, 8, 18, 19 |
| Week 4. | Eigenvalues, eigenvectors, inner products | 3.6-3.7 | HW 4. p.154 #16, 20, 21, 22, p.158 #9, 10, 13, 14, p.167 #5, 6, 13, 14, 16, p.171 #3, 4, 5, 7, 8 |
| Week 5. | Midterm 1 Practice midterm, Practice midterm solutions, Midterm 1, Midterm 1 solutions | ||
| Week 6. | Differential operators, complex solutions, higher order equations, non-homogeneous equations | 11.1-11.2 | HW 5. p.498 #7, 21, 33, 40, p.506 #12, 16, 34, 35, p.512 #8, 24, 42, 51 |
| Week 7. | Laplace transform, convolution | 11.2-11.4 | HW 6. p.520 #18, 30, 43, 45, p.528 #4, 11, 15, 31, p.537 #12, 14, 31, 34 |
| Week 8. | Vector fields, linear systems | 11.5-11.6 | HW 7. p.547 #1, 3, 11, 18, 23, 24, p.552 #6, 11, 17, 22, p.557 #4, 8, 17, 18 |
| Week 9. | Sequences and series of normed vectors, matrix exponential | 12.1-12.2 | HW 8. p.578 #5, 13, 18, 25, 32, p.584 #5, 6, 7, 8, p.592 #2, 6, 8, 12, 18, 28 |
| Week 10. | Jordan canonical form, matrix exponential | 13.1-13.2 | HW 9. p.602 #6, 15, 16, 24, 25, 27, p.612 #10, 11, 16, 17, 18, 21 |
| Week 11. | Midterm 2 Practice midterm 2, Practice midterm 2 solutions, Midterm 2, Midterm 2 solutions | ||
| Week 12. | Non-homogeneous linear equations, power series solutions | 13.4 | HW 10. p.624 #10, 11, 13, p.630 #12, 17, 21, p.636 #5, 9, 12, p.639 #1, 5, 10 |
| Week 13. | Equilibrium and stability | 14.6-14.7 | HW 11. p.644 #3, 6, 13, 18, p.652 #3, 9, 13, 19, p.657 #5, 6, 8, 9 |
| Week 14. | Final exam review | HW 12. p.663 #45, p.670 #28, p.673 #21, p.681 #6, 9, 18, 42, p.687 #3, 4, 7 | HW 13. p.712 #1, 2, 5, 22, 23, 29, p.720 #2, 3, 7, 8, 12, 24, 25, p.727 #8, 3, 5, 15, 23, 27, p.731 #5, 6, 7, 9 |
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