| Lec. | Date | Sec./pages covered | Topics |
|---|---|---|---|
| 1 | 1/12 | Sec. 1.2; p.18-22 | Definitions, direction fields. Linear ODEs of first order: homogeneous case |
| 2 | 1/14 | pp. 22-29 | Linear ODEs of first order: non-homogeneous case. Existence and uniqueness of solutions, applications |
| - | 1/19 | - MLK Day - | |
| 3 | 1/21 | Sec. 2.4; Ex.9 p.61 | Separable and homogeneous equations. |
| 4 | 1/26 | Sec. 2.5 | Exact equations and integrating factors. |
| 5 | 1/28 | Sec. 3.2, 3.3 | Linear dependence/independence of functions. General solution of a linear homogeneous equation. |
| 6 | 2/2 | Sec.3.4: p.91-96 | Review: complex numbers, circular and hyperbolic functions. Homogeneous equations with constant coefficients: order 2. |
| 7 | 2/4 | Sec.3.4: p.97-107 | Homogeneous equations with constant coefficients: higher order, the case of repeated roots, stability. |
| 8 | 2/9 | p.115 Ex.8; Sec.3.6 p.117-120 |
An application: pendulum. Cauchy-Euler equations: x>0. |
| 9 | 2/11 | Sec.3.6 p.121-125 p.132 Ex.7 |
Cauchy-Euler equations: x<0, reduction to a constant-coefficien equation. Homogeneous equations with non-constant coefficients: reduction of order. |
| 10 | 2/16 | Review | |
| 11 | 2/18 | Exam 1 | |
| 12 | 2/23 | Exam solutions, Sec.3.7: p.133-136 |
Solutions of nonhomogeneous linear equations -- general statements. |
| 13 | 2/25 | Sec.3.7: p.136-144 | The method of undetermined coefficients, variation of parameters. |
| 14 | 3/1 | Sec.3.8: p.149-151 Sec.3.9: p.157, 160-162 |
An application: forced oscillation. Systems of linear equations: definition, existence and uniqueness, reduction to a first-order system. |
| 15 | 3/3 | Sec.3.9: p.162-166 | Systems of linear equations: solution by elimination. |
| 16 | 3/8 | p.170 Ex.9 Sec 4.2: p.176-178 |
Motion of a charged particle in a uniform magnetic field. Series - review. |
| 17 | 3/10 | Sec.4.2: p.178-189 | Power series, Taylor series - review. Power series solution of differential equations. |
| - | 15-21 | - Spring Break - | |
| 18 | 3/22 | Sec.4.2: p.186-189 | Power series solution of differential equations (cont.) |
| 19 | 3/24 | Sec. 4.3 | The method of Frobenius. |
| 20 | 3/29 | Sec. 4.4, 4.5, 4.6 | Legendre functions, Gamma function, Bessel functions. |
| 21 | 3/31 | Review | |
| 22 | 4/5 | Exam 2 | |
| 23 | 4/7 | p.218-222 | Exam solutions. Improper integrals - review. |
| 24 | 4/12 | Sec.5.2, 5.3 | Laplace transform: existence, calculation, properties. |
| 25 | 4/14 | Sec.5.4 Sec.5.5: p.269-271 |
Laplace transform: application to solution of DE.
Heaviside step function. |
| 26 | 4/19 | Sec.5.5: p.271-274 Sec.5.7: p.281-286 |
Discontinuous forcing function. Additional properties of Laplace transform. |
| 27 | 4/21 | Sec.5.7: p.287-288 Sec.7.2 |
Laplace transform of a periodic function. Phase plane. |
| 28 | 4/26 | Sec. 7.2 | Phase plane -- more examples. |
| 29 | 4/28 | Review |