Lec. |
Date |
Topics |
Suggested Reading |
UNIT I: FIRST-ORDER DIFFERENTIAL EQUATIONS |
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| #0 | Feb 3 (T) | (recitation) natural growth models, separable equations | EP 1.1, 1.4; Notes D |
| #1 | Feb 4 (W) | direction fields, existence and uniqueness of solutions (notes) | EP 1.2, 1.3; Notes G.1-2 |
| #2 | Feb 6 (F) | numerical methods (notes) | EP 6.1, 6.2 |
| #3 | Feb 9 (M) | linear first-order ODEs, integrating factors, models (notes) | EP 1.5 |
| #4 | Feb 11 (W) | linear first-order ODEs continued: models and change of variables (notes) | EP 1.6 |
| #5 | Feb 13 (F) | complex numbers, complex exponentials (notes) | Notes C.1-3 |
| #6 | Feb 17 (T) | more about complex exponentials, roots of unity (notes) | Notes C.4, IR.6 |
| #7 | Feb 18 (W) | linear system response to exponential and sinusoidal input (notes) |
Notes IR.1-3, 5 |
| #8 | Feb 20 (F) | autonomous equations, the phase line, stability (notes) | EP 1.7, 7.1 |
| #9 | Feb 23 (M) | review, linear vs nonlinear (notes) | |
| #10 | Feb 25 (W) | HOUR EXAM I | |
UNIT II: SECOND-ORDER LINEAR EQUATIONS |
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| #11 | Feb 27 (F) | second-order ODEs of the form y''+ay'+by=0 (notes) | EP 2.1 (skip Theorems 2, 3), 2.3 (p.129-132) |
| #12 | Mar 2 (M) | damping, complex roots (notes) | EP 2.3, 2.4 |
| #13 | Mar 4 (W) | main theorems about linear second-order ODEs (notes) | EP 2.1 (Theorems 1, 2, 4) |
| #14 | Mar 6 (F) | particular solutions to inhomogeneous equations: exponential response formula (notes) | Notes S, O.1, 2, 4; EP 2.6 |
| #15 | Mar 9 (M) | undetermined coefficients (notes) | EP 2.5 (pp. 148-157) |
| #16 | Mar 11 (W) | frequency response (notes) | EP 2.7 |
| #17 | Mar 13 (F) | frequency response continued, applications (notes - Warning: A square root is missing in the last expression of A(omega) at the bottom of page 1.) |
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| #18 | Mar 16 (M) | review | |
| #19 | Mar 18 (W) | HOUR EXAM II | |
UNIT III: FOURIER SERIES, DIRAC DELTA FUNCTION, AND LAPLACE TRANSFORM |
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| #20 | Mar 20 (F) | introduction to Fourier series (notes) | EP 8.1 |
| #21 | Mar 30 (M) | operations on Fourier series (notes) | EP 8.2, 8.3 |
| #22 | Apr 1 (W) | Fourier series solutions to ODEs (notes) | EP 8.3, 8.4 |
| #23 | Apr 3 (F) | convergence of Fourier series (notes) | Notes H |
| #24 | Apr 6 (M) | step and delta functions, step and impulse responses (notes) | Notes IR.4; EP 4.6 (p.316-7, 320) |
| #25 | Apr 8 (W) | convolution and fundamental solutions (notes) | Notes IR.1, CG.3, 4 |
| #26 | Apr 10 (F) | Laplace transform I: basic properties (notes) | EP 4.1; Notes H |
| #27 | Apr 13 (M) | Laplace transform II: solving ODEs (notes) | EP 4.2, 4.3 |
| #28 | Apr 15 (W) | Laplace transform III: convolution, weight functions (notes) | EP 4.4 |
| #29 | Apr 17 (F) | Laplace transform IV: pole diagram (notes) | |
| #30 | Apr 22 (W) | review (notes) | |
| #31 | Apr 24 (F) | HOUR EXAM III | |
UNIT IV: FIRST-ORDER SYSTEMS |
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| #32 | Apr 27 (M) | linear systems, matrix notation (notes) | EP 5.1-5.3; Notes LS.1 |
| #33 | Apr 29 (W) | eigenvalues and eigenvectors (notes) | EP 5.4; Notes LS.2 |
| #34 | May 1 (F) | complex eigenvalues, repeated eigenvalues (notes) | Notes LS.3-4; EP 5.4, 5.6 (up to p.398) |
| #35 | May 4 (M) | fundamental matrices, the exponential matrix (notes) | Notes LS.6; EP 5.7 |
| #36 | May 6 (W) | inhomogeneous systems, variation of parameters (notes) | Notes LS.5-6; EP 5.8 |
| #37 | May 8 (F) | nonlinear systems (notes) | EP 7.2, 7.3 |
| #38 | May 11 (M) | examples of nonlinear systems (notes - updated May 12 with a picture included) |
EP 7.4, 7.5 |
| #39 | May 13 (W) | nonlinear systems: limit cycles, strange attractors (notes) | |
May 20 (W) |
THREE-HOUR COMPREHENSIVE FINAL EXAM (9:00-12:00, Johnson upstairs) |