Week | Topic | Reading | Homework (ANSWERS at back of book) | Lecture Notes |
---|---|---|---|---|
January 11 | I. Introduction: what is a DE, order, linear and nonlinear, solutions, direction fields. II. First Order Equations: solution of linear ODE, separable equations, integrating factors. |
Chap. 1, 2.1-2.2. | 1.1: 5, 9, 13, 15-20, 21, 23
1.3: 1, 3, 5, 7, 11, 17, 19 2.1: 7, 11, 15, 17, 19, 23, 31, 33 2.2: 7, 17, 19, 21, 25, 27, 30, 31, 33 |
Lecture 1
Lecture 2 Lecture 3 Lecture 4 and bonus examples |
January 19 | II. First Order Equations: integrating factors, modeling and applications, linear vs nonlinear equations / existence & uniqueness, autonomous equations & population dynamics | 2.3 - 2.5, 2.8. |
2.3: 5, 9, 13, 27, 29
2.4: 5, 11, 13, 25, 27, 29 2.5: 5, 7, 13, 15, 17, 19, 21, 23 Enrichment problems, not required: The Brachistochrone: 2.3.32 More bifurcations: 2.5.25, 27 |
Lecture 5
Lecture 6 Lecture 7 Bead on a hoop: setup |
January 25 | II. First Order Equations: Exact equations & integrating factors, homogeneous equations | 2.6, 3.1 - 3.2 |
2.6: 7, 11, 15, 21, 27, 29
3.1: 5, 7, 15, 19, 21,23, 25 3.2: 9, 13, 15 Enrichment problems, not required: Exact equations: 3.2.41, 43 |
Lecture 8
Lecture 9 Lecture 10 Lecture 11 |
February 1 | III. Second order linear equations: The Wronskian, characteristic equations, real, complex, an repeated roots, reduction of order. | 3.2 - 3.4 |
3.2: 15, 17, 28, 31
3.3: 9, 17, 19, 21, 25 3.4: 9, 11, 13, 15, 23, 27, 37, 38 Enrichment problems, not required: Euler equations: 3.4.34, 35 Try also the substitution y(t)=t^{r}, solve for r, then write down the general solution. This is the usual sub for Euler eqs. |
Lecture 12
Lecture 13 Lecture 14 Lecture 15 |
February 8 | III. Second order linear equations: vibrations, nonhomogeneous equations, method of undetermined coefficients, variation of parameters. | 3.5-3.7 |
3.5: 9, 11, 13, 14, 17, 19, 25a, 27a, 29, 31
3.6: 3, 7, 19, 29 3.7: 3, 7, 11, 17, 20, 24 Note: 3.5.13, 14 involve hyperbolic functions. If these are new to you, see the note on hyperbolic functions in 'Documents'. |
Lecture 16
Lecture 17 Lecture 18 Lecture 19 |
February 15 |
III. Second order linear equations: forced vibrations, application: mechanical and electrical vibrations. IV. Higher order linear equations: Existence & uniqueness of solutions, solving constant-coefficient higher-order linear equations. |
3.8, 4.1, 4.2 |
3.7: 8
3.8: 9, 13, 15, 17, 18, 19, 24 4.1: 5, 9, 15, 19, 23, 27 (don't have to show #26) 4.2: 5, 9, 23, 35, 39 Enrichment problems, not required: 4.1.20, 4.2.41 Method of undetermined coefficients: 4.3.17 Variation of parameters: 4.4.13 |
Lecture 20
Lecture 21 Lecture 22 Lecture 23 |
February 22 | VI. Laplace Transform: definition, initial value problems.
MIDTERM I |
6.1, 6.2 |
6.1: 3, 9, 17, 23, 27
6.2: 7, 9, 19, 21, 23, 27, 29 Enrichment problems, not required: Gamma functions: 6.1.30, 31 |
Lecture 24
Lecture 25 Lecture 26 |
February 29 | VI. Laplace Transform: step functions, IVPs with discontinuous functions, impulse functions. | 6.3 - 6.5 |
6.3: 5, 11, 15, 17, 23, 34, 35
6.4: 9, 13, 15, 19 6.5: 9, 11, 13, 18, 23 |
Lecture 27
Lecture 28 Lecture 29 Lecture 30 |
March 7 | SPRING BREAK | |||
March 14 |
VI. Laplace Transform: Convolution integrals.
VII. Systems of first order linear equations: 2x2 matrices, linear systems of differential equations. |
6.6, 7.1-7.5 |
6.6: 1, 7, 9, 11, 17, 19, 23
7.1: 1, 7, 18, 23 7.2: 1, 9, 23 7.3: 13, 17, 21, 29 7.5: 5, 15, 27, 33 Enrichment problems, not required: The Tautochrone: 6.6.29 |
Lecture 31
Lecture 32 Lecture 33 Lecture 34 |
March 21 | VII. Systems of first order linear equations: Linear systems of differential equations. | 7.6 - 7.9 |
7.5: 19, 20, 25
7.6: 5, 15, 21, 26, 28 7.8: 3, 9, 13, 16 7.9: 3, 5, 7, 13 Enrichment problems, not required: Variation of parameters: 7.9.15 Laplace transforms: 7.9.18 |
Lecture 36
Lecture 37 Lecture 38 Example from Lecture 38. |
March 28 | IX. Nonlinear Systems: Nonlinear systems of equations and stability. | 9.1 - 9.4 |
9.1: 9, 11, 13, 16, 18, 20, 21
9.2: 3, 11, 13, 15, 17, 24 9.3: 3, 13, 15, 17, 23 9.4: 3, 5, 12, 17 Enrichment problems, not required: Bifurcations: 9.4.13, 15 |
Lecture 39
Lecture 40 Lecture 41 Lecture 42 |
April 4 | X. PDEs and Fourier Series: Two-point boundary value problem, Fourier Series and convergence
MIDTERM II |
10.1 - 10.3 |
10.1: 16, 19
10.2: 3, 7, 11, 15, 21, 25 10.3: 3, 7, 14, 17 Sample Mathematica script to help you plot partial sums and errors. Enrichment problems, not required: 10.1: 11, 13, 21 |
Lecture 43
Lecture 44 Lecture 45 Lectures 44/45 MATLAB demo script. |
April 11 | X. PDEs and Fourier Series: even & odd functions, separation of variables, heat conduction. | 10.4 - 10.6 |
10.4: 1, 2, 3, 4, 11, 19, 21, 23, 35, 37
10.5: 3, 5, 7, 12, 17 (omit (d)), 18 10.6: 7, 9, 13, 21, 23 |
Lecture 46
Lecture 47 Lecture 47 MATLAB demo script. Lecture 48 Lecture 49 |
April 18 | X. PDEs and Fourier Series: Wave equation, Laplace equation. | 10.7 - 10.8 |
10.7: 7 (omit (d)), 9, 11, 15, 21, 22, 23
10.8: 3, 5, 7, 9, 11, 14, 16 |
Lecture 50
Lecture 51 Lecture 52 Lecture 53 |
April 25 | X. PDEs and Fourier Series: More wave equations, d'Alembert solution of the wave equation in an infinite string.
FINAL EXAM REVIEW |
10.8 | Lecture 54
Lecture 55 Lecture 54 & 55 MATLAB demo script. |