| Lecture | Readings | Topics | Assignments |
|---|---|---|---|
| 1 | 5.1, 5.2 | Course overview; Laplace transforms, introduction. | Problems Read Entrance guide and try the problems |
| 2 | 5.3, 5.4 | Laplace transforms and applications to ode. | Problems Solutions, problem set 1 |
| 3 | 5.5, 5.6, 4.1, 4.2 | Laplace transforms and applications to ODE | Problem Set 2 |
| 4 | 4.2 | Taylor series, radius of convergence. | Problem Set 2 |
| 5 | 4.3 | Method of Frobenius. | Problem Set 2 Solutions, problem set 2 Solution to problem 7 e) in section 4.2 |
| 6 | 4.3, 4.5 (Gamma function only) | Method of Frobenius Fully worked example | Problem Set 3 |
| 7 | 4.3 and 4.6 | Method of Frobenius, Bessel functions; | |
| 8 | 4.6 | Bessel functions | Problem Set 4 |
| 9, 10/3 | 7.2--7.3 | Phase plane; phase portraits, singular points, stability. | |
| 10, 10/5 | 7.3 | Elementary singularities; examples. | |
| 11, 10/10 | 7.4 | Phase plane applications. Worked example of phase portrait analysis of a nonlinear planar system. |
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| 12, 10/12 | FIRST EXAM, IN CLASS | Review problems for exam | |
| 13, 10/17 | 7.3 | Phase portraits of linear systems, continued | |
| 14, 10/19 | 7.4 | Phase portraits of nonlinear system | |
| 15, 10/24 | 7.5 | Limit Cycles | |
| 16, 10/26 | 9.6--9.10 | Introduction to vector spaces; vector spaces of functions; inner product; orthonormal bases. |
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| 17, 10/31 | 17.1--17.2 | Vector spaces of functions; best approximation Intro to Fourier Series. Handout on Gram-Schmidt |
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| 18; 11/2 | 17.3 | Introduction to Fourier series. | |
| 19, 11/7 | 17.4--17.6 | Half and quarter range expansions; Manipulating Fourier series. |
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| 20, 11/9 | 17.7, 11.3 | Symmetric matrices. Sturm-Liouville theory. Lecture Notes for this lecture Worked example of Fourier series calculations |
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| 21, 11/14 | 17.8 | More Sturm-Liouville theory. | |
| 22, 11/16 | Exam II | November 16 | Review problems Review problem solutions, part I Review problem solutions, part II |
| 23, 11/21 | 18.1--18.3 | Separation of variables; application of Sturm-Liouville theory. |
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| 24, 11/28 | 18.1--18.3 | Separation of variables continued; Review. |
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| 25, 11/30 | 17.9,17.10, 18.4 | Fourier integral and Fourier transform. | |
| 26, 12/5 | 18.4 | Fourier transform method continued. | |
| 27, 12/7 | 19.1--19.2 | The wave equation. | |
| 28, 12/12 | 19.1--19.2 | The wave equation. |