| Lecture | Readings | Topics | Assignments | |
|---|---|---|---|---|
| 1 | 5.1, 5.2 | Course overview; Laplace transforms, introduction. | 5.2: 1, 5-8, 10;Solutions Entrance problems Entrance problems solutions |
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| 2 | 5.3, 5.4 | Laplace transforms and applications to ode. | 5.3: 1, 3b,e,f 10a,c,d; 5.4: 1a,b,d,g,h,j,l,m,q,r,s,v Hand in 5.4 1(h),(l),(m) Solutions |
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| 3 | 5.5, 5.6, 4.1, 4.2 | Dirac delta functions and Laplace transforms. | 5.5: 1a,b,g, 5a,b,d,f 5.6: 1a,c,d,e,i Hand in: 5.5: 5(f); 5.6: 1(c),(d), (e) Solutions |
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| 4 | 4.2 | Taylor series, radius of convergence. | 4.2: 1,3,9 Hand in 1(c), (j); 3(e),(l) Solutions |
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| 5 | 4.3 | Method of Frobenius. | 4.3 1, 2, 3, 6; Hand in 1(b)(n), 2(a), 6(b) Solutions |
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| 6 | 4.5, 4.6 | Method of Frobenius, continued Fully worked example from lecture | 4.3 1, 2, 3, 6; Hand in 1(b)(n), 2(a), 6(b) | |
| 7 | 4.6 continued, 7.1-2. | Bessel and Hankel functions; | 4.6: 1-3, 5-7, 12a)-d); Hand in 2, 6(a), 12(b) Solutions. |
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| 8 | 7.2--7.3 | Phase plane; phase portraits, singular points, stability. | 7.2: 1,4,5,10; 7.3: 1. Hand in 7.2: 4(b), 5(d), 10. Solutions. | |
| 9 | 7.3 | Elementary singularities; examples. | 7.3: 1, 9, 11. Hand in 9(a), (b): Solutions. | |
| 10 | 7.4 | Phase plane applications. Worked example of phase portrait analysis of a nonlinear planar system. |
7.4: 2(a)-(e), (j)-(n); Hand in 2(c) (e) Sketch a graph of the trajectories near each singular point, if you have enough information to do so. Solutions. |
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| 11 | 7.5 | Limit cycles; van der Pol equation; Exam 1 review. | 7.5 4. Hand in 4(c). Solutions. | |
| Some review problems | ||||
| 12 | October 11! | EXAM #1. | ||
| 13 | Handout [pp. 500-519], Web notes of Prof. Chan |
Regular and singular perturbation expansions. | Problem in Prof. Chan's notes; Hand this problem in. Handout: 25.8, 25.9, 25.10 Solutions. |
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| 14 | Catch up | |||
| 15; Oct. 20. | 9.6--9.10 | Introduction to vector spaces; vector spaces of functions; inner product; orthonormal bases. |
9.6: 1, 10-12, 14; 9.9: 11. 12 (b,c). Hand in 9.6: 12, 9.9:
11 Solutions |
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| 16; Oct. 25 | 17.1--17.2 | Vector spaces of functions; best approximation. | 17.2: 5(a-h), 12(all). Hand in 5 (b),(d), 12(j),(l). | |
| 17; Oct. 27. | 17.3 | Introduction to Fourier series. | 17.3: 1, 4(a,c,g,l), 8. Hand in 1, 4(a,c,g,l) Solutions |
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| 18; Nov. 1; | 17.4--17.6 | Half and quarter range expansions; Manipulating Fourier series. |
17.4 2(a-d); 17.5: 2(a,b), 17.6: 2(a--d) Hand in 17.4: 2(b,d), 17.5: 2(b), 17.6: 2(a,b,c). Solutions, 17.4 Solutions, 17.5, 17.6 |
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| 19; Nov. 3. | 17.7, 11.3 | Symmetric matrices. Sturm-Liouville theory. | 11.3: 1(a,b,e), 15(a,b); 17.7: 1(all), 8, 9(a--c) Hand in 1(c-f), 9(a-c) Solutions, 17.7 | |
| 20; Nov. 8. | 17.8 | More Sturm-Liouville theory. | 17.8: 2(a--d),4,5; Hand in 2(a,b), 4, 5 Solutions, part I Solutions, part II |
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| 21; Nov. 10. | 18.1--18.3 | Separation of variables; application of Sturm-Liouville theory. |
18.3: 6(a--h) | |
| 22; Nov. 15 | Exam II | November 15 | ||
| 23; Nov. 17. | 18.1--18.3 | Separation of variables continued; Review. |
18.3: 4 Solutions, to 18.3, 4,6 | |
| 24 | 17.9,17.10, 18.4 | Fourier integral and Fourier transform. | 17.10: 3, 4, 6(b,f,j,l), 12
Solutions 18.3: 15, 16 (b)(d), 17 (b) Hand in 18.3: 6 (b); 17.10: 6, 12 |
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| 25 | 18.4 | Fourier transform method continued. | 18.4: 6, 8, 10; 18.3: 19 Hand in 18.4, 10 and 18.3, 19 on Dec. 8 Solutions | |
| 26 | 19.1--19.2 | The wave equation. | ||
| 27 | 19.1--19.2 | The wave equation. | 19.2; 5(b),(c), 6, 8 19.4; 2(a), 7 |
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| 28 | Review |