| Date | Topic | Reading | Assignments |
|---|---|---|---|
| Jan 27-31 | Introduction to Fourier series Even & odd expansions, sine & cosine series |
1.1 1.2 |
Homework 1 (Due Feb 5) 1.1: 1abc, 2ad, 4, 7b, 8 1.2: 1, 7, 10b |
| Feb 3-7 | Convergence of Fourier series Uniform conergence of Fourier series |
1.3 1.4 |
Homework 2 (Due Feb 12) 1.3: 1abd, 2ad, 5, 6 1.4: 1ae |
| Feb 10-14 | Operations on Fourier series The heat equation |
1.5 2.1 |
Homework 3 (Due Feb 19) 1.4: 2, 3ab, 5bc 1.5: 2, 5, 8, 9 |
| Feb 17-21 | The heat equation Steady-state & transient solutions |
2.1 2.2 |
Homework 4 (Due Feb 26) page 120: 19, 20 [use a=3] 2.1: 2, 9 2.2: 2, 6, 7 |
| Feb 24-28 | Fixed end temperatures Insulated bar |
2.3 2.4 |
Homework 5 (Due Mar 11) 2.3: 6, 8 [use a=π] 2.4: 4 [use a=π], 5, 8 2.5: 4, 5 [use a=π], 6 |
| Mar 2 | Midterm I
(in class) |
Cumulative 1.1-1.5 and 2.1-2.4 |
Practice exams from previous semesters:
Practice 1 (Solutions) Practice 2 (Solutions) Practice 3 (with solutions) Practice 4 (Solutions) Practice 5 (with solutions) |
| Mar 2-6 | Different boundary conditions | 2.5 | |
| Mar 9-13 | Convection Sturm-Liouville Problems |
2.6 2.7 |
Homework 6 (Due Mar 30) 2.6: 7, 9, 10 2.7: 1, 3abc, 7 |
| Mar 16-20 | Spring Break No classes in session |
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| Mar 23-27 | Spring Break No classes in session |
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| Mar 30 - Apr 3 | Updated Syllabus Series of eigenfunctions Fourier integral & applications to PDEs |
2.8 1.9 |
Homework 7 (Due Apr 8) 2.8: 1 1.9: 1abc, 3a 2.10: 3, 4 |
| Apr 6-10 | Semi-infinite rod
The wave equation Solution of the vibrating string problem |
2.10 3.1 3.2 |
Homework 8 (Due Apr 15) 3.2: 3, 4, 5, 7 3.3: 1, 2, 5 |
| Apr 13-17 | D'Alembert's solution The wave equation: generalizations Laplace's equation |
3.3 3.4 4.1 |
Homework 9 (Due Apr 29) 3 (Misc. exercises) pages 252-257: 4, 5, 31, 32 4.1: 2, 6 4.2: 5, 6 |
| Apr 20 | Review | ||
| Apr 22 | Midterm II
(during lecture time) |
Cumulative (with focus on material after Midterm I) 2.3-2.8, 2.10, 1.9, 3.1-3.4 |
Practice exams from previous semesters:
Practice 1 (Solutions) Practice 2 (Solutions) Practice 3 (with solutions) |
| Apr 24 | Potential in a rectangle | 4.2 | |
| Apr 27 - May 1 | Potential in a rectangle: examples Potential in unbounded regions Potential in a disk |
4.3 4.4 4.5 |
Homework 10 (Due May 6) 4.3: 1a, 2b 4.4: 4a, 5ab 4.5: 1, 4 |
| May 4-8 | Potential in a disk: examples Two-dimensional heat equation Review |
4.5 5.3 |
Homework 11 (not to be turned in; for practice only) 5.3: 5, 7abc, 10 |
| May 20 | Final Exam
8:00-10:30am (administered through Blackboard) |
Cumulative All sections included in Midterms I, II plus 4.1-4.5, 5.3 |
Practice exams from previous semesters:
Practice 1 Practice 2 Practice 3 (Solutions) |
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