Date   | Lecture   | Topics   | References   | Remarks   |
8/29 | 1 | Introduction (derivation of some common PDE)  | ||
9/3 | 2 | Background (calculus, topology)   | Strauss A.1, A.3  
Evans C.2, C.3 |
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9/5 | 3  | Background (convolution, distributions)  | Strauss 12.1  | |
9/8 | 4  | Laplace/Poisson (fundamental solution)  | Strauss 6.1, 7.2,  
Evans 2.2.1 |
|
9/10 | 5  | Laplace/Poisson (Green's functions)  | Strauss 7.3
Evans 2.2.4 |
Homework 1 Due  |
9/12 | 6  | Laplace/Poisson (Green's functions, mean value property)  | Strauss 7.4, 7.1  
Evans 2.2.4, 2.2.2   |
  |
9/15 | 7   | Laplace/Poisson (maximum principle, uniqueness)  | Strauss 6.1, 7.1 Evans 2.2.3 (a)   |
  |
9/17 | 8   | Heat Equation (fundamental solution)   | Strauss 2.4 Evans 2.3.1   |
Homework 2 Due   |
9/19 | 9  | Heat Equation (mean value property)   | Evans 2.3.2   |   |
9/22 | 10   | Heat Equation (maximum principle, uniqueness)   | Strauss 2.3 Evans 2.3.3   |
  |
9/24 | 11  | Wave Equation (fundamental solution in 1d)  | Strauss 2.1, 2.2 Evans 2.4.1   |
Homework 3 Due  |
9/26 | 12  | Wave Equation (solution in 3d)  | Strauss 9.1, 9.2 Evans 2.4.1  |
  |
9/29 | 13  | Wave Equation (solution in 2d) | Strauss 9.1 Evans 2.4.1, 2.4.3  |
  |
10/1 | 14  | Wave Equation (energy methods)  | Evans 2.4.3  |   |
10/3 |   | Review  |   | Homework 4 Due   |
10/6 |   | Midterm 1   |   | Midterm 1  |
10/8 | 15  | Separation of variables, Fourier series  | Strauss 1.4, 4.1, 4.2   |   |
10/10 | 16   | Separation of variables, Fourier series   | Strauss 5.1, 5.2, 5.3, 5.4  |   |
10/13 | 17   | Separation of variables, Fourier series   | Strauss 5.1, 5.2, 5.3, 5.4  |   |
10/15 | 18  | Fourier transform   | Strauss 12.3 Evans 4.3.1  |
Homework 5 Due  |
10/17 | 19  | Fourier transform   | Strauss 12.3 Evans 4.3.1  |
  |
10/20 | 20  | Fourier transform   | Strauss 12.3, 12.4 Evans 4.3.1  |
  |
10/22 | 21   | Tempered distributions   | Strauss 12.1, 12.3  | Homework 6 Due  |
10/24 | 22  | Duhamel's principle   | Strauss 3.4   |   |
10/27 | 23   | Method of characteristics  | Evans 3.2   |   |
10/29 | 24   | Method of characteristics Scalar conservation laws  |
Evans 3.2, 3.4, Strauss 14.1   |
Homework 7 Due   |
10/31 | 25  | Scalar conservation laws  | Evans 3.4, Strauss 14.1  |
  |
11/3 | 26  | Calculus of variations  | Strauss 7.1, 11.1, 14.3 Evans 8.1   |
  |
11/5 | 27  | Calculus of variations  | Strauss 7.1, 11.1, 14.3 Evans 8.1   |
  |
11/7 |   | Review   |   | Homework 8 Due  |
11/10 |   | Midterm 2   |   | Midterm 2  |
11/12 | 28   | Numerical methods   | Strauss 8.1, 8.2  |   |
11/14 | 29   | Numerical methods   | Strauss 8.3, 8.5   |   |
11/17 | 30  | Classical mechanics   |   |   |
11/19 | 31   | Quantum mechanics   | Strauss 9.4, 9.5  | Homework 9 Due  |
11/21 | 32   | Quantum mechanics   | Strauss 9.4, 9.5  |   |
11/24 | 33   | Quantum mechanics  | Strauss 10.3, 10.6  |   |
11/26 | 34   | Quantum mechanics  | Strauss 10.3, 10.6  | Homework 10 Due  |
12/1 | 35   | Electromagnetism   | Strauss 13.1  |   |
12/3 | 36  | Elementary particles   | Strauss 13.5   |   |
12/5 |   | Conclusion and review  |   |   |
12/8 |   | RRR Office hours  |   | Moffitt 102, 1–3pm Homework 11 Due   |
12/9 |   | RRR Office hours  |   | Moffitt 102, 1–3pm |
12/10 |   | RRR Office hours  |   | Moffitt 102, 1–3pm |