Date

Topic(s)

1

1/26

Introductory class meeting; Review of ODEs

2

1/28

Review of ODEs

3

1/30

Boundary value problems for ODEs

4

2/2

Boundary value problems for ODEs; singular BVPs

5

2/4

Fourier series

6

2/6

Fourier series

7

2/9

Fourier series

8

2/11

Convergence of Fourier series

9

2/13

Fourier integral

10

2/16

Fourier integral

11

2/18

Complex Fourier series

12

2/20

Fourier series and ODEs

13

2/23

Heat equation and the product method

14

2/25

Heat equation and the product method

15

2/27

Heat equation and the product method

16

3/2

Sturm-Liouville problems

17

3/4

Expansion in series of eigenfunctions

18

3/6

Heat equation in unbounded region: semi-infinite case

19

3/9

Heat equation in unbounded region: infinite case

20

3/11

Catch-up class

21

3/13

Midterm Exam

22

3/16

Wave equation and the product method

23

3/18

Wave equation and the product method

24

3/20

Wave equation and the D’Alembert’s solution

25

3/23

Wave equation in unbounded regions

26

3/25

Potential equation in a rectangular region

27

3/27

Potential equation in a disk

28

4/8

Potential equation in unbounded regions

29

4/10

Harmonic functions

30

4/13

Classification of second-order partial differential equations

31

4/15

Higher-dimensional wave equation

32

4/17

Higher-dimensional wave equation

33

4/20

Vibrations of a membrane

34

4/22

Potential problem in spherical coordinates

35

4/24

Legendre polynomials

36

4/27

Laplace transform solutions

37

4/29

Fourier transform solutions

38

5/1

Numerical methods

39

5/4

Numerical and Monte-Carlo methods

40

5/6

Catch-Up Class

41

5/8

Research project presentations

42

5/11

Research project presentations

5/20

Final exam (2:00 - 4:30)