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Math 312
Topics in Applied Mathematics II
Spring 1997

• About the course

• First-day handout

• Examinations (Adobe Acrobat PDF format): first || second || third || final

• Other handouts (PostScript format)

16 January 1997

class exercise: the superposition principle

homework: introduction to the heat equation

21 January 1997

class exercise & homework: separation of variables

23 January 1997

class exercise: trigonometric identities

homework: calculating a Fourier series

28 January 1997

class exercise: more Fourier series

homework: symmetry, Fourier series, and jumps

30 January 1997

solutions to Fourier series exercise from last time

class exercise and homework: solving the heat equation with Fourier series

4 February 1997

Exam 1 from 1994

6 February 1997

Solutions to Exam 1 from 1994

13 February 1997

class exercise and homework: the heat equation with transcendental eigenvalues

18 February 1997

Class exercise and homework: introduction to Sturm-Liouville problems

20 February 1997

Homework: the heat equation on unbounded domains

25 February 1997

Class exercise: some improper integrals

Class exercise and homework: solving the heat equation on an unbounded domain by using Fourier integrals

27 February 1997

Class exercise and homework: solving the wave equation with Fourier series

4 March 1997

Class exercise: D'Alembert's method for solving the wave equation

6 March 1997

Exam 2 from 1994 and solutions
Class exercise: the wave equation on an unbounded domain

27 March 1997

Class exercise: Laplace's equation in a square
Homework: the Laplacian in polar coordinates

1 April 1997

Class exercise and homework: introduction to Bessel's equation

3 April 1997

Class exercise: more on Bessel functions
Homework: solving the wave equation on a disk

10 April 1997

Exam 3 from 1994 and solutions

22 April 1997

Class exercise: convergence of Fourier series

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