PHYSICS 312
Introduction to mathematical physics.
Birger Bergersen

This page contains links to a html-version of material presented on transparencies in class January-April 1999. Some additional material is also included.

Not all lectures will be posted. When the material presented in class follows the text fairly closely I will only give a reference to the relevant pages in the text.

The notes will be modified from time to time to correct for typos and other errors, awkward formulations etc. Therefore, you are adviced not to make a hard copy until you actually need it.

Readers of these notes are encouraged to send comments to
birger@physics.ubc.ca


My postal address is:
Department of Physics and Astronomy
University of British Columbia
Vancouver, B.C. Canada V6T 1Z1


Telephone: (604) 822-2754

TABLE OF CONTENTS:

L0

About PHYS 312.

L1

Partial differential equations of physics.

L2

Review of ordinary differential equations.

L3

Solving differential equations with Maple.

L4

Boundary value problems for ordinary differential equations.

L5

Fourier series.

L6

Complex Fourier series. Evaluation of Fourier coefficients in Maple..

L7

Fourier integral. Examples of Fourier transforms..

L8

LRC circuit. Example of LRC circuit with periodic forcing.

L9

Dirac delta-function. LRC-circuit with non-periodic forcing

L10

Heat equation in one dimension.

L11

Separation of variables. Sturm-Liouville Problem.

L12

Convective boundary conditions.. Numerical example.

L13

Generalizations of the heat equation.

L14

Infinite and semi-infinite rods.

L15

Wave equation.

L16

Examples of solutions to wave equation.

L17

The potential equation.

L18

Laplace equation in polar coordinates.

L19

Derivation of 2 dimensional wave equation and 3 dimensional heat equation.

L20

Bessel's equation.

L21

Vibrating membrane.Vibrating membrane with Maple.

L22

Heat equation in cylindrical coordinates. Cooking a roast with Maple.

L23

Separation of variables in spherical coordinates.

L24

Legendre polynomials.Legendre polynomials with Maple.

L25

Spherical Bessel functions.

L26

A model for genetic drift.

L27

Some boundary value problems associated with diffusion.

M

Midterm exam February 1999

M

Solution to Midterm exam

MR

Midterm review problem set

FR

End of term review problem set

P1

Problem set 1.

P2

Problem set 2

P3

Problem set 3

P4

Problem set 4

P5

Problem set 5

P5

Problem set 5

PR

End of term project

R

References.

S1

Solution to problem set 1.

S2

Solution to problem set 2.

S3

Solution to problem set 3.

S4

Solution to problem set 4.

S5

Solution to problem set 5.