A Set of Appendices

on

Mathematical Methods

for

Physics Students

Authors: Anne Fry BMC '90

Amy Plofker HC '90

Sarah-marie Belcastro HC '91

Advisor/Editor Lyle Roelofs


Version 1.3.1 -- Spring, 1996

 

In academic year '90-'91 advanced physics students, 2 from HC and 1 from BMC, wrote this set of 'Math Appendices' with a bit of assistance and direction from me. They undertook this project because they felt that something of the sort would have been helpful to them in their physics courses.

 

The result of their work is this 90-page document covering useful mathematical background for physics students at all undergraduate levels. It has since been edited and revised periodically. (Dan Fromowitz, HC '95, provided a careful proofreading.) New sections on converting sums to integrals, the binomial expansion, integration tricks for gaussion and exponential integrals and converting between the MKS and CGS unit systems have recently been added.

The booklet is available at the bookstores of Haverford and Bryn Mawr Colleges for a very modest price. As of Spring '01 it is also available on the web, with individual chapters downloadable as .pdf's. Scroll down for a table of contacts from which you can select chapters for downloading.

If you use these materials, I would be interested in your comments and suggestions, and if you wish to contribute a section to future editions I would be happy to discuss the possibility with you.

Lyle Roelofs,
Physics Department
Haverford College
610-896-1201
LROELOFS@HAVERFORD.EDU


TABLE OF CONTENTS
(Click on a chapter to download in the form of a .pdf file)

Trigonometric Identities ..................................................................................................1

Matrices........................................................................................................................7

Determinants............................................................................................................... 10

Row Reduction............................................................................................................ 13

Eigenvalues and Eigenvectors......................................................................................... 17

Differentiation and the Chain Rule.................................................................................. 23

Intro To Differential Equations....................................................................................... 25

Partial Differentiation and Wave Equations....................................................................... 36

Introduction to Integration............................................................................................. 38

L'Hopital's Rule.......................................................................................................... 46

Mathematical Proofs by Induction................................................................................... 49

Taylor Series Expansions and Approximations.................................................................... 51

Fourier Analysis and Transforms...................................................................................... 58

Spherical and Cylincrical Coordinate Systems..................................................................... 70

Definitions/Notation...................................................................................................... 73

Notation for General Relativity and Other Advanced Topics................................................... 75

Converting Sums to Integrals.......................................................................................... 78

Notes on Binomial Expansions and Approximations*........................................................... 80

A Brief Discussion of Unit Systems.................................................................................. 84

Useful References........................................................................................................... 88

.Index.......................................................................................................................... 90

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*Adapted from notes written by Charles Holbrow and J.N. Lloyd, in use at Colgate University