Mathematical Tools for Physics

Physics 315, University of Miami

James Nearing

This text is in PDF format, and is my attempt to provide a less expensive alternative to some of the printed books currently available for this course. If you find any mistakes or any parts that are unclear or any topics that you think I should not have omitted, please tell me.

I intend this for the undergraduate level, providing a one-semester bridge between some of the introductory math courses and the physics courses in which we expect to use the mathematics. This is the course typically called Mathematical Methods in Physics. The text itself has been expanded so that it now contains far more than a one semester course.

The text is available as a single file to download and save, or as the separate chapters. The advantage of the single file is that the internal hyperlinks will take you anywhere in the book, while the internal links in the separate chapters are confined to that chapter. The single file contains a full index (also linked).

In the body of the text, the equation references are linked, so that clicking on the reference will take you to that equation. The index is also linked, and there are a few links to web sites within the text. If you want to read this on the screen there are two formats. The first is for a smaller screen and is formatted so that the page is wider than it is tall. On a tablet, rotate it to landscape mode. The format for a large monitor is designed with small margins, so that you can more easily use a two-page display.

The link to Example Solutions  below contains solutions to about 20% of the problems in the text.

The printed and bound version of this book is available from Dover Publications, and links to a couple of sources appear below. Though it lacks the hyperlinks of the pdfs, people seem to prefer the printed page.

Complete Text, formatted
for a smaller screen (pdf)
Mathematical Tools for Physics
Dover Publications
Amazon Books
Example Solutions
Complete Text formatted for
a larger screen or for
a two page display (pdf).
Mathematical Tools for Physics

Nearing, home page
OR as separate chapters:
 1 Basic Stuff 10 Partial Differential Equations
 2 Infinite Series 11 Numerical Analysis
 3 Complex Algebra 12 Tensors
 4 Ordinary Differential Equations 13 Vector Calculus II
 5 Fourier Series 14 Complex Variables
 6 Vector Spaces 15 Fourier Analysis
 7 Operators and Matrices 16 Calculus of Variations
 8 Multivariable Calculus 17 Densities, Distributions
 9 Vector Calculus I  
Fourier Animations
Power Series Animations
Drumhead Oscillations
Group Velocity

Mechanics Text by Nearing: Mechanics (draft)
Online Text by Ed Connell: Abstract and Linear Algebra
Online Text by Sean Mauch: Applied Math
Online Books: U Penn
Textbooks etc. Mathematics
Textbooks etc. Science et al.

UMiami Physics Dept o   University of Miami