Mathematical Tools for Physics
by James Nearing, Physics Dept., University of Miami 2006-11
Introduction
I wrote this text for a one semester course at the sophomore-junior level. Our experience with students taking our junior physics courses is that even if they’ve had the mathematical prerequisites, they usually need more experience using the mathematics to handle it efficiently and to possess usable intuition about the processes involved. If you’ve seen infinite series in a calculus course, you may have no idea that they’re good for anything. If you’ve taken a differential equations course, which of the scores of techniques that you’ve seen are really used a lot? The world is (at least) three dimensional so you clearly need to understand multiple integrals, but will everything be rectangular? How do you learn intuition? When you’ve finished a problem and your answer agrees with the back of the book or with your friends or even a teacher, you’re not done. The way do get an intuitive understanding of the mathematics and of the physics is to analyze your solution thoroughly. Does it make sense? There are almost always several parameters that enter the problem, so what happens to your solution when you push these parameters to their limits? In a mechanics problem, what if one mass is much larger than another? Does your solution do the right thing? In electromagnetism, if you make a couple of parameters equal to each other does it reduce everything to a simple, special case? When you’re doing a surface integral should the answer be positive or negative and does your answer agree? When you address these questions to every problem you ever solve, you do several things. First, you’ll find your own mistakes before someone else does. Second, you acquire an intuition about how the equations ought to behave and how the world that they describe ought to behave. Third, It makes all your later efforts easier because you will then have some clue about why the equations work the way they do. It reifies algebra.
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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. To return to your original position, either click on the left arrow (Previous View) at the top (or sometimes bottom), or use a keyboard shortcut [ Command<-- on Mac, Alt<-- on Windows, Control<-- on Linux ]. The table of contents and the index are also linked. There are also 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. The format for a large monitor is designed with small margins, so that you can more easily use a two-page display. If you choose to print the book and have a printer that does two-sided copy, or if you upload it to a commercial printer, there is a version with identical content, but with margins shifted for such printing and binding. It is 465 pages. This version uses a Times font so that its printed appearance is more like what people are used to, but its appearance on the screen is not as good as with the other formats. This is a corrected and slightly revised version of the original: Nov, 2006. http://ifile.it/g8b15e/jamesnearingmathematicaltoolsforphysics2006-11.rar http://rapidshare.com/files/23232422/jamesnearingmathematicaltoolsforphysics2006-11.rar http://www.4shared.com/file/38029305/997e9dcd/mathematical_tools_for_physics.html?dirPwdVerified=113293a7 http://rapidshare.com/files/243452392/jamesnearingmathematicaltoolsforphysics2006-11.rar http://www.box.net/shared/na6doil9nb
