Mathematical Handbooks

The 4th edition of Intermediate Physics for Medicine and Biology assumes mathematical knowledge through calculus. Some of our readers with a weak math background may wonder where they can look to brush up on long-forgotten facts and formulas. The obvious starting place is the textbook you learned your calculus from. (I hope you are not the type of person who sells their textbooks back to the book store at the end of the semester.) Another place is the appendices in our book, which review many mathematical topics. For those who may need a bit more help, I have the following advice.

Mathematical Handbook
for Formulas and Tables.

If you want an inexpensive, light-weight, easy-to-use reference, I suggest  Schaum's Outline: Mathematical Handbook of Formulas and Tables, 2nd Edition, by Murray Spiegel and John Liu. I use it every day, and it has most of the mathematical information you’ll ever need. The handbook has a large table of integrals, and covers trigonometric and hyperbolic functions, series expansions, Laplace transforms, Fourier analysis, Bessel functions, and Legendre polynomials. The one thing the handbook lacks is information on vector calculus in spherical and cylindrical coordinates. I recommend xeroxing Table 1 from Appendix L of our book and taping it to the inside cover of your Schuam’s Outline.

Handbook of Mathematical Functions,
by Abramowtiz and Stegun.

For those occasions when I need more extensive information, I turn to the  Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables, by Abramowitz and Stegun (cited on page 201 of our book). This classic covers many of the same topics as does Schuam’s Outline, but in much more detail. [Note: after posting this blog entry, my graduate student told me that you can download Abramowitz and Stegun online. Look at http://www.math.sfu.ca/~cbm/aands/. Apparently because this book was prepared by employees of the US government, there is no copyright issue to prevent downloading.]
 

Table of Integrals, Series, and Products,
by Gradshteyn and Ryzhik.

When you really need an integral but can’t find it anywhere else, I suggest the Table of Integrals, Series, and Products, Seventh Edition by Gradshteyn and Ryzhik. If you can’t find the integral there, you probably can’t find it anywhere. I have never used the new edition with the CD ROM, but the hardback copy I consult for my most difficult integrals is invaluable. I suggest letting the library buy this one, since you will probably only need it occasionally.