Mathematical Methods in the Physical Sciences

In my school, we do not have a mathematical methods course for science, so I decided to take on a math minor to take all the classes neccesary to do physics "right." This included a class on ODEs, Fourier Series & PDEs, Linear Algebra, and Complex Variables. These classes, although helpful, cover a lot of stuff that is not quite useful for understanding physics concepts, often undermining or dampening the stuff that is actually applicable.

What makes this book so great is that it combines all the essential math concepts into one compact, clearly written reference. If I could do it all over again, I would easily rather take a two semester Math Methods course (like they do in many schools) using a book like Boas than take all these obtuse math courses. With this book, it makes it so handy to review previously learned concepts or actually learn poorly presented topics ( for a physicist anyway) in mathematics classes... (Things like Coordinate Transformations, Tensors, Special Functions & PDEs in spherical & cylindrical coordinates, Diagonilzation, the list goes on.....)

Keep this gem handy when doing homework and studying for exams, learning the math tools from this book enables you to concentrate squarely on the physics in your other textbooks... (since mathematical background information, understandably, is often cut short...)


A Nice Balance Between Procedural Math and Cookbook Physics   September 23, 2005
John Matlock (Winnemucca, NV)
22 out of 24 found this review helpful

When I was in college working to a double major in math and physics, it was as though the two fields didn't really know each other. The mathematicians were concerned with procedural processes where the mathematical techniques were asimportant, if not more so than the resulting formula. The physicists, on the other hand were concerned with using that formula to describe what's happening. Now the situation is even worse as computers have come in to allow the use of numerical techniques in many areas of physics that can be treated in a completely different by the mathematicians.

There seems to be a trend to develop math and computer science courses to be taught in the science departments. This is the course in math to be taught by the physics department. It strikes a nice balance between procedural math and cookbook physics.

This is the third edition. It has been updated based on feedback from requests. There is also additional information on the use of personal computers. She points out to students buth the usefulness and the pitfalls of computer use in most topics.


A must have for every physics student   July 26, 2005
S. A. Iqbal (Manchester, UK)
12 out of 12 found this review helpful

Well I must say the last reviewer was very harsh on Boas. I think the book satisfies the needs of most of the physical science students. In the preface of the book author already mentioned that this is a Physicists or chemists maths book. If you really need proofs look elsewhere. Having said that I must add Boas gives satisfactory explanations (if not proofs) to every derivation. Look into the Gamma function chapter. The way she introduced the Gamma function is really enlightning. Instead of just putting the definition- as usual in mathematics books- she gave a derivation of Gamma function!!! Isn't it great!


An excellent book for those who need applied mathematics.   April 23, 2007
Keith Dow (Folsom, CA USA)
12 out of 12 found this review helpful

This is an excellent book for undergraduates in science and engineering. This book is not for mathematics majors. So anyone who complains about the proofs or lack of rigor is off target. You are not the intended audience.

I include the chapter titles below since they indicate the coveraqe of the book.

1. Infinite series, power series
2. Complex numbers
3. Linear algebra
4. Partial differentiation
5. Multiple integrals
6. Vector analysis
7. Fourier series and transforms
8. Ordinary differential equations
9. Calculus of variations
10. Tensor analysis
11. Special functions
12. Series solutions of differential equations, legendre, bessel, hermite, and laguerre functions
13. Partial differential equations
14. Functions of a complex variable
15. Probability and statistics

Enjoy!


Concise Reference   March 11, 2006
Frank Carnley (Altoona PA)
10 out of 10 found this review helpful

I used this book for a one-semester, senior-level, math-physics-course. At the time of the class, I used the book for the homework problems-mostly. While in graduate school I used the book as a refresher on Laurent Series and residues. When used as a reference, I have yet to find a better text. A well written section on the calculus of variation is very useful as it is rarely taught in undergraduate math courses. To fully take advantage of Boas, I would suggest that you take a proper math course sharing the title of all 15 chapters of her text, and use Boas as a reference. If you are too impatient to study that much math, then please do not suggest this book lacks detail. Further, if you are in high school and understand that properties of orthogonally can be used to find the solutions of most separable, linear-PDEs then there is no need to study this book (another reviewer suggested the topics were written at a high school level).

I would suggest this text without hesitation for anyone in the physical and mathematical sciences-physics, applied math, chemistry, mechanics, acoustics, etc. Also, this book is as `cookie-cutter' as you want it to be. Just change some boundary conditions or make up some unique forcing functions and the section on PDEs becomes a lot of fun.

A great study aid, a great tool for comprehensive exams, and a great reference.