Mathematical Methods in the Physical Sciences (英語) ハードカバー – 2004/2
Kindle 端末は必要ありません。無料 Kindle アプリのいずれかをダウンロードすると、スマートフォン、タブレットPCで Kindle 本をお読みいただけます。
Now in its third edition, Mathematical Concepts in the Physical Sciences, 3rd Edition provides a comprehensive introduction to the areas of mathematical physics. It combines all the essential math concepts into one compact, clearly written reference.This book is intended for students who have had a two-semester or three-semester introductory calculus course. Its purpose is to help students develop, in a short time, a basic competence in each of the many areas of mathematics needed in advanced courses in physics, chemistry, and engineering. Students are given sufficient depth to gain a solid foundation (this is not a recipe book). At the same time, they are not overwhelmed with detailed proofs that are more appropriate for students of mathematics. The emphasis is on mathematical methods rather than applications, but students are given some idea of how the methods will be used along with some simple applications.
“Bottom line: a good choice for a first methods course for physics majors. Serious students will want to follow this with specialized math courses in some of these topics.” (MAA Reviews, 13 November 2015)商品の説明をすべて表示する
Amazon.com で最も参考になったカスタマーレビュー (beta)
1. Infinite Series, Power series:
Great coverage of series and series representations of functions. Introduces several methods of determining convergence or divergence and techniques to convert essentially any function into a series as well as determining accuracies in representations. These are invaluable tools to solve difficult and non-analytic functions that show up everywhere in physics.
2. Complex Numbers:
A great introduction to complex analysis, starts off slow and easy and picks up the tempo with powers and roots of complex functions. This chapter is missing a discussion on the argument of a function and its meaning and kind of sweeps under the rug a few more technical things that a real complex analysis course would cover but nevertheless well done.
3. Linear Algebra:
The linear algebra section is pretty solid as well and it went a bit further than my regular linear algebra course. The placement of planes and lines is a bit awkward and doesn't really deal with matrices in the sense that you don't need to write out matrices but still an appropriate spot. It is missing some discussion on abstract vector spaces and doesn't delve too deep into the theoretical side of things; a mild discussion of group theory ends the chapter.
4. Partial Differentiation:
(No comment - did not cover)
5. Multiple Integrals; Applications of Integration:
(No comment - did not cover)
6. Vector Analysis
(No comment - did not cover)
7. Fourier Series and Transform:
A great section to learn about fourier series, usually special series are left out of real analysis courses (or covered only slightly) but in physics we use these a lot. You learn how to represent oscillatory systems as a superposition of waves, that is a series, which is a really neat idea, at least to me. My only complaint is that the fourier transform is only limited to one section and I think it's a bit more important and deserves a more in depth discussion.
8. Ordinary Differential Equations:
The bread and butter of physics. No matter what you do in physics you'll always encounter ODE's. Even if you have never seen them you might be surprised to learn that a simple equation such as F = ma is, in fact, a differential equation. It gives you the tools you need to solve the problems you will encounter and gives you discussions on how to solve special cases that occur frequently in physics. It ends with Laplace transforms (related to Fourier transforms), convolution, dirac-delta functions (mathematicians cringe at our use of the term function here), and greens functions which are a bit more advanced topics but great introduction and are definitely worth looking at.
9. Calculus of Variations:
The most important principle you take out of variations is the principle of least action. Once you start doing big boy physics you'll be calculation Lagrangians and Hamiltonians to easily solve for systems. Definitely a good mathematical approach to variations and something that will be essential throughout physics.
10. Tensor Analysis:
I didn't really cover most of the chapter, and what I did cover was in such a short amount of time that I can't possibly write a review without being biased. All I have to say though, is that for those General Relativity lovers, this is going to be your best friend.
11. Special Functions:
As the chapter title itself says, these are just formulas and quick derivations for a variety of special functions that are everywhere in physics. You don't necessarily need to study these in great detail as they only help you solve integrals, but they are of some theoretical interest. Definitely a must read chapter.
12. Series Solutions of Differential Equations; Legendre, Bessel, Hermite, and Laguerre Functions:
Solutions to partial differential equations everywhere, and I mean everywhere. Chapter 12 and 13 go hand in hand, first you learn the math stuff in chapter 12 without really knowing it's purpose and then jump into chapter 13 and find out these are solutions to partial differential equations. Just like ODE's, these are essential and found everywhere in physics. This chapter is very meaty and full of solutions to differential equations and chances are, if you ever run into a differential equation in your undergrad career the solutions are here.
13. Partial Differential Equations
See chapter 12 summary, they go hand in hand.
14. Functions of a Complex Variable
I still think this is an odd location for the second part of a complex analysis course, ideally I would have preferred right after chapter 2 or possibly 3 but nevertheless a good coverage and sum of complex analysis. You learn how to solve some really nasty integrals in a really trivial way using complex analysis.
15. Probability and Statistics
Arguably the worst of all chapters, at least in my opinion. The notation convention Boas uses isn't the most intuitive or the most frequently used and the explanation to some of the probability problems are not really helpful. Some are more naturally talented in probability, I however, am not thus found this chapter to be really annoying and confusing. Still, something worth knowing and if it works for you then let it be.
Overall this is a book I will be using for years and will keep coming back for years. It's not exactly mathematics and it's not exactly physics it fits that missing link between the two and helps clarify topics in advanced mathematics that will be useful in all undergraduate physics. I'm glad I went through this book and having seen these things at least once, even if I didn't understand it fully initially, definitely helped give me the courage to tackle my undergraduate physics courses. I recommend it to every physics student.
Lots of pages are misplaced and chapter 9 to 13 are missing. Unless you want to use a incomplete book, buy the original edition.