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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.

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“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)

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  • ハードカバー: 864ページ
  • 出版社: Wiley; 3版 (2004/02)
  • 言語: 英語
  • ISBN-10: 0471198269
  • ISBN-13: 978-0471198260
  • 発売日: 2004/02
  • 商品パッケージの寸法: 18.3 x 3.4 x 25.5 cm
  • おすすめ度: 5つ星のうち 5.0 1 件のカスタマーレビュー
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 高校の微積分を理解して間もない状態であれば、非常に読み易くて、問題も簡単且つ合理的です。高校の内容から大学院の内容まで含まれています。しかし、説明も問題も分かり易くする為に長たらしく書かれている傾向があるので、既に物理数学をある程度学んでいれば(学部生高学年までの内容を理解していれば)内容の半分も理解していなかったとしても、すぐに飽きていやになります。

 まとめると、数学を微積分程度しかやった事のない方であれば、これほど分かり易い物理数学書は存在しないと思います。ある程度学んでいる人はArfkenをすすめます。特に理論系である程度物理数学を学んでいればHassaniをおすすめします。
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Amazon.com: 5つ星のうち HASH(0x8f994888) 122 件のカスタマーレビュー
124 人中、122人の方が、「このレビューが参考になった」と投票しています。
5つ星のうち HASH(0x8f7af6fc) indispensable Mathematical hanbook for physics students 2002/8/15
投稿者 カスタマー - (Amazon.com)
形式: ハードカバー
To put it quite simply, if you are a physics student, you must own this book. What does this book do for you? Consider this...
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...)
83 人中、78人の方が、「このレビューが参考になった」と投票しています。
5つ星のうち HASH(0x909beaec) An excellent book for those who need applied mathematics. 2007/4/23
投稿者 Keith Dow - (Amazon.com)
形式: ハードカバー Amazonで購入
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!
37 人中、35人の方が、「このレビューが参考になった」と投票しています。
5つ星のうち HASH(0x92715e94) Concise Reference 2006/3/11
投稿者 Frank Carnley - (Amazon.com)
形式: ハードカバー
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.
21 人中、21人の方が、「このレビューが参考になった」と投票しています。
5つ星のうち HASH(0x8f9bd930) This book will make a man out of you. 2012/2/11
投稿者 CutzmanX - (Amazon.com)
形式: ハードカバー Amazonで購入
Let me start off by saying, I have essentially covered every single chapter (with the exception of the multivariable calculus section, I took a separate course on that), and every single section in a 3-quarter mathematical methods course as part of my physics undergraduate requirements. And let me repeat this again, this book will make a man out of you. After you conquer this book, you will be on your way to conquering all undergraduate physics with ease; mathematics will no longer be a problem and the real learning of physics will begin.

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.
54 人中、46人の方が、「このレビューが参考になった」と投票しています。
5つ星のうち HASH(0x8f96eb94) A Nice Balance Between Procedural Math and Cookbook Physics 2005/9/24
投稿者 John Matlock - (Amazon.com)
形式: ハードカバー
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.
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