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内容説明
Well-organized text designed to complement graduate-level physics texts in classical mechanics, electricity, magnetism, and quantum mechanics. Topics include theory of vector spaces, analytic function theory, Green's function method of solving differential and partial differential equations, theory of groups, more. Many problems, suggestions for further reading.
Book Description
Graduate-level text offers unified treatment of mathematics applicable to many branches of physics. Theory of vector spaces, analytic function theory, theory of integral equations, group theory, more. Many problems. Bibliography.
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カスタマーレビュー
最も参考になったカスタマーレビュー
16 人中、16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。
形式:ペーパーバック
目次
VOLUME ONE
1. Vectors in Classical Physics
2. Calcul of Variations
3. Vectors and Matrices
4. Vector Spaces in Physics
5. Hilbert Space - Complete Othonormal Sets of Functions
VOLUME TWO
6. Elements and Applications of the Theory of Analytic Funcions
7. Green's Functions
8. Introductions to Integral Equations
9. Integral Equations in Hilbert Space
10. Introduction to Group Theory
コロンビア大学で行われた授業をもとにした、大学院1年生向けの教科書。
前書きによればこの本のバックボーンは第1部3,4,5章のベクトル空間の理論である。
第2部は数学の諸分野へのイントロダクション的な意味合いが強い。
目次を見てわかるとおり、この本では微分方程式は扱われていない。
物理を学ぶ上で現れた数学上の概念を数学側からまとめなおした印象である。
例が豊富であり物理のどの問題で用いられる手法か、掴みやすいのはこの本の
美徳だと思う。背表紙にあるとおり基本的には"self-contained"であるので
学部の基本的な物理を知っていれば読み進めることができる。
上に書いたように物理的な応用が各セクションで必ず取り上げられているので
途中で飽きづらいというのも良い点だと思う。
VOLUME ONE
1. Vectors in Classical Physics
2. Calcul of Variations
3. Vectors and Matrices
4. Vector Spaces in Physics
5. Hilbert Space - Complete Othonormal Sets of Functions
VOLUME TWO
6. Elements and Applications of the Theory of Analytic Funcions
7. Green's Functions
8. Introductions to Integral Equations
9. Integral Equations in Hilbert Space
10. Introduction to Group Theory
コロンビア大学で行われた授業をもとにした、大学院1年生向けの教科書。
前書きによればこの本のバックボーンは第1部3,4,5章のベクトル空間の理論である。
第2部は数学の諸分野へのイントロダクション的な意味合いが強い。
目次を見てわかるとおり、この本では微分方程式は扱われていない。
物理を学ぶ上で現れた数学上の概念を数学側からまとめなおした印象である。
例が豊富であり物理のどの問題で用いられる手法か、掴みやすいのはこの本の
美徳だと思う。背表紙にあるとおり基本的には"self-contained"であるので
学部の基本的な物理を知っていれば読み進めることができる。
上に書いたように物理的な応用が各セクションで必ず取り上げられているので
途中で飽きづらいというのも良い点だと思う。
Amazon.com で最も参考になったカスタマーレビュー (beta)
Amazon.com:
27件のカスタマーレビュー
149 人中、147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。
An introduction to the basic mathematics of physics
1999/6/6
形式:ペーパーバック
This book introduces the reader to the basic mathematical structures of theoretical physics: mainly Quantum Mechanics, Electromagnetic Theory, And Classical Mechanics. I used this at UC San Diego for a year long graduate course on Mathematical methods in physics and engineering. If one has the time, there is really a lot to be gained by carefully studying this book. A big part of the book is geared toward developing in detail the mathematics of the Quantum Theory. This is a good thing because in my experience most QM books are too eager to "get to the physics". It is true that you can get by with a superficial understanding of functional analysis and still do QM, but this book will give you an immensely deeper understanding of the underlying structure of the theory. In particular, the treatment of Green's functions and integral equations is good. There is chapter on Group Theory and it's uses in QM. Also is a chapter on Complex analysis, although it is a wise idea to read a book entirely devoted to this subject. Overall, I like this book very much.
45 人中、44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。
ridiculously good
2005/9/27
形式:ペーパーバック
The first chapter on vector analysis from the component view is the best treatment of the subject I've seen anywhere. I worked through it and the subsequent chapters on linear algebra before going to college, and it literally doubled or tripled my mathematical confidence/ability.
Now that i've had some more physics, i've been going through some of the other chapters. The treatment of each subject is framed in a way that makes immediate application to physics natural and intuitive. However, while the level of rigor falls somewhat short of many pure math analysis textbooks (ex: lebesque integration is discussed qualitatively, whereas ideally one would have studied measure theory and lebesque integration before hilbert spaces and other topics), the author does a good job of giving appropriate mathematical caveats this book (in my opinion) strikes an excellent balance of practicality without sacrificing rigor. I think this makes the book useful for physicists who would like a rigorous intro to the math without getting bogged down in (relatively) unappliable mathematical constructs.
Overall, this book is a must. I'd recommend the book early (as soon as one's taken multivariable calculus). There won't be any math in any physics course that you won't feel comfortable with after you've read through this book.
Now that i've had some more physics, i've been going through some of the other chapters. The treatment of each subject is framed in a way that makes immediate application to physics natural and intuitive. However, while the level of rigor falls somewhat short of many pure math analysis textbooks (ex: lebesque integration is discussed qualitatively, whereas ideally one would have studied measure theory and lebesque integration before hilbert spaces and other topics), the author does a good job of giving appropriate mathematical caveats this book (in my opinion) strikes an excellent balance of practicality without sacrificing rigor. I think this makes the book useful for physicists who would like a rigorous intro to the math without getting bogged down in (relatively) unappliable mathematical constructs.
Overall, this book is a must. I'd recommend the book early (as soon as one's taken multivariable calculus). There won't be any math in any physics course that you won't feel comfortable with after you've read through this book.
90 人中、83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。
Important Information
2003/5/29
形式:ペーパーバック
This book is not, and I repeat, IS NOT for the inexperienced. This book is a GRADUATE LEVEL TEXT on mathematical physics. If you are an undergraduate student taking a physics class, this book will be of no use to you. I recommend that anyone interested in purchasing this book have a somewhat decent amount of mathematical background. I personally recommend Calculus I-IV, Advanced Calculus and Linear Algebra.
If, though, you have this background, then this book is may just be for you. It is concise, to the point and presents a clear and well written discussion of mathematical physics.
I just felt that before you dive, head first, into the world of mathematical physics, somebody needed to warn you about what you were getting yourself into.
If, though, you have this background, then this book is may just be for you. It is concise, to the point and presents a clear and well written discussion of mathematical physics.
I just felt that before you dive, head first, into the world of mathematical physics, somebody needed to warn you about what you were getting yourself into.
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