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More About This Textbook
Overview
What can a physicist gain by studying mathematics? By gathering together everything a physicist needs to know about mathematics in one comprehensive and accessible guide, this is the question Mathematics for Physics and Physicists successfully takes on.
The author, Walter Appel, is a renowned mathematics educator hailing from one of the best schools of France's prestigious Grandes écoles, where he has taught some of his country's leading scientists and engineers. In this unique book, oriented specifically toward physicists, Appel shows graduate students and researchers the vital benefits of integrating mathematics into their study and experience of the physical world. His approach is mathematically rigorous yet refreshingly straightforward, teaching all the math a physicist needs to know above the undergraduate level. Appel details numerous topics from the frontiers of modern physics and mathematics—such as convergence, Green functions, complex analysis, Fourier series and Fourier transform, tensors, and probability theory—consistently partnering clear explanations with cogent examples. For every mathematical concept presented, the relevant physical application is discussed, and exercises are provided to help readers quickly familiarize themselves with a wide array of mathematical tools.
Mathematics for Physics and Physicists is the resource today's physicists must have to strengthen their math skills and to gain otherwise unattainable insights into their fields of study
Editorial Reviews
Zentralblatt MATH Database
There is a law, if not a physical law, that ensures that whenever one is using a standard mathematical technique for a physical problem it is always the special case or a first principles argument that is required. Nothing is straightforward! For such a situation this book is ideal. It presents clear definitions and the rationale for such definitions. The style of the book is very readable and an interesting biographical asides of the mathematicians associated with the topics provide light relief from the depth of the the analysis. The book is both a valuable reference book and is a good pedagogic treatment of mathematical physics. It is a book that should be on many bookshelves.— Brian L. Burrows
Zentralblatt Math
There is a law, if not a physical law, that ensures that whenever one is using a standard mathematical technique for a physical problem it is always the special case or a first principles argument that is required. Nothing is straightforward! For such a situation this book is ideal. It presents clear definitions and the rationale for such definitions. The style of the book is very readable and an interesting biographical asides of the mathematicians associated with the topics provide light relief from the depth of the the analysis. The book is both a valuable reference book and is a good pedagogic treatment of mathematical physics. It is a book that should be on many bookshelves.
— Brian L. Burrows
MAA Review  William J. Satzer
Throughout the book Appel maintains a nice balance between rigorous mathematics and physical applications.Choice  J.T. Zerger
The majority of applied mathematical fields presently require so much specialization that mathematics often takes a back seat to the particular field of study. This book not only contains a great deal of the mathematics necessary to seriously study physics but also encourages physicists and potential physicists to embrace mathematics.Zentralblatt Math  Brian L. Burrows
There is a law, if not a physical law, that ensures that whenever one is using a standard mathematical technique for a physical problem it is always the special case or a first principles argument that is required. Nothing is straightforward! For such a situation this book is ideal. It presents clear definitions and the rationale for such definitions. The style of the book is very readable and an interesting biographical asides of the mathematicians associated with the topics provide light relief from the depth of the the analysis. The book is both a valuable reference book and is a good pedagogic treatment of mathematical physics. It is a book that should be on many bookshelves.Time Magazines Higher Education
Walter Appel, a theoretical physicist and mathematics educator who currently teaches mathematics at the Henri Poincaré School in France, seeks in his book—appearing here in translation—to cover all the mathematics that a physicist requires above undergraduate level, including recent topics such as convergence, Green functions and Fourier series, as well as offering biographical sketches of mathematicians and problem sets.From the Publisher
"Throughout the book Appel maintains a nice balance between rigorous mathematics and physical applications."—William J. Satzer, MAA Review"The majority of applied mathematical fields presently require so much specialization that mathematics often takes a back seat to the particular field of study. This book not only contains a great deal of the mathematics necessary to seriously study physics but also encourages physicists and potential physicists to embrace mathematics."—J.T. Zerger, Choice
"Walter Appel, a theoretical physicist and mathematics educator who currently teaches mathematics at the Henri Poincaré School in France, seeks in his book—appearing here in translation—to cover all the mathematics that a physicist requires above undergraduate level, including recent topics such as convergence, Green functions and Fourier series, as well as offering biographical sketches of mathematicians and problem sets."—Times Higher Education
"There is a law, if not a physical law, that ensures that whenever one is using a standard mathematical technique for a physical problem it is always the special case or a first principles argument that is required. Nothing is straightforward! For such a situation this book is ideal. It presents clear definitions and the rationale for such definitions. The style of the book is very readable and an interesting biographical asides of the mathematicians associated with the topics provide light relief from the depth of the the analysis. The book is both a valuable reference book and is a good pedagogic treatment of mathematical physics. It is a book that should be on many bookshelves."—Brian L. Burrows, Zentralblatt Math
"Mathematics for Physics and Physicists is a wellorganized resource today's physicists must have to strengthen their math skills and to gain otherwise unattainable insights into their fields of study. Mathematics has always been and is still a precious. . . . One is delighted to see Appel's book maintains a nice balance between rigorous mathematics and physical applications. . . . It will lead potential physicists to embrace mathematics and they will benefit substantially."—Current Engineering Practice
MAA Review
Throughout the book Appel maintains a nice balance between rigorous mathematics and physical applications.— William J. Satzer
Choice
The majority of applied mathematical fields presently require so much specialization that mathematics often takes a back seat to the particular field of study. This book not only contains a great deal of the mathematics necessary to seriously study physics but also encourages physicists and potential physicists to embrace mathematics.— J.T. Zerger
Times Higher Education
Walter Appel, a theoretical physicist and mathematics educator who currently teaches mathematics at the Henri Poincaré School in France, seeks in his book—appearing here in translation—to cover all the mathematics that a physicist requires above undergraduate level, including recent topics such as convergence, Green functions and Fourier series, as well as offering biographical sketches of mathematicians and problem sets.Current Engineering Practice
Mathematics for Physics and Physicists is a wellorganized resource today's physicists must have to strengthen their math skills and to gain otherwise unattainable insights into their fields of study. Mathematics has always been and is still a precious. . . . One is delighted to see Appel's book maintains a nice balance between rigorous mathematics and physical applications. . . . It will lead potential physicists to embrace mathematics and they will benefit substantially.Current Engineering Practice
Mathematics for Physics and Physicists is a wellorganized resource today's physicists must have to strengthen their math skills and to gain otherwise unattainable insights into their fields of study. Mathematics has always been and is still a precious. . . . One is delighted to see Appel's book maintains a nice balance between rigorous mathematics and physical applications. . . . It will lead potential physicists to embrace mathematics and they will benefit substantially.Product Details
Meet the Author
Walter Appel holds a Ph.D. in theoretical physics. He taught mathematics for physics for seven years at the Ecole Normale Superieure de Lyon in France and currently teaches mathematics at the Henri Poincare School.
Table of Contents
A book's apology xviii
Index of notation xxii
Chapter 1: Reminders: convergence of sequences and series 1
Chapter 2: Measure theory and the Lebesgue integral 51
Chapter 3: Integral calculus 73
Chapter 4: Complex Analysis I 87
Chapter 5: Complex Analysis II 135
Chapter 6: Conformal maps 155
Chapter 7: Distributions I 179
Chapter 8: Distributions II 223
Chapter 9: Hilbert spaces; Fourier series 249
Chapter 10: Fourier transform of functions 277
Chapter 11: Fourier transform of distributions 299
Chapter 12: The Laplace transform 331
Chapter 13: Physical applications of the Fourier transform 355
Chapter 14: Bras, kets, and all that sort of thing 377
Chapter 15: Green functions 407
Chapter 16: Tensors 433
Chapter 17: Differential forms 463
Chapter 18: Groups and group representations 489
Chapter 19: Introduction to probability theory 509
Chapter 20: Random variables 521
Chapter 21: Convergence of random variables: central limit theorem 553
Appendices
A: Reminders concerning topology and normed vector spaces 573
B: Elementary reminders of differential calculus 585
C: Matrices 593
D: A few proofs 597
Tables
Fourier transforms 609
Laplace transforms 613
Probability laws 616
Further reading 617
References 621
Portraits 627
Sidebars 629
Index 631