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.
Inhaltsverzeichnis
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