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
Return to Book Description File created: 4/25/2013 | 
