Includes bibliographical references (p. [617]-626) and index.
In English translated from the French.

In English translated from the French.

1. A book's apology xviii
2. Index of notation xxii
3. Chapter 1: Reminders: convergence of sequences and series 1
4. Chapter 2: Measure theory and the Lebesgue integral 51
5. Chapter 3: Integral calculus 73
6. Chapter 4: Complex Analysis I 87
7. Chapter 5: Complex Analysis II 135
8. Chapter 6: Conformal maps 155
9. Chapter 7: Distributions I 179
10. Chapter 8: Distributions II 223
11. Chapter 9: Hilbert spaces; Fourier series 249
12. Chapter 10: Fourier transform of functions 277
13. Chapter 11: Fourier transform of distributions 299
14. Chapter 12: The Laplace transform 331
15. Chapter 13: Physical applications of the Fourier transform 355
16. Chapter 14: Bras, kets, and all that sort of thing 377
17. Chapter 15: Green functions 407
18. Chapter 16: Tensors 433
19. Chapter 17: Differential forms 463
20. Chapter 18: Groups and group representations 489
21. Chapter 19: Introduction to probability theory 509
22. Chapter 20: Random variables 521
23. Chapter 21: Convergence of random variables: central limit theorem 553
24. Appendices
25. A: Reminders concerning topology and normed vector spaces 573
26. B: Elementary reminders of differential calculus 585
27. C: Matrices 593
28. D: A few proofs 597
29. Tables
30. Fourier transforms 609
31. Laplace transforms 613
32. Probability laws 616
33. Further reading 617
34. References 621
35. Portraits 627
36. Sidebars 629
37. Index 631