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Source Book in Classical Analysis

by Garrett Birkhoff

Source Book in Classical Analysis cover
  • ISBN: 9780674822450
  • ISBN10: 0674822455

Source Book in Classical Analysis

by Garrett Birkhoff

  • List Price: $164.50
  • Binding: Hardcover
  • Publisher: Harvard Univ Pr
  • Publish date: 06/01/1973
  • ISBN: 9780674822450
  • ISBN10: 0674822455
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Description: PART 1: FOUNDATIONS OF REAL ANALYSIS A. Cauchy's Partial Rigorization 1a. Cauchy on Limits and Continuity 1b. Cauchy on convergence 1c. Cauchy on the Radius of Convergence 2. Cauchy on the Derivative as a Limit 3. Cauchy on Maclaurin's Theorem 4. Cauchy-Moigno on the Fundamental Theorem of the Calculus B. Continuity and Integrability 5. Bolzano on Continuity and Limits 6. Riemann on Fourier Series and the Riemann Integral 7a. Heine Discusses Fourier Series 7b. Heine on the Foundations of Function Theory 8. Stieltjes on the Stieltjes Integral PART 2: FOUNDATIONS OF COMPLEX ANALYSIS A. Early Developments 9. Cauchy's Integral Theorem 10. Cauchy's Integral Formula 11. Cauchy's Calculus of Residues 12a. Cauchy on Liouville's Theorem 12b. Jordan on Liouville's Theorem B. Riemann's Influence 13. Riemann on the Cauchy-Riemann Equations 14. Riemann on Riemann Surfaces 15. Schwarz on Conformal Mapping PART 3: CONVERGENT EXPANSIONS A. The Convergence of Power Series 16. Gauss on the Hypergeometric Series 17. Abel on the Binomial Series B. The Influence of Weierstrass 18. Weierstrass on Analytic Functions of several Variables 19. Picard on Picard's Theorem 20a. Weierstrass on Infinite Products 20b. Mittag-Leffier's Theorem PART 4: ASYMPTOTIC EXPANSIONS A. Analytic Number Theory 21. Riemann on the Riemann Zeta Function 22. Hadamard on the Distribution of Primes B. Asymptotic Series 23. Stirling's Formula 24. Laplace on Generating Functions 25. Abel on the Laplace Transform 26. Poincareacute; on Asymptotic Series 27. Lereh on Lerch's Theorem PART 5: FOURIER SERIES AND INTEGRALS A. Fourier Series 28. Fourier on Heat Flow in a Slab 29a. Fourier on Expansions in Sine Series 29b. Fourier on Heat Flow in a Ring 30. Dirichlet on the Convergence of Fourier Series 31. Wilbraham on the Gibbs Phenomenon 32. Fejreacute; on the Convergence of Fourier Series B. The Fourier Integral 33a-b. Cauchy on the Fourier Integral 34. Fourier on the Fourier Integral 35. Cauchy on Linear Partial Differential Equations with Constant Coefficients PART 6: ELLIPTIC AND ABELIAN INTEGRALS 36. Legendre on Elliptic Integrals 37. Abel's Addition Theorem 38. Abel on Hyperelliptic Integrals 39a. Riemann on Abelian Integrals 39b. Roch on the Riemann-Roch Theorem PART 7: ELLIPTIC AND AUTOMORPHIC FUNCTIONS A. Elliptic and Hyperelliptic Functions 40. Abel on Elliptic Functions 41. Jacobi on Elliptic Functions 42. Jacobi on Some Identities 43. Jacobi on the Jacobi Theta Functions 44. Weierstrass's Al Functions B. Automorphic Functions 45. Poincareacute; on Automorphic Functions 46. Klein on Fundamental Regions of Discontinuous Groups PART 8: ORDINARY DIFFERENTIAL EQUATIONS. I. A. Existence and Uniqueness Theorems 47. Cauchy on the Cauchy Polygon Method 48. Lipschitz on the Lipschitz Condition 49. Picard on the Picard Method 50. Osgood's Existence Theorem B. Sturm-Liouville Theory 51. Storm on Sturm's Theorems 52. Liouville on Sturm-Liouville Expansions. I. 53. Liouville on Sturm-Liouville Expansions. II. PART 9: ORDINARY DIFFERENTIAL EQUATIONS. II. A. Regular Singular Points 54. Fuchs on Isolated Singular Points 55. Frobenius on Regular Singula
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