SOURCE BOOKS IN THE HISTORY OF THE SCIENCES
Cover: A Source Book in Classical Analysis in HARDCOVER

A Source Book in Classical Analysis

Edited by Garrett Birkhoff

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Product Details

HARDCOVER

$169.50 • £135.95 • €152.50

ISBN 9780674822450

Publication Date: 01/01/1973

Short

486 pages

7 x 10 inches

18 line illustrations

Source Books in the History of the Sciences

World

  • I. 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
  • II. 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
  • III. 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
  • IV. 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. Poincaré on Asymptotic Series
      • 27. Lerch on Lerch’s Theorem
  • V. 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. Fejré 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
  • VI. Elliptical 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
  • VII. 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. Poincaré on Automorphic Functions
      • 46. Klein on Fundamental Regions of Discontinuous Groups
  • VIII. 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. Sturm on Sturm’s Theorems
      • 52. Liouville on Sturm-Liouville Expansions I
      • 53. Liouville on Sturm-Liouville Expansions II
  • IX. Ordinary Differential Equations II
    • A. Regular Singular Points
      • 54. Fuchs on Isolated Singular Points
      • 55. Frobenius on Regular Singular Points
    • B. Other Fundamental Contributions
      • 56. Lie on Groups of Transformations
      • 57. Poincaré on the Qualitative Theory of Differential Equations
      • 58. Peano on the Peano Series
  • X. Partial Differential Equations
    • A. The Cauchy-Kowalewski Theorem
      • 59. Cauchy on the Cauchy-Kowalewski Theorem
      • 60. Kowalewski on the Cauchy-Kowalewski Theorem
    • B. Beginnings of Potential Theory
      • 61. Laplace on the Laplacian Operator
      • 62. Legendre on Legendre Polynomials
      • 63. Poisson on the Poisson Equation
    • C. Potential Theory Develops
      • 64. Green on Green’s Identities
      • 65. Gauss on Potential Theory
      • 66. Kelvin on Inversion
  • XI. Calculus of Variations
    • A. Variational Principles of Dynamics
      • 67. Lagrange on Properties Related to Least Action
      • 68. Hamilton on Hamilton’s Principle
      • 69. Jacobi on the Hamilton-Jacobi Equations
    • B. Intuitive Uses of Variational Principles
      • 70a. Kelvin on the Dirichlet Principle
      • 70b. Kelvin on a Variational Principle of Hydrodynamics
      • 71a. Dirichlet on the Dirichlet Principle
      • 71b. Rayleigh on the Rayleigh-Ritz Method
    • C. Rigorous Existence Theorems
      • 72. Du Bois-Reymond on the Fundamental Theorem of the Calculus of Variations
      • 73. Poincaré on His Methode du Balayage
      • 74. Hilbert on Dirichlet’s Principle
  • XII. Wave Equations and Characteristics
      • 75. Riemann on Plane Waves of Finite Amplitude
      • 76. Helmholtz on the Helmholtz Equation
      • 77. Kirchhoff’s Identities for the Wave Equation
      • 78. Volterra on Characteristics
  • XIII. Integral Equations
      • 79. Abel’s Integral Equation
      • 80. Volterra on Inverting Integral Equations
      • 81. Fredholm on the Theory of Integral Equations
  • Short Bibliography
  • Index

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