Page:Elements of the Differential and Integral Calculus - Granville - Revised.djvu/18

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CONTENTS
  1. CHAPTER XVII
    SERIES

  2. SECTIONPAGE
  3. 134.
    Introduction
    ................................................................................................................................................................................................................................................................................................................................................................................................
    212
  4. 135.
    Infinite series
    ................................................................................................................................................................................................................................................................................................................................................................................................
    213
  5. 136.
    Existence of a limit
    ................................................................................................................................................................................................................................................................................................................................................................................................
    215
  6. 137.
    Fundamental test for convergence
    ................................................................................................................................................................................................................................................................................................................................................................................................
    216
  7. 138.
    Comparison test for convergence
    ................................................................................................................................................................................................................................................................................................................................................................................................
    217
  8. 139.
    Cauchy's ratio test for convergence
    ................................................................................................................................................................................................................................................................................................................................................................................................
    218
  9. 140.
    Alternating series
    ................................................................................................................................................................................................................................................................................................................................................................................................
    220
  10. 141.
    Absolute convergence
    ................................................................................................................................................................................................................................................................................................................................................................................................
    220
  11. 142.
    Power series
    ................................................................................................................................................................................................................................................................................................................................................................................................
    223
  12. CHAPTER XVIII
    EXPANSION OF FUNCTIONS

  13. 143.
    Introduction
    ................................................................................................................................................................................................................................................................................................................................................................................................
    227
  14. 144.
    Taylor's Theorem and Taylor's Series
    ................................................................................................................................................................................................................................................................................................................................................................................................
    228
  15. 145.
    Maclaurin's Theorem and Maclaurin's Series
    ................................................................................................................................................................................................................................................................................................................................................................................................
    230
  16. 146.
    Computation by series
    ................................................................................................................................................................................................................................................................................................................................................................................................
    234
  17. 147.
    Approximate formulas derived from series. Interpolation
    ................................................................................................................................................................................................................................................................................................................................................................................................
    237
  18. 148.
    Taylor's Theorem for functions of two or more variables
    ................................................................................................................................................................................................................................................................................................................................................................................................
    240
  19. 149.
    Maxima and minima of functions of two independent variables
    ................................................................................................................................................................................................................................................................................................................................................................................................
    243
  20. CHAPTER XIX
    ASYMPTOTES. SINGULAR POINTS

  21. 150.
    Rectilinear asymptotes
    ................................................................................................................................................................................................................................................................................................................................................................................................
    249
  22. 151.
    Asymptotes found by method of limiting intercepts
    ................................................................................................................................................................................................................................................................................................................................................................................................
    249
  23. 152.
    Method of determining asymptotes to algebraic curves
    ................................................................................................................................................................................................................................................................................................................................................................................................
    250
  24. 153.
    Asymptotes in polar coördinates
    ................................................................................................................................................................................................................................................................................................................................................................................................
    254
  25. 154.
    Singular points
    ................................................................................................................................................................................................................................................................................................................................................................................................
    255
  26. 155.
    Determination of the tangent to an algebraic curve at a given point by inspection
    ................................................................................................................................................................................................................................................................................................................................................................................................
    255
  27. 156.
    Nodes
    ................................................................................................................................................................................................................................................................................................................................................................................................
    258
  28. 157.
    Cusps
    ................................................................................................................................................................................................................................................................................................................................................................................................
    259
  29. 158.
    Conjugate or isolated points
    ................................................................................................................................................................................................................................................................................................................................................................................................
    260
  30. 159.
    Transcendental singularities
    ................................................................................................................................................................................................................................................................................................................................................................................................
    260
  31. CHAPTER XX
    APPLICATIONS TO GEOMETRY OF SPACE

  32. 160.
    Tangent line and normal plane to a skew curve whose equations are given in parametric form
    ................................................................................................................................................................................................................................................................................................................................................................................................
    262
  33. 161.
    Tangent plane to a surface
    ................................................................................................................................................................................................................................................................................................................................................................................................
    264