Page:Elements of the Differential and Integral Calculus - Granville - Revised.djvu/13

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  1. CONTENTS

    DIFFERENTIAL CALCULUS

    CHAPTER I
    COLLECTION OF FORMULAS

  2. SECTIONPAGE
  3. 1.
    Formulas from Algebra, Trigonometry, and Analytic Geometry
    ................................................................................................................................................................................................................................................................................................................................................................................................
    1
  4. 2.
    Greek alphabet
    ................................................................................................................................................................................................................................................................................................................................................................................................
    3
  5. 3.
    Rules for signs in the four quadrants
    ................................................................................................................................................................................................................................................................................................................................................................................................
    3
  6. 4.
    Natural values of the trigonometric functions
    ................................................................................................................................................................................................................................................................................................................................................................................................
    4
  7. 5.
    Tables of logarithms
    ................................................................................................................................................................................................................................................................................................................................................................................................
    5
  8. CHAPTER II
    VARIABLES AND FUNCTIONS

  9. 6.
    Variables and constants
    ................................................................................................................................................................................................................................................................................................................................................................................................
    6
  10. 7.
    Interval of a variable
    ................................................................................................................................................................................................................................................................................................................................................................................................
    6
  11. 8.
    Continuous variation
    ................................................................................................................................................................................................................................................................................................................................................................................................
    6
  12. 9.
    Functions
    ................................................................................................................................................................................................................................................................................................................................................................................................
    7
  13. 10.
    Independent and dependent variables
    ................................................................................................................................................................................................................................................................................................................................................................................................
    7
  14. 11.
    Notation of functions
    ................................................................................................................................................................................................................................................................................................................................................................................................
    8
  15. 12.
    Values of the independent variable for which a function is defined
    ................................................................................................................................................................................................................................................................................................................................................................................................
    8
  16. CHAPTER III
    THEORY OF LIMITS

  17. 13.
    Limit of a variable
    ................................................................................................................................................................................................................................................................................................................................................................................................
    11
  18. 14.
    Division by zero excluded
    ................................................................................................................................................................................................................................................................................................................................................................................................
    12
  19. 15.
    Infinitesimals
    ................................................................................................................................................................................................................................................................................................................................................................................................
    13
  20. 16.
    The concept of infinity ()
    ................................................................................................................................................................................................................................................................................................................................................................................................
    13
  21. 17.
    Limiting value of a function
    ................................................................................................................................................................................................................................................................................................................................................................................................
    14
  22. 18.
    Continuous and discontinuous functions
    ................................................................................................................................................................................................................................................................................................................................................................................................
    14
  23. 19.
    Continuity and discontinuity of functions illustrated by their graphs
    ................................................................................................................................................................................................................................................................................................................................................................................................
    16
  24. 20.
    Fundamental theorems on limits
    ................................................................................................................................................................................................................................................................................................................................................................................................
    18
  25. 21.
    Special limiting values
    ................................................................................................................................................................................................................................................................................................................................................................................................
    20
  26. 22.
    The limit of as
    ................................................................................................................................................................................................................................................................................................................................................................................................
    21
  27. 23.
    The number
    ................................................................................................................................................................................................................................................................................................................................................................................................
    22
  28. 24.
    Expressions assuming the form
    ................................................................................................................................................................................................................................................................................................................................................................................................
    23

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