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

1. CONTENTS

    

   DIFFERENTIAL CALCULUS

    

   CHAPTER I
   COLLECTION OF FORMULAS

2. SECTION

   PAGE

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 ($\scriptstyle {\infty }$) ................................................................................................................................................................................................................................................................................................................................................................................................

    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 $\scriptstyle {\frac {\sin x}{x}}$ as $\scriptstyle {x\doteq 0}$ ................................................................................................................................................................................................................................................................................................................................................................................................

    21

27. 23.

    The number $\scriptstyle {e}$ ................................................................................................................................................................................................................................................................................................................................................................................................

    22

28. 24.

    Expressions assuming the form $\scriptstyle {\frac {\infty }{\infty }}$ ................................................................................................................................................................................................................................................................................................................................................................................................

    23

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