CALCULUS I BY HEART

TABLE OF CONTENTS

1. WELCOME TO CALCULUS
        DEFINITIONS
        MERCIFUL ALGEBRA REVIEW
2. ABSOLUTE VALUE
        TRIGONOMETRY REVIEW (EXACT ANSWERS)
3. FUNCTIONS: COMPOSITION, LOGS
CALCULUS BEGINS
4.  LIMITS (INTUITIVELY)
5.  LEFT AND RIGHT HAND LIMITS (INTUITIVELY)
6.  RIGOROUS DEFINITION OF LIMIT
7.  QUADRATIC RIGOROUS LIMIT PROOFS
8.  LIMIT THEOREMS
9.  CONTINUITY
10. INTERMEDIATE VALUE THEOREM
        LIMITS AS x GOES TO INFINITY
11. CURVE SKETCHING WITH ASYMPTOTE INFORMATION
12. DERIVATIVES, TANGENT LINES, VELOCITY
13. EQUIVALENT FORMULATION OF DERIVATIVE
14. DERIVATIVE NOTATION, DERIVATIVES & CONTINUITY
15. DERIVATIVE FORMULAS
16. PRODUCT & QUOTIENT DERIVATIVE FORMULAS
17. DERIVATIVE APPLICATION TO PHYSICS
18. DERIVATIVE APPLICATION TO ECONOMICS
19. DERIVATIVES OF TRIGONOMETRIC FUNCTIONS
20. DERIVATIVE OF COMPOSITIONS (CHAIN RULE)
21. IMPLICIT DIFFERENTIATION
22. DERIVATIVES OF INVERSE TRIGONOMETRIC FUNCTIONS
23. HIGHER DERIVATIVES
24. DERIVATIVES OF LOGARITHMS
25. HYPERBOLIC FUNCTIONS
26. RELATED RATES
27. MORE RELATED RATES
        DIFFERENTIALS
28. INTRODUCTION TO MAX AND MIN VALUES
29. MAX\MIN VALUES ON A CLOSED INTERVAL
30. ROLLE’S THEOREM AND MEAN VALUE THEOREM
31. 1ST DERIVATIVE, INCREASING, DECREASING, EXTREMA.
32. 2ND DERIVATIVE, CONCAVITY, 2ND DERIVATIVE TEST
33. INDETERMINANT FORMS AND L’HOSPITAL’S RULE
34. CURVE SKETCHING USING MANY WEAPONS
35. MAX\MIN WORD PROBLEMS
36. NEWTON’S METHOD
37. ANTIDERIVATIVES
ANSWERS TO SELECTED HOMEWORK PROBLEMS
BASIC KNOWLEDGE QUESTIONS

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