The Calculus Primer (2011)

INTRODUCTION

Part I. Functions, Rates, and Limits

Chapter 1. VARIABLES AND FUNCTIONS

Chapter 2. AVERAGE AND INSTANTANEOUS RATES

Chapter 3. THE LIMIT CONCEPT

Chapter 4. SOME SPECIAL LIMITS

Part II. The Derivative of a Function

Chapter 5. INCREMENT NOTATION

Chapter 6. THE MEANING OF THE DERIVATIVE

Chapter 7. DIFFERENTIATION: FINDING THE DERIVATIVE

Part III. Differentiation of Algebraic Functions

Chapter 8. THE DERIVATIVE OF A CONSTANT, A VARIABLE, AND A SUM

Chapter 9. DERIVATIVE OF THE POWER FUNCTION

Chapter 10. DERIVATIVE OF PRODUCTS AND QUOTIENTS

Chapter 11. DIFFERENTIATION OF IMPLICIT FUNCTIONS

Part IV. Using the Derivative

Chapter 12. THE DERIVATIVE AS A TOOL

Chapter 13. INSTANTANEOUS RATES OF CHANGE

Chapter 14. DISTANCE, VELOCITY, AND ACCELERATION

Chapter 15. MAXIMA AND MINIMA

Part V. Differentiation of Transcendental Functions

Chapter 16. DERIVATIVES OF LOGARITHMIC FUNCTIONS

Chapter 17. DERIVATIVES OF EXPONENTIAL FUNCTIONS

Chapter 18. DERIVATIVES OF TRIGONOMETRIC FUNCTIONS

Chapter 19. DERIVATIVES OF THE INVERSE TRIGONOMETRIC FUNCTIONS

Part VI. Further Applications of the Derivative

Chapter 20. SLOPES, TANGENTS, AND NORMALS

Chapter 21. POINTS OF INFLECTION AND CURVE TRACING

Chapter 22. PARAMETRIC EQUATIONS

Chapter 23. RECTILINEAR AND CIRCULAR MOTION

Chapter 24. RELATED TIME RATES

Part VII. Differentials

Chapter 25. INCREMENTS AND INFINITESIMALS

Chapter 26. USING DIFFERENTIALS

Chapter 27. SUMMARY OF DIFFERENTIAL NOTATION

Chapter 28. APPROXIMATE CALCULATIONS

Part VIII. Curvature

Chapter 29. LENGTH OF ARC

Chapter 30. MEANING OF CURVATURE

Chapter 31. CIRCLE OF CURVATURE

Chapter 32. THE EVOLUTE

Part IX. Indeterminate Forms

Chapter 33. THEOREM OF MEAN VALUE

Chapter 34. EVALUATION OF INDETERMINATE FORMS

Part X. Partial Differentiation

Chapter 35. PARTIAL DERIVATIVES

Chapter 36. THE TOTAL DERIVATIVE

Chapter 37. SIGNIFICANCE OF PARTIAL AND TOTAL DERIVATIVES

Chapter 38. SINGULAR POINTS OF A CURVE

Part XI. Expansion of Functions

Chapter 39. INFINITE SERIES AND SIGMA NOTATION

Chapter 40. TESTS FOR CONVERGENCE AND DIVERGENCE

Chapter 41. POWER SERIES

Chapter 42. EXPANSION OF FUNCTIONS

Chapter 43. THE VALUE OF π; EULER’S FORMULA

Part XII. General Methods of Integration

Chapter 44. INTEGRATION AS THE INVERSE OF DIFFERENTIATION

Chapter 45. FUNDAMENTAL PRINCIPLES OF INTEGRATION

Chapter 46. STANDARD ELEMENTARY INTEGRAL FORMS

Part XIII. Special Methods of Integration

Chapter 47. INTEGRATION BY PARTS

Chapter 48. TRIGONOMETRIC INTEGRALS

Chapter 49. INTEGRATION BY SUBSTITUTION; CHANGE OF VARIABLE

Chapter 50. TABLES OF INTEGRALS

Chapter 51. INTEGRATION OF RATIONAL FRACTIONS

Part XIV. The Definite Integral

Chapter 52. INTEGRATION BETWEEN LIMITS

Chapter 53. AREA UNDER A CURVE

Chapter 54. THE DEFINITE INTEGRAL AND ITS LIMITS

Chapter 55. DERIVED CURVES AND INTEGRAL CURVES

Part XV. Integration as a Process of Summation

Chapter 56. A BASIC PRINCIPLE

Chapter 57. AREAS OF PLANE CURVES

Chapter 58. LENGTH OF A CURVE

Chapter 59. SOLIDS OF REVOLUTION

Part XVI. Successive and Partial Integration; Approximate Integration

Chapter 60. MULTIPLE INTEGRALS

Chapter 61. AREAS AND VOLUMES

Chapter 62. APPROXIMATE INTEGRATION

Chapter 63. PRACTICAL APPLICATIONS

Tables

Reference Material from Other Branches of Mathematics

Answers to Problems