The Calculus Primer (2011)
Part I. Functions, Rates, and Limits
Chapter 1. VARIABLES AND FUNCTIONS
Chapter 2. AVERAGE AND INSTANTANEOUS RATES
Chapter 4. SOME SPECIAL LIMITS
Part II. The Derivative of a Function
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
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 30. MEANING OF CURVATURE
Chapter 31. CIRCLE OF CURVATURE
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 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 57. AREAS OF PLANE CURVES
Chapter 59. SOLIDS OF REVOLUTION
Part XVI. Successive and Partial Integration; Approximate Integration
Chapter 60. MULTIPLE INTEGRALS
Chapter 62. APPROXIMATE INTEGRATION
Chapter 63. PRACTICAL APPLICATIONS