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Index
Title Page Copyright Page Dedication Contents Chapter 1 Sets and Functions
1. Sets 2. Ordered n-Tuples. Cartesian Products 3. Relations, Functions and Mappings 4. Real Functions 5. Operations on Functions 6. Counting and Induction 7. Binomial Coefficients. The Binomial Theorem
Chapter 2 Numbers and Coordinates
8. Rational Numbers 9. Incompleteness of the Rational Number System 10. Decimals and Real Numbers 11. Completeness of the Real Number System 12. The Real Line: Coordinates 13. The Real Line: Intervals
Chapter 3 Graphs
14. Rectangular Coordinates 15. Graphs in General 16. Graphs of Functions 17. Trigonometric Functions: Basic Properties 18. Trigonometric Functions: Graphs and Addition Formulas 19. Straight Lines and Their Equations 20. More About Straight Lines
Chapter 4 Limits
21. The Limit Concept 22. More About Limits 23. One-Sided Limits 24. Infinite Limits. Indeterminate Forms 25. Limits at Infinity. Asymptotes 26. The Limit of a Sequence 27. Continuous Functions
Chapter 5 Derivatives
28. The Derivative Concept 29. More About Derivatives 30. Curves and Tangents 31. Technique of Differentiation 32. Differentials. Further Notation 33. Implicit Differentiation. Related Rates 34. Higher-Order Derivatives
Chapter 6 Well-behaved Functions
35. More About Continuous Functions. Absolute Extrema 36. Uniform Continuity 37. Inverse Functions 38. Exponentials and Logarithms 39. More About Exponentials and Logarithms 40. Hyperbolic Functions 41. The Mean Value Theorem. Antiderivatives 42. Relative Extrema 43. Concavity and Inflection Points 44. Applications
Chapter 7 Integrals
45. Indefinite Integrals 46. Integration by Substitution and by Parts 47. Definite Integrals 48. Properties of Definite Integrals 49. The Connection Between Definite and Indefinite Integrals 50. Evaluation of Definite Integrals 51. Area of a Plane Region 52. First-Order Differential Equations 53. Second-Order Differential Equations 54. Work and Energy
Chapter 8 Analytic Geometry in R2
55. Shifts and Scale Changes. Coordinate Transformations 56. Point Transformations and Invariance 57. Parabolas 58. Ellipses and Their Equations 59. More About Ellipses 60. Hyperbolas and Their Equations 61. More About Hyperbolas 62. Tangents to Conics 63. Polar Coordinates 64. Tangents and Areas in Polar Coordinates 65. Rotations and Rigid Motions 66. The General Quadratic Equation
Chapter 9 Curves and Vectors in R2
67. Curves in General. Parametric Equations 68. Length of a Plane Curve 69. Arc Length as a Parameter. Curvature 70. Scalars and Vectors 71. Linear Dependence. Bases and Components 72. The Scalar Product 73. Vector Functions 74. Mechanics in the Plane
Chapter 10 Linear Algebra
75. Determinants and Their Properties 76. Cofactors and Minors 77. Systems of Linear Equations. Cramer’s Rule and Elimination 78. Three-Dimensional Rectangular Coordinates 79. Vectors in R3 80. The Vector Product 81. Triple Products of Vectors
Chapter 11 Analytic Geometry in R3
82. Planes and Straight Lines 83. Space Curves. Orbital Motion 84. Cylinders, Cones and Conics 85. Surfaces of Revolution 86. Quadrics 87. Cylindrical and Spherical Coordinates
Chapter 12 Partial Differentiation
88. Regions, Limits and Continuity 89. Partial Derivatives 90. Differentiable Functions and Differentials 91. The Chain Rule 92. The Implicit Function Theorem 93. The Tangent Plane and Normal to a Surface 94. The Directional Derivative and Gradient 95. Exact Differentials 96. Line Integrals
Chapter 13 Multiple Integration
97. Double Integrals 98. Iterated Integrals 99. Applications of Double Integrals 100. Moments of Inertia 101. Surface Area. Improper Integrals 102. Pappus’ Theorems 103. Triple Integrals 104. Change of Variables in Multiple Integrals
Chapter 14 Further Computations
105. L’Hospital’s Rule 106. Taylor’s Theorem 107. Extrema of Functions of Several Variables 108. Integration of Rational Functions 109. Rationalizing Substitutions 110. Numerical Integration
Chapter 15 Infinite Series
111. Basic Concepts 112. Convergence Tests 113. More on Improper Integrals 114. Power Series 115. Taylor Series
Answers and Solutions Tables
Table 1. Trigonometric Functions Table 2. Exponential Functions Table 3. Natural Logarithms Table 4. Hyperbolic Functions Table 5. Greek Alphabet
Index Errata
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