Modern Calculus and Analytic Geometry 9780486793986, 2002023778, 0486793982, 9781306771702, 1306771706

Table of contents :
Cover
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 General16. 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 Notation33. 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 Integrals49. 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 Coordinates65. 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.