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Page
- 1. cover page
- 2. title page
- 3. copyright page
- 4. Contents
- 10. Preface
- 18. 1 - Functions
- 31. 1.2 Combining Functions; Shifting and Scaling Graphs
- 39. 1.3 - Trigonometric Functions
- 47. 1.4 - Graphing with Calculators and Computers
- 51. Review
- 56. 2 - Limits and Continuity
- 63. 2.2 - Limit of a Function and Limit Laws
- 74. 2.3 - The Precise Definition of a Limit
- 83. 2.4 - One-Sided Limits
- 90. 2.5 - Continuity
- 101. 2.6 - Limits Involving Infinity; Asymptotes of Graphs
- 113. Review
- 119. 3 - Differentiation
- 123. 3.2 - The Derivative as a Function
- 132. 3.3 - Differentiation Rules
- 141. 3.4 - The Derivative as a Rate of Change
- 152. 3.5 - Derivatives of Trigonometric Functions
- 159. 3.6 - The Chain Rule
- 166. 3.7 - Implicit Differentiation
- 172. 3.8 - Related Rates
- 181. 3.9 - Linearization and Differentials
- 192. Review
- 201. 4 - Applications of Derivatives
- 209. 4.2 - The Mean Value Theorem
- 215. 4.3 - Monotonic Functions and the First Derivative Test
- 220. 4.4 - Concavity and Curve Sketching
- 231. 4.5 - Applied Optimization
- 242. 4.6 - Newton's Method
- 247. 4.7 - Antiderivatives
- 256. Review
- 263. 5 - Integration
- 273. 5.2 - Sigma Notation and Limits of Finite Sums
- 279. 5.3 - The Definite Integral
- 291. 5.4 - The Fundamental Theorem of Calculus
- 301. 5.5 - Indefinite Integrals and the Substitution Method
- 308. 5.6 - Substitution and Area Between Curves
- 317. Review
- 325. 6 - Applications of Definite Integrals
- 336. 6.2 - Volumes Using Cylindrical Shells
- 343. 6.3 - Arc Length
- 349. 6.4 - Areas of Surfaces of Revolution
- 354. 6.5 - Work and Fluid Forces
- 363. 6.6 - Moments and Centers of Mass
- 374. Review
- 378. 7 - Transcendental Functions
- 386. 7.2 - Natural Logarithms
- 394. 7.3 - Exponential Functions
- 404. 7.4 - Exponential Change and Seperable Differential Equations
-
413.
7.5 -
Indeterminate Forms and L'Hopital's Rule -
421.
7.6 -
Inverse Trigonometric Functions -
433.
7.7 -
Hyperbolic Functions -
441.
7.8 -
Relative Rates of Growth - 446. Review
- 452. 8 - Techniques of Integration
-
461.
8.2 -
Trigonometric Integrals -
466.
8.3 -
Trigonometric Substitutions -
470.
8.4 -
Integration of Rational Functions by Partial Fractions -
480.
8.5 -
Integral Tables and Computer Algebra Systems -
485.
8.6 -
NumericaL Integration -
495.
8.7 -
Improper Integrals - 506. Review
- 513. 9 - First-Order Differential Equations
-
521.
9.2 -
First-Order Linear Equations -
527.
9.3 -
Applications -
533.
9.4 -
Graphical Solutions of Autonomous Equations -
540.
9.5 -
Systems of Equations and Phase Planes - 546. Review
- 549. 10 - Infinite Sequences and Series
-
561.
10.2 -
Infinite Series -
570.
10.3 -
The Integral Test -
575.
10.4 -
Comparison Tests -
580.
10.5 -
The Ratio and Root Tests -
585.
10.6 -
Alternating Series, Absolute and Conditional Convergence -
592.
10.7 -
Power Series -
601.
10.8 -
Taylor and Maclaurin Series - 606. 10.9 - Convergence of Taylor Series
- 613. 10.10 - The Binomial Series and Applications of Taylor Series
- 622. Review
- 627. 11 - Parametric Equations and Polar Coordinates
-
635.
11.2 -
Calculus with Parametric Curves - 644. 11.3 - Polar Coordinates
-
648.
11.4 - Graphing in Polar
Coordinates - 652. 11.5 - Areas and Lengths in Polar Coordinates
- 656. 11.6 - Conic Sections
- 665. 11.7 - Conics in Polar Coordinates
- 671. Review
- 677. 12 - Vectors and the Geometry of Space
- 682. 12.2 - Vectors
- 691. 12.3 - The Dot Product
- 699. 12.4 - The Cross Product
- 705. 12.5 - Lines and Planes in Space
- 713. 12.6 - Cylinders and Quadric Surfaces
- 718. Review
- 724. 13 - Vector-Valued Functions and Motion in Space
- 732. 13.2 - Integrals of Vector Functions; Projectile Motion
- 741. 13.3 - Arc Length in Space
- 745. 13.4 - Curvature and Normal Vectors of a Curve
- 751. 13.5 - Tangential and Normal Components of Acceleration
- 756. 13.6 - Velocity and Acceleration in Polar Coordinates
- 759. Review
- 764. 14 - Partial Derivatives
- 772. 14.2 - Limits and Continuity in Higher Dimensions
- 781. 14.3 - Partial Derivatives
- 792. 14.4 - The Chain Rule
- 801. 14.5 - Directional Derivatives and Gradient Vectors
- 808. 14.6 - Tangent Planes and Differentials
- 819. 14.7 - Extreme Values and Saddle Points
- 828. 14.8 - Lagrange Multipliers
- 837. 14.9 - Taylor's Formula for Two Variables
- 841. 14.10 - Partial Derivatives with Constrained Variables
- 846. Review
- 853. 15 - Multiple Integrals
- 858. 15.2 - Double Integrals over General Regions
- 867. 15.3 - Area by Double Integration
- 870. 15.4 - Double Integrals in Polar Form
- 876. 15.5 - Triple Integrals in Rectangular Coordinates
- 885. 15.6 - Moments and Centers of Mass
- 892. 15.7 - Triple Integrals in Cylindrical and Spherical Coordinates
- 904. 15.8 - Substitutions in Multiple Integrals
- 913. Review
- 918. 16 - Integration in Vector Fields
- 924. 16.2 - Vector Fields and Line Integrals: Work, Circulation, and Flux
- 937. 16.3 - Path Independence, Conservative Fields, and Potential Functions
- 948. 16.4 - Green's Theorem in the Plane
- 960. 16.5 - Surfaces and Area
- 970. 16.6 - Surface Integrals
- 979. 16.7 - Stoke's Theorem
- 989. 16.8 - The Divergence Theorem and a Unified Theory
- 1000. Review
- 1006. 17 - Second-Order Differential Equations
- 1013. 17.2 - Nonhomogeneous Linear Equations
- 1022. 17.3 - Applications
- 1028. 17.4 - Euler Equations
- 1031. 17.5 - Power-Series Solutions
- 1038. Appendices
- 1043. A.2 - Mathematical Induction
- 1047. A.3 - Lines, Circles, and Parabolas
- 1055. A.4 - Proofs of Limit Theorems
- 1058. A.5 - Commonly Occuring Limits
- 1060. A.6 - Theory of the Real Numbers
- 1062. A.7 - Complex Numbers
- 1072. A.8 - The Distributive Law for Vector Cross Products
- 1073. A.9 - The Mixed Derivative Theorem and the Increment Theorem
- 1078. Answers to Odd-Numbered Exercises
- 1083. Chapter 2
- 1086. Chapter 3
- 1092. Chapter 4
- 1100. Chapter 5
- 1102. Chapter 6
- 1104. Chapter 7
- 1108. Chapter 8
- 1112. Chapter 9
- 1115. Chapter 10
- 1119. Chapter 11
- 1127. Chapter 12
- 1131. Chapter 13
- 1133. Chapter 14
- 1140. Chapter 15
- 1145. Chapter 16
- 1147. Appendices
- 1150. Chapter 17
- 1152. Index
- 1166. A Brief Table of Integrals
- 1172. Credits
- 1173. Formulas
- 1174. Geometry Formulas
- 1175. Limits
- 1176. Differentiation Rules
- 1177. Integration Rules
- 1178. Trigonometry Formulas
- 1179. Series
