Efnisyfirlit

• Title Page
• Copyright Page
• Contents
• Preface
• Acknowledgments
• Credits
• 1 Functions
• 1.1 Review of Functions
• 1.2 Representing Functions
• 1.3 Inverse, Exponential, and logarithmic Functions
• 1.4 Trigonometric Functions and Their inverses
• Review Exercises
• 2 Limits
• 2.1 The idea of limits
• 2.2 Definitions of limits
• 2.3 Techniques for computing limits
• 2.4 Infinite limits
• 2.5 Limits at infinity
• 2.6 Continuity
• 2.7 Precise definitions of limits
• Review Exercises
• 3 Derivatives
• 3.1 Introducing the derivative
• 3.2 Working with derivatives
• 3.3 Rules of differentiation
• 3.4 The Product and Quotient rules
• 3.5 Derivatives of Trigonometric Functions
• 3.6 Derivatives as rates of change
• 3.7 The chain rule
• 3.8 Implicit differentiation
• 3.9 Derivatives of logarithmic and Exponential Functions
• 3.10 Derivatives of inverse Trigonometric Functions
• 3.11 Related rates
• Review Exercises
• 4 Applications of the derivative
• 4.1 Maxima and minima
• 4.2 What derivatives Tell us
• 4.3 Graphing Functions
• 4.4 Optimization Problems
• 4.5 Linear approximation and differentials
• 4.6 Mean Value Theorem
• 4.7 L’hôpital’s rule
• 4.8 Newton’s method
• 4.9 Antiderivatives
• Review Exercises
• 5 Integration
• 5.1 Approximating areas under curves
• 5.2 Definite integrals
• 5.3 Fundamental Theorem of calculus
• 5.4 Working with integrals
• 5.5 Substitution rule
• Review Exercises
• 6 Applications of integration
• 6.1 Velocity and net change
• 6.2 Regions between curves
• 6.3 Volume by slicing
• 6.4 Volume by shells
• 6.5 Length of curves
• 6.6 Surface area
• 6.7 Physical applications
• 6.8 Logarithmic and Exponential Functions revisited
• 6.9 Exponential models
• 6.10 Hyperbolic Functions
• Review Exercises
• 7 Integration Techniques
• 7.1 Basic approaches
• 7.2 Integration by Parts
• 7.3 Trigonometric integrals
• 7.4 Trigonometric substitutions
• 7.5 Partial Fractions
• 7.6 Other integration strategies
• 7.7 Numerical integration
• 7.8 Improper integrals
• 7.9 Introduction to differential Equations
• Review Exercises
• 8 Sequences and infinite series
• 8.1 An overview
• 8.2 Sequences
• 8.3 Infinite series
• 8.4 The divergence and integral Tests
• 8.5 The ratio, root, and comparison Tests
• 8.6 Alternating series
• Review Exercises
• 9 Power series
• 9.1 Approximating Functions with Polynomials
• 9.2 Properties of Power series
• 9.3 Taylor series
• 9.4 Working with Taylor series
• Review Exercises
• 10 Parametric and Polar curves
• 10.1 Parametric Equations
• 10.2 Polar coordinates
• 10.3 Calculus in Polar coordinates
• 10.4 Conic sections
• Review Exercises
• 11 Vectors and Vector-Valued Functions
• 11.1 Vectors in the Plane
• 11.2 Vectors in Three dimensions
• 11.3 Dot Products
• 11.4 Cross Products
• 11.5 Lines and curves in space
• 11.6 Calculus of Vector-Valued Functions
• 11.7 Motion in space
• 11.8 Length of curves
• 11.9 Curvature and normal Vectors
• Review Exercises
• 12 Functions of several Variables
• 12.1 Planes and surfaces
• 12.2 Graphs and level curves
• 12.3 Limits and continuity
• 12.4 Partial derivatives
• 12.5 The chain rule
• 12.6 Directional derivatives and the Gradient
• 12.7 Tangent Planes and linear approximation
• 12.8 Maximum/minimum Problems
• 12.9 Lagrange multipliers
• Review Exercises
• 13 Multiple integration
• 13.1 Double integrals over rectangular regions
• 13.2 Double integrals over General regions
• 13.3 Double integrals in Polar coordinates
• 13.4 Triple integrals
• 13.5 Triple integrals in cylindrical and spherical coordinates
• 13.6 Integrals for mass calculations
• 13.7 Change of Variables in multiple integrals
• Review Exercises
• 14 Vector calculus
• 14.1 Vector Fields
• 14.2 Line integrals
• 14.3 Conservative Vector Fields
• 14.4 Green’s Theorem
• 14.5 Divergence and curl
• 14.6 Surface integrals
• 14.7 Stokes’ Theorem
• 14.8 Divergence Theorem
• Review Exercises
• Appendix A Algebra review
• Appendix B Proofs of selected Theorems
• Answers
• Index
• A
• B
• C
• D
• E
• F
• G
• H
• I
• J
• K
• L
• M
• N
• O
• P
• Q
• R
• S
• T
• U
• V
• W
• X
• Y
• Z
• Table of integrals