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chapter one FUNCTIONS
1.1 Functions
1.2 Arithmetic Operations on and Composition of Functions
1.3 Families of Functions
1.4 Inverse Functions; Inverse Trigonometric Functions
1.5 Exponential and Logarithmic Functions
1.6 Parametric Equations
chapter two LIMITS AND CONTINUITY
2.1 Limits(An Intuitive Approach)
2.2 Computing Limits
2.3 Limits at Infinity; End Behavior of a Function
2.4 Limits (Discussed More Rigorously)
2.5 Continuity
2.6 Continuity of Trigonometric and Inverse Functions
chapter three THE DERIVATIVE
3.1 Tangent Lines, Velocity, and General Rates of Change
3.2 The Derivative Function
3.3 Techniques of Differentiation
3.4 The Product and Quotient Rules
3.5 Derivatives of Trigonometric Functions
3.6 The Chain Rule
3.7 Related Rates
3.8 Local Linear Approximation; Differentials
chapter four DERIVATIVES OF LOGARITHMIC, EXPONENTIAL, AND INVERSE TRIGONOMETRIC FUNCTIONS
4.1 Implicit Differentiation
4.2 Derivatives of Logarithmic Functions
4.3 Derivatives of Exponential and Inverse Trigonometric Functions
4.4 L’H pital’s Rule; Indeterminate Forms
chapter five THE DERIVATIVE IN GRAPHING AND APPLICATIONS
5.1 Analysis of Functions I: Increase, Decrease, and Concavity
5.2 Analysis of Functions II: Relative Extrema
5.3 More on Curve Sketching: Rational Functions; Curves with Cusps and Vertical Tangent Lines; Using Technology
5.4 Absolute Maxima and Minima
5.5 Applied Maximum and Minimum Problems
5.6 Rolle’s Theorem; Mean-Value Theorem
chapter six INTEGRATION
6.1 An Overview of the Area Problem
6.2 The Indefinite Integral
6.3 Integration by Substitution
6.4 The Definition of Area as a Limit
6.5 The Definite Integral
6.6 The Fundamental Theorem of Calculus
6.7 Evaluating Definite Integrals by Substitution
6.8 Logarithmic Functions from the Integral Point of View
chapter seven APPLICATIONS OF THE DEFINITE INTEGRAL IN GEOMETRY AND ENGINEERING
7.1 Area Between Two Curves
7.2 Volumes by Slicing; Disks and Washers
7.3 Volumes by Cylindrical Shells
7.4 Length of a Plane Curve
7.5 Work
7.6 Fluid Pressure and Force
chapter eight PRINCIPLES OF INTEGRAL EVALUATION
8.1 Integration by Parts
8.2 Trigonometric Integrals
8.3 Trigonometric Substitutions
8.4 Integrating Rational Functions by Partial Fractions
8.5 Improper Integrals
chapter nine MATHEMATICAL MODELING WITH DIFFERENTIAL EQUATIONS
9.1 First-Order Differential Equations and Applications
9.2 Modeling with First-Order Differential Equations
9.3 Second-Order Linear Homogeneous Differential Equations; The Vibrating Spring
chapter ten INFINITE SERIES
10.1 Sequences
10.2 Monotone Sequences
10.3 Infinite Series
10.4 Convergence Tests
10.5 The Comparison, Ratio, and Root Tests
10.6 Alternating Series; Conditional Convergence
10.7 Maclaurin and Taylor Polynomials
10.8 Maclaurin and Taylor Series; Power Series
10.9 Convergence of Taylor Series
10.10 Differentiating and Integrating Power Series
chapter eleven THREE-DIMENSIONAL SPACE; VECTORS
11.1 Rectangular Coordinates in 3-Space; Spheres; Cylindrical Surfaces
11.2 Vectors
11.3 Dot Product; Projections
11.4 Cross Product
11.5 Parametric Equations of Lines
11.6 Planes in 3-Space
11.7 Quadric Surfaces
11.8 Cylindrical and Spherical Coordinates
chapter twelve VECTOR-VALUED FUNCTIONS
12.1 Introduction to Vector-Valued Functions
12.2 Calculus of Vector-Valued Functions
chapter thirteen PARTIAL DERIVATIVES
13.1 Functions of Two or More Variables
13.2 Limits and Continuity
13.3 Partial Derivatives
13.4 Differentiability, Differentials, and Local Linearity
13.5 The Chain Rule
13.6 Directional Derivatives and Gradients
13.7 Tangent Planes and Normal Vectors
13.8 Maxima and Minima of Functions of Two Variables
13.9 Lagrange Multipliers
chapter fourteen MULTIPLE INTEGRALS
14.1 Double Integrals
14.2 Double Integrals over Nonrectangular Regions
14.3 Double Integrals in Polar Coordinates
14.4 Parametric Surfaces; Surface Area
14.5 Triple Integrals
14.6 Triple Integrals in Cylindrical and Spherical Coordinates
14.7 Change of Variables in Double Integrals; Jacobians
chapter fifteen TOPICS IN VECTOR CALCULUS
15.1 Vector Fields
15.2 Line Integrals
15.3 Independence of Path; Conservative Vector Fields
15.4 Green’s Theorem
15.5 Surface Integrals
15.6 Applications of Surface Integrals; Flux
15.7 The Divergence Theorem
15.8 Stokes’ Theorem
appendix
SELECTED PROOFS
ANSWERS TO SELECTED EXERCISES
GLOSSARY
