Table of Contents
Preface
1 Limits
	1.1 An Introduction To Limits
	1.2 Epsilon-Delta Definition of a Limit
	1.3 Finding Limits Analytically
	1.4 One Sided Limits
	1.5 Continuity
	1.6 Limits Involving Infinity
2 Derivatives
	2.1 Instantaneous Rates of Change: The Derivative
	2.2 Interpretations of the Derivative
	2.3 Basic Differentiation Rules
	2.4 The Product and Quotient Rules
	2.5 The Chain Rule
	2.6 Implicit Differentiation
	2.7 Derivatives of Inverse Functions
3 The Graphical Behavior of Functions
	3.1 Extreme Values
	3.2 The Mean Value Theorem
	3.3 Increasing and Decreasing Functions
	3.4 Concavity and the Second Derivative
	3.5 Curve Sketching
4 Applications of the Derivative
	4.1 Newton's Method
	4.2 Related Rates
	4.3 Optimization
	4.4 Differentials
5 Integration
	5.1 Antiderivatives and Indefinite Integration
	5.2 The Definite Integral
	5.3 Riemann Sums
	5.4 The Fundamental Theorem of Calculus
	5.5 Numerical Integration
6 Techniques of Antidifferentiation
	6.1 Substitution
	6.2 Integration by Parts
	6.3 Trigonometric Integrals
	6.4 Trigonometric Substitution
	6.5 Partial Fraction Decomposition
	6.6 Hyperbolic Functions
	6.7 L'Hôpital's Rule
	6.8 Improper Integration
7 Applications of Integration
	7.1 Area Between Curves
	7.2 Volume by Cross-Sectional Area; Disk and Washer Methods
	7.3 The Shell Method
	7.4 Arc Length and Surface Area
	7.5 Work
	7.6 Fluid Forces
8 Sequences and Series
	8.1 Sequences
	8.2 Infinite Series
	8.3 Integral and Comparison Tests
	8.4 Ratio and Root Tests
	8.5 Alternating Series and Absolute Convergence
	8.6 Power Series
	8.7 Taylor Polynomials
	8.8 Taylor Series
9 Curves in the Plane
	9.1 Conic Sections
	9.2 Parametric Equations
	9.3 Calculus and Parametric Equations
	9.4 Introduction to Polar Coordinates
	9.5 Calculus and Polar Functions
10 Vectors
	10.1 Introduction to Cartesian Coordinates in Space
	10.2 An Introduction to Vectors
	10.3 The Dot Product
	10.4 The Cross Product
	10.5 Lines
	10.6 Planes
11 Vector Valued Functions
	11.1 Vector–Valued Functions
	11.2 Calculus and Vector–Valued Functions
	11.3 The Calculus of Motion
	11.4 Unit Tangent and Normal Vectors
	11.5 The Arc Length Parameter and Curvature
12 Functions of Several Variables
	12.1 Introduction to Multivariable Functions
	12.2 Limits and Continuity of Multivariable Functions
	12.3 Partial Derivatives
	12.4 Differentiability and the Total Differential
	12.5 The Multivariable Chain Rule
	12.6 Directional Derivatives
	12.7 Tangent Lines, Normal Lines, and Tangent Planes
	12.8 Extreme Values
13 Multiple Integration
	13.1 Iterated Integrals and Area
	13.2 Double Integration and Volume
	13.3 Double Integration with Polar Coordinates
	13.4 Center of Mass
	13.5 Surface Area
	13.6 Volume Between Surfaces and Triple Integration
	13.7 Triple Integration with Cylindrical and Spherical Coordinates
14 Vector Analysis
	14.1 Introduction to Line Integrals
	14.2 Vector Fields
	14.3 Line Integrals over Vector Fields
	14.4 Flow, Flux, Green's Theorem and the Divergence Theorem
	14.5 Parametrized Surfaces and Surface Area
	14.6 Surface Integrals
	14.7 The Divergence Theorem and Stokes' Theorem
A Solutions To Selected Problems
Index