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Chapter 1: Functions
1.1 Review of Functions
1.2 Representing Functions
1.3 Inverse, Exponential, and Logarithm Functions
1.4 Trigonometric Functions and Their Inverses
Chapter 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
Chapter 3: Derivatives
3.1 Introducing the Derivative
3.2 Rules of Differentiation
3.3 The Product and Quotient Rules
3.4 Derivatives of Trigonometric Functions
3.5 Derivatives as Rates of Change
3.6 The Chain Rule
3.7 Implicit Differentiation
3.8 Derivatives of Logarithmic and Exponential Functions
3.9 Derivatives of Inverse Trigonometric Functions
3.10 Related Rates
Chapter 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 Antiderivatives
Chapter 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
Chapter 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 Physical Applications
Chapter 7: Integration Techniques
7.1 Integration by Parts
7.2 Trigonometric Integrals
7.3 Trigonometric Substitution
7.4 Partial Fractions
7.5 Other Integration Strategies
7.6 Numerical Integration
7.7 Improper Integrals
7.8 Introduction to Differential Equations
Chapter 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 and Comparison Tests
8.6 Alternating Series
Chapter 9: Power Series
9.1 Approximating Functions with Polynomials
9.2 Power Series
9.3 Taylor Series
9.4 Working with Taylor Series
Chapter 10: Parametric and Polar Curves
10.1 Parametric Equations
10.2 Polar Coordinates
10.3 Calculus in Polar Coordinates
10.4 Conic Sections
Chapter 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
Chapter 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
Chapter 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
Chapter 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
14.6 Stokes’ Theorem
14.8 Divergence Theorem
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The Used, Rental and eBook copies of this book are not guaranteed to include any supplemental materials. Typically, only the book itself is included. This is true even if the title states it includes any access cards, study guides, lab manuals, CDs, etc.
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