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Contents
Sequences and Infinite Series
10.1 An Overview
10.2 Sequences
10.3 Infinite Series
10.4 The Divergence and Integral Tests
10.5 Comparison Tests
10.6 Alternating Series
10.7 The Ratio and Root Tests
10.8 Choosing a Convergence Test
Review Exercises
Power Series
11.1 Approximating Functions with Polynomials
11.2 Properties of Power Series
11.3 Taylor Series
11.4 Working with Taylor Series
Review Exercises
Parametric and Polar Curves
12.1 Parametric Equations
12.2 Polar Coordinates
12.3 Calculus in Polar Coordinates
12.4 Conic Sections
Review Exercises
Vectors and the Geometry of Space
13.1 Vectors in the Plane
13.2 Vectors in Three Dimensions
13.3 Dot Products
13.4 Cross Products
13.5 Lines and Planes in Space
13.6 Cylinders and Quadric Surfaces
Review Exercises
Vector-Valued Functions
14.1 Vector-Valued Functions
14.2 Calculus of Vector-Valued Functions
14.3 Motion in Space
14.4 Length of Curves
14.5 Curvature and Normal Vectors
Review Exercises
Functions of Several Variables
15.1 Graphs and Level Curves
15.2 Limits and Continuity
15.3 Partial Derivatives
15.4 The Chain Rule
15.5 Directional Derivatives and the Gradient
15.6 Tangent Planes and Linear Approximation
15.7 Maximum/Minimum Problems
15.8 Lagrange Multipliers
Review Exercises
Multiple Integration
16.1 Double Integrals over Rectangular Regions
16.2 Double Integrals over General Regions
16.3 Double Integrals in Polar Coordinates
16.4 Triple Integrals
16.5 Triple Integrals in Cylindrical and Spherical Coordinates
16.6 Integrals for Mass Calculations
16.7 Change of Variables in Multiple Integrals
Review Exercises
Vector Calculus
17.1 Vector Fields
17.2 Line Integrals
17.3 Conservative Vector Fields
17.4 Green's Theorem
17.5 Divergence and Curl
17.6 Surface Integrals
17.7 Stokes' Theorem
17.8 Divergence Theorem
Review Exercises
D2 Second-Order Differential Equations ONLINE
D2.1 Basic Ideas
D2.2 Linear Homogeneous Equations
D2.3 Linear Nonhomogeneous Equations
D2.4 Applications
D2.5 Complex Forcing Functions
Review Exercises
Appendices
A. Proofs of Selected Theorems
B. Algebra Review ONLINE
C. Complex Numbers ONLINE
Answers
Index
Table of Integrals
