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Table of Contents
Chapter 1: Parametric Equations and Polar Coordinates
1.1 Parametric Equations
1.2 Calculus of Parametric Curves
1.3 Polar Coordinates
1.4 Area and Arc Length in Polar Coordinates
1.5 Conic Sections
Chapter 2: Vectors in Space
2.1 Vectors in the Plane
2.2 Vectors in Three Dimensions
2.3 The Dot Product
2.4 The Cross Product
2.5 Equations of Lines and Planes in Space
2.6 Quadric Surfaces
2.7 Cylindrical and Spherical Coordinates
Chapter 3: VectorValued Functions
3.1 VectorValued Functions and Space Curves
3.2 Calculus of VectorValued Functions
3.3 Arc Length and Curvature
3.4 Motion in Space
Chapter 4: Differentiation of Functions of Several Variables
4.1 Functions of Several Variables
4.2 Limits and Continuity
4.3 Partial Derivatives
4.4 Tangent Planes and Linear Approximations
4.5 The Chain Rule
4.6 Directional Derivatives and the Gradient
4.7 Maxima/Minima Problems
4.8 Lagrange Multipliers
Chapter 5: Multiple Integration
5.1 Double Integrals over Rectangular Regions
5.2 Double Integrals over General Regions
5.3 Double Integrals in Polar Coordinates
5.4 Triple Integrals
5.5 Triple Integrals in Cylindrical and Spherical Coordinates
5.6 Calculating Centers of Mass and Moments of Inertia
5.7 Change of Variables in Multiple Integrals
Chapter 6: Vector Calculus
6.1 Vector Fields
6.2 Line Integrals
6.3 Conservative Vector Fields
6.4 Green’s Theorem
6.5 Divergence and Curl
6.6 Surface Integrals
6.7 Stokes’ Theorem
6.8 The Divergence Theorem
Chapter 7: SecondOrder Differential Equations
7.1 SecondOrder Linear Equations
7.2 Nonhomogeneous Linear Equations
7.3 Applications
7.4 Series Solutions of Differential Equations
Appendix A: Table of Integrals
Appendix B: Table of Derivatives
Appendix C: Review of PreCalculus
Index
