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This learning resource is built upon the online textbook, Calculus, vol 3, available free of charge from OpenStax University. The textbook material, itself, is provided in the PDF format. This means you should have a PDF reader, such as Acrobat Reader. It is available here for downloading, free of charge--tap the Acrobat Reader image to begin the installation process.

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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: Vector-Valued Functions

3.1 Vector-Valued Functions and Space Curves

3.2 Calculus of Vector-Valued 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 Greenís Theorem

6.5 Divergence and Curl

6.6 Surface Integrals

6.7 Stokesí Theorem

6.8 The Divergence Theorem

Chapter 7: Second-Order Differential Equations

7.1 Second-Order 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 Pre-Calculus




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David L. Heiserman, Editor

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Revised: June 06, 2015