Calculus Volume 3

Preface
1. About OpenStax
2. About OpenStax's resources
3. About Calculus Volume 3
4. Additional resources
5. About the authors
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*
Glossary
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*
Glossary
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*
Glossary
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*
Glossary
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*
Glossary
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*
Glossary
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*
Glossary
Appendix A. Table of Integrals*
A.1. Basic Integrals
A.2. Trigonometric Integrals
A.3. Exponential and Logarithmic Integrals
A.4. Hyperbolic Integrals
A.5. Inverse Trigonometric Integrals
A.6. Integrals Involving a2 + u2, a > 0
A.7. Integrals Involving u2 − a2, a > 0
A.8. Integrals Involving a2 − u2, a > 0
A.9. Integrals Involving 2au − u2, a > 0
A.10. Integrals Involving a + bu, a ≠ 0
Appendix B. Table of Derivatives*
B.1. General Formulas
B.2. Trigonometric Functions
B.3. Inverse Trigonometric Functions
B.4. Exponential and Logarithmic Functions
B.5. Hyperbolic Functions
B.6. Inverse Hyperbolic Functions
Appendix C. Review of Pre-Calculus*
C.1. Formulas from Geometry
C.2. Formulas from Algebra
C.3. Formulas from Trigonometry
Solutions
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Index
CalculusVolume3.pdf
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