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
	Blank Page