Calculus

Description

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