Calculus Volume 2 2

Calculus is designed for the typical two- or three-semester general calculus course, incorporating innovative features to enhance student learning. The book guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them. Due to the comprehensive nature of the material, we are offering the book in three volumes for flexibility and efficiency. Volume 2 covers integration, differential equations, sequences and series, and parametric equations and polar coordinates. Please note that this title is published under a CC BY-NC-SA 4.0 license, which means that you are free to use and adapt, but not for commercial purposes. Changes you make need to be shared using this license. Preface 1. About OpenStax 2. About OpenStax's Resources 3. About Calculus Volume 2 4. Additional Resources 5. About The Authors Chapter 1. Integration 1.1. Approximating Areas* 1.2. The Definite Integral* 1.3. The Fundamental Theorem of Calculus* 1.4. Integration Formulas and the Net Change Theorem* 1.5. Substitution* 1.6. Integrals Involving Exponential and Logarithmic Functions* 1.7. Integrals Resulting in Inverse Trigonometric Functions* Glossary Chapter 2. Applications of Integration 2.1. Areas between Curves* 2.2. Determining Volumes by Slicing* 2.3. Volumes of Revolution: Cylindrical Shells* 2.4. Arc Length of a Curve and Surface Area* 2.5. Physical Applications* 2.6. Moments and Centers of Mass* 2.7. Integrals, Exponential Functions, and Logarithms* 2.8. Exponential Growth and Decay* 2.9. Calculus of the Hyperbolic Functions* Glossary Chapter 3. Techniques of Integration 3.1. Integration by Parts* 3.2. Trigonometric Integrals* 3.3. Trigonometric Substitution* 3.4. Partial Fractions* 3.5. Other Strategies for Integration* 3.6. Numerical Integration* 3.7. Improper Integrals* Glossary Chapter 4. Introduction to Differential Equations 4.1. Basics of Differential Equations* 4.2. Direction Fields and Numerical Methods* 4.3. Separable Equations* 4.4. The Logistic Equation* 4.5. First-order Linear Equations* Glossary Chapter 5. Sequences and Series 5.1. Sequences* 5.2. Infinite Series* 5.3. The Divergence and Integral Tests* 5.4. Comparison Tests* 5.5. Alternating Series* 5.6. Ratio and Root Tests* Glossary Chapter 6. Power Series 6.1. Power Series and Functions* 6.2. Properties of Power Series* 6.3. Taylor and Maclaurin Series* 6.4. Working with Taylor Series* Glossary Chapter 7. Parametric Equations and Polar Coordinates 7.1. Parametric Equations* 7.2. Calculus of Parametric Curves* 7.3. Polar Coordinates* 7.4. Area and Arc Length in Polar Coordinates* 7.5. Conic Sections* 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 Calculus Vol 2.pdf Blank Page "Calculus is designed for the typical two- or three-semester general calculus course, incorporating innovative features to enhance student learning. The book guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them. Due to the comprehensive nature of the material, we are offering the book in three volumes for flexibility and efficiency. Volume 2 covers integration, differential equations, sequences and series, and parametric equations and polar coordinates."-- OpenStax, Rice University "Calculus is designed for the typical two- or three-semester general calculus course, incorporating innovative features to enhance student learning. The book guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them. Due to the comprehensive nature of the material, we are offering the book in three volumes for flexibility and efficiency. Volume 2 covers integration, differential equations, sequences and series, and parametric equations and polar coordinates."--Open Textbook Library Calculus is designed for the typical two- or three-semester general calculus course, incorporating innovative features to enhance student learning. The book guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them. -- Provided by publisher