Calculus Volume 1

Description

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 1 covers functions, limits, derivatives, and integration. 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 1 4. Additional resources 5. About the authors Chapter 1. Functions and Graphs 1.1. Review of Functions* 1.2. Basic Classes of Functions* 1.3. Trigonometric Functions* 1.4. Inverse Functions* 1.5. Exponential and Logarithmic Functions* Glossary Chapter 2. Limits 2.1. A Preview of Calculus* 2.2. The Limit of a Function* 2.3. The Limit Laws* 2.4. Continuity* 2.5. The Precise Definition of a Limit* Glossary Chapter 3. Derivatives 3.1. Defining the Derivative* 3.2. The Derivative as a Function* 3.3. Differentiation Rules* 3.4. Derivatives as Rates of Change* 3.5. Derivatives of Trigonometric Functions* 3.6. The Chain Rule* 3.7. Derivatives of Inverse Functions* 3.8. Implicit Differentiation* 3.9. Derivatives of Exponential and Logarithmic Functions* Glossary Chapter 4. Applications of Derivatives 4.1. Related Rates* 4.2. Linear Approximations and Differentials* 4.3. Maxima and Minima* 4.4. The Mean Value Theorem* 4.5. Derivatives and the Shape of a Graph* 4.6. Limits at Infinity and Asymptotes* 4.7. Applied Optimization Problems* 4.8. L’Hôpital’s Rule* 4.9. Newton’s Method* 4.10. Antiderivatives* Glossary Chapter 5. Integration 5.1. Approximating Areas* 5.2. The Definite Integral* 5.3. The Fundamental Theorem of Calculus* 5.4. Integration Formulas and the Net Change Theorem* 5.5. Substitution* 5.6. Integrals Involving Exponential and Logarithmic Functions* 5.7. Integrals Resulting in Inverse Trigonometric Functions* Glossary Chapter 6. Applications of Integration 6.1. Areas between Curves* 6.2. Determining Volumes by Slicing* 6.3. Volumes of Revolution: Cylindrical Shells* 6.4. Arc Length of a Curve and Surface Area* 6.5. Physical Applications* 6.6. Moments and Centers of Mass* 6.7. Integrals, Exponential Functions, and Logarithms* 6.8. Exponential Growth and Decay* 6.9. Calculus of the Hyperbolic Functions* 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 Index CalculusVolume1.pdf Blank Page