Calculus Volume 1

Description

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 CalculusVolume1.pdf Blank Page