Calculus Volume 1

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
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