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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