Calculus Volume 2

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
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