Calculus Volume 2

Preface
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