Calculus Volume 2

• Preface
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• Appendix A: Table of Integrals
• Appendix B: Table of Derivatives
• Appendix C: Review of Pre-Calculus