Calculus Volume 1

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