第一章 Functions and Model

• 1.5 Exponential Functions
  1.6 Inverse Functions and Logarithms

• 2.2 The Limit of a Function
  2.3 Calculating Limits Using the Limit Laws
  2.4 The Precise Definition of a Limit
  2.5 Continuity
  2.6 Limits at Infinity; Horizontal Asymptotes
  2.7 Derivatives and Rates of Change
  2.8 The Derivative as a Function

• 3.1 Derivatives of Polynomials and Exponential Functions
  3.2 The Product and Quotient Rules
  3.3 Derivatives of Trigonometric Functions
  3.4 The Chain Rule
  3.5 Implicit Differentiation
  3.6 Derivatives of Logarithmic Functions
  3.9 Related Rates
  3.10 Linear Approximations and Differentials

• 4.1 Maximum and Minimum Values
  4.2 The Mean Value Theorem
  4.3 How Derivatives Affect the Shape of a Graph
  4.4 Indeterminate Forms and L’Hospital’s Rule
  4.5 Summary of Curve Sketching
  4.7 Optimization Problems
  4.9 Antiderivatives

• 5.1 Areas and Distances
  5.2 The Definite Integral
  5.3 The Fundamental Theorem of Calculus
  5.4 Indefinite Integrals and the Net Change Theorem
  5.5 The Substitution Rule

• 6.1 Areas between Curves
  6.2 Volumes
  6.3 Volumes by Cylindrical Shells
  6.5 Average Value of a Function

• 7.1 Integration by Parts
  7.2 Trigonometric Integrals
  7.3 Trigonometric Substitution
  7.4 Integration of Rational Functions by Partial Fractions
  7.7 Approximate Integration
  7.8 Improper Integrals

• 8.1 Arc Length
  8.2 Area of a Surface of Revolution
  8.5 Probability

• 10.1 Curves Defined by Parametric Equations
  10.2 Calculus with Parametric Curves