V.  OUTLINE

The material will cover chapters 1-5 of the text.

1. Introduction
   1. Course requirements
   2. Grading

2. Preliminaries
   1. Real numbers
   2. Functions
   3. Trigonometry

3. Limits
   1. Rules for finding limits
   2. Formal definition of a limit
   3. Continuity
   4. Tangent lines

4. Derivatives
   1. Tangent
   2. Differentiation Rules
   3. Rates of change
   4. Trigonometric Functions
   5. Chain Rule
   6. Implicit Differentiation

5. Applications of Derivatives
   1. Related rates of change
   2. Extreme values
   3. Asymptotes
   4. Optimization
   5. Linearization
   6. Differentials
   7. Newton's Method

6. Integration
   1. Indefinite Integrals
   2. Integration by substitution
   3. Differential Equations
   4. Riemann Sums
   5. Definite Integrals
   6. Mean Value Theorem
   7. Fundamental Theorem of Calculus
   8. Numerical Integration

7. Applications
   1. Areas between curves
   2. Finding volumes
      1. slicing
      2. disks and washers
      3. cylindrical shells
   3. Lengths of plane curves
   4. Moments and center of mass
   5. Physics
      1. work
      2. pressures and forces