Math 131 Calculus I List of Topics

The sections listed below are from the Stewart text.

• 2.1. The tangent and velocity problems
• 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; see also 1.5
• 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; see also 1.6
• 3.7. Rates of change in the natural and social sciences
• 3.8. Exponential growth and decay
• 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
• 4.7. Optimization problems
• 4.8. Newton's Method
• 4.9. Antiderivatives
• 5.1. Areas and distances
• 5.2. The definite integral