# Course Syllabus

Math 113 - Elements of Calculus, Section 4

Fall 2006

### Chapters

## Chapter 1: Functions, Graphs and Limits

- The Cartesian Plane and the Distance Formula
- Graphs of Equations
- Lines in the Plane and Slope
- Functions
- Limits
- Continuity

## Chapter 2: Differentiation

- The Derivative and the Slope of a Graph
- Some Rules for Differentiation
- Rates of Change: Velocity and Marginals
- The Product and Quotient Rules
- The Chain Rule
- Higher-Order Derivatives
- Implicit Differentiation
- Related Rates

## Chapter 3: Applications of the Derivative

- Increasing and Decreasing Functions
- Extrema and the First Derivative Test
- Concavity and the Second Derivative Test
- Optimization Problems
- Asymptotes
- Curve Sketching: A Summary

## Chapter 4: Exponential and Logarithmic Functions

- Exponential Functions
- Natural Exponential Functions
- Derivatives of Exponential Functions
- Logarithmic Functions
- Derivatives of Logarithmic Functions
- Exponential Growth and Decay

## Chapter 5: Integration and its Applications

- Antiderivatives and Indefinite Integrals
- The General Power Rule
- Exponential and Logarithmic Integrals
- Area and the Fundamental Theorem of Calculus
- The Area of a Region Bounded by Two Graphs

## Chapter 6: Techniques of Integration

- Integration by Substitution
- Integration by Parts
- Improper Integrals