MAT 164 - Calculus for Busn/Social Sci

1. Perform basic operations with numbers, functions, and graphs
   1. Graph elementary equations
   2. Find distances in the plane
   3. Graph special types of functions
   4. Add, subtract, multiply, and divide elementary functions
   5. Find the composite of two functions
2. Establish the limit of a function
   1. Find the slope of a curve at a specific point
   2. Calculate the limit of a function at a specific point
   3. Define continuity
   4. Calculate one-sided limits
   5. Calculate limits at infinity
3. Differentiate functions
   1. Define the derivative for real-valued functions of one real variable
   2. Calculate the derivative of certain elementary functions directly from the definition
   3. Calculate derivatives using various elementary rules: sum, product, quotient, power, etc
   4. Calculate derivatives using the Chain Rule
   5. Compute derivatives by the method of implicit differentiation
4. Apply the derivative
   1. Locate Increasing and Decreasing Functions
   2. Discuss the concavity of a function
   3. Find any relative extrema of a function
   4. Find any absolute extrema of a function
   5. Sketch many general functions
   6. Solve general applied Maximum-Minimum problems
   7. Set up and solve applications to Economics and Business
   8. Set up and solve related rate problems
   9. Apply the mean value theorem
5. Calculate the indefinite and definite integrals
   1. Calculate indefinite integrals for elementary functions
   2. Use indefinite integrals to calculate definite integrals
   3. Calculate definite and indefinite integrals by substitution
6. Apply the integral
   1. Find areas by integration
   2. Apply the definite integral to economics and business
   3. Find volumes by integration
7. Solve problems involving exponential and logarithmic functions
   1. Differentiate both exponential and logarithmic functions
   2. Integrate both exponential and logarthmic functions
   3. Solve exponential growth and decay problems