Outline of MA 111 (4/29/09) Pre-Calculus – Functions Different ways to represent functions New functions from old Elementary functions: algebraic (power functions, polynomials, rational functions) and transcendental functions (exponential and log functions, trig functions, inverse trig functions)

Outline continued Calculus – Limits and the Derivative Concept of limit; limits of functions Definition of the derivative as a limit Calculating Derivatives: The Facts and the Rules 2 nd derivatives and concavity Differentiability Implicit differentiation

Outline continued Applications of the Derivative: Rates of change in natural & social science Exponential growth and decay Critical points, extrema, inflection points Optimization problems Related rate problems

Outline continued Definite Integrals and Antiderivatives Concept and calculation of antiderivatives (most general and specific, given an initial condition) The definite integral of a function on an interval and connection to areas Approximating definite integrals via Riemann sums (rectangles and trapezoids) Finding exact definite integrals via the Fundamental Theorem of Calculus Part 1 Manufacturing antiderivatives via FTC Part 2 Average value (height) of a function on an interval