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Outline of MA 111 (4/29/09)

Outline of MA 111 (4/29/09). Pre-Calculus – Functions Different ways to represent functions New functions from old

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Outline of MA 111 (4/29/09)

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  1. 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)

  2. 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 • 2nd derivatives and concavity • Differentiability • Implicit differentiation

  3. 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

  4. 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

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