MA 141 - Analytic Geometry and Calculus I

Overview

Introduction - Four ways to represent a function - Mathematical Models - New Functions from Old - graph shifts, composite functions - Mathematical Models - polynomials, asymptotes, intercepts, power, log, transcendental - Lines, Circles - Conic Sections - Exponential Functions - hyperbolic - Inverse Functions and Logs - Parametric Curves (plotting, eliminating t, cycloid) - Tangent and Velocity problems (Secant and Tangent slopes) - The limit of a function - Squeeze Theorem - Continuity - Limits Involving Infinity - Derivatives - Derivatives of Trigonometric Functions - Chain Rule - Implicit Differentiation - Orthogonal Trajectories - Derivatives of Logarithmic Functions - Linear Approximation and Derivatives - Maximum and Minimum Values - Derivative and the Shapes of Curves - Newton's Method - Antiderivatives - Areas and Distance - Definite Integral - Evaluating Definite Integrals - The substitution Rule - Partial Fractions when Numerator is greater than Denominator - Trigonometric Integrals -