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MA 141 - Analytic Geometry and Calculus I

Lecture 1

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Lecture Details :

Course Introduction
1.1 Four ways to represent a function
1.2 Mathematical Models
1.3 New Functions from Old (graph shifts, composite functions)

Course Description :

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 -

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