MA 131 – Calculus for Life and Management Sciences A

North Carolina State University , Prof.Marilyn McCollum

LECTURE1 :

Lecture #1

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Lecture Description

Overview of the course Supplements (not textbook): 10.1 Intro to Differential Equations 10.2 Solutions to Differential Equations

Course Description

Introduction to Differential Equations – Graphing by plotting points and analysis – Review slopes of lines and equations of lines – Intro to the derivative: slope of a curve at a point – Slopes of curves at points – The derivative: Notations, Rules Power Rule – Limits and the limit definition of the derivative – Continuity and differentiability at a point – More rules for derivatives – Derivatives as a rate of change – Describing graphs using words and derivaives – Using Derivatives for Curve Sketching – Optimization – Product and Quotient Rule for finding the derivative – Optimization: Geometric, Inventory, Business and Economics – Geometric,Inventory,Business and Economics – Exponential Functions – Derivative of f(x) = ex – Chain Rule for derivatives – Derivatives of y = e u where u = f(x) – Natural Logarithms – Derivative y = ln x – Applications of the Natural Exponential Function – ntidifferentiation – Integration – Riemann Sums and the Definite Integral – Consumer’s and Producer’s Surplus – Future Value of a Continuous Stream – Present value of a Continuous Stream

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