### Lecture 1:

##### Lecture Details :

Course Description:

Math 31A is a course that provides insight into differential calculus and applications as well as an introduction to integration.

About the Professor:

Steve Butler is a NSF Postdoctoral Scholar and Assistant Adjunct Professor of the UCLA Department of Mathematics. He received his Ph. D. from UCSD in June of 2008 and has been at UCLA since the Fall of 2008 (where he will be staying for a total of three years). His area of research consists of Combinatorics as well as particular spectral graph theory, combinatorial geometry, and recreational mathematics (i.e., juggling).

Course Webpage: http://www.math.ucla.edu/~butler/2010/math31a/

Professors Webpage: www.math.ucla.edu/~butler

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##### Course Description :

Introduction - Limit Laws, Limits and Continuity - Evaluating Limits Algebraically - Trigonometric Limits, Limits at Infinity - Intermediate Value Theorem - Definition of the Derivative - The Derivative as a Function - Product and Quotient Rules - Higher Derivatives, Trig Functions - The Chain Rule - Implicit Differentiation - Related Rates - Midterm - Linear Approximation, Extreme Values

Extreme Values continued - Mean Value Theorem - The Shape of a Graph - Graph Sketching - Applied Optimization - Newton's Method, Area - The Definite Integral - Midterm - The Indefinite Integral - Fundamental Theorem - The Substitution Method - Areas Between Curves, Average Value - Volumes of Revolution - Method of Cylindrical Shells

##### Other Resources

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