Review Course for Entering Mathematics Graduate Students at UCLA, August 2008 --Analysis Section

Professor Robert E. Greene

Monday-Thursday: 10:15 am-noon in MS6627

Summary of Lecture 1 --Monday,August 11--and exercises

Summary of Lecture 2--Tuesday, August 12

Summary of Lecture 3--Wednesday,August 13

Summary of Lecture 4--Thursday,August 14

Summary of Lecture 5--Monday,August 18

Here is your first HW assignment. It is due on Monday August 25.

Summary of Lecture 6--Tuesday,August 19

Supplementary notes for Lecture 6

Summary of Lecture 7--Wednesday,August 20

Here is your second HW assignment.

Summary of Lecture 8--Power Series and Taylor Expansion

Here are some misc. exercises for you to work on.

Summary of Lecture 9--Differentiability of Functions of Several Variables

Summary of Lecture 10--Inverse Function Theorem

Summary of Lecture 11--Inverse Function Theorem Examples and Equality of mixed partials

Summary of Lecture 12--Line Integrals, Independence of Path , Related Topics , Vector Calculus

A Baire Category Theorem Example: Supplementary Material

Here is your third HW assignment.

Lagrange Multipliers

Weierstrass Approximation Theorem

Simpsons Rule

Sample Basic Examination Analysis Solutions

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