analysissyllabus - 5. Functions: sequences and series...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Topics for the Ph.D. Preliminary Examination ANALYSIS Fundamentals of Analysis (MAT 601-602) The basic material is contained in Rudin's "Principles of Mathematical Analysis" 3rd Edition, Chapters 1 through 9. Important topics are: 1. Properties of real and complex numbers. 2. Elementary topology of metric spaces: compactness, completeness, etc. 3. Numerical sequences and series. 4. Functions: continuity, differentiation, Riemann-Stieltjes integration.
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 5. Functions: sequences and series (uniform convergence and applications, equicontinuous families, Stone-Weierstrass Theorems, power series). 6. Calculus of several variables: differentiation, Inverse and Implicit Function Theorems. References 1. Rudin (listed above). 2. W. Flemming, "Functions of Several Variables"....
View Full Document

This note was uploaded on 06/19/2011 for the course MATH 600 taught by Professor Na during the Spring '11 term at University of North Carolina School of the Arts.

Ask a homework question - tutors are online