MAT 425 -- Introduction to Real Analysis I 
Course Description

E-mail: bradley@gauss.umemat.maine.edu
Website: http://www.umemat.maine.edu/faculty/bradley/index.html

Text: Walter Rudin, "Principles of Mathematical Analysis ," (3rd ed.) McGraw-Hill, New York, 1976.

References:

• Ralph P. Boas, Jr., "A Primer of Real Functions," (4th ed. revised and updated by Harold P. Boas) Carus Mathematical Monographs 13, The Mathematical Association of America, 1996.
• Robert G. Bartle & Donald R. Sherbert, "Introduction to Real Analyis," (3rd ed.) John Wiley & Sons, New York, 2000.
• Jerrold E. Marsden, "Elementary Classical Analysis," W. H. Freeman and Company, New York, 1974.

Syllabus: Chapters 1-4 and 9 of Rudin. In slightly more detail:

• Euclidean Spaces
• Topology of Metric Spaces
• Continuity and connectedness
• Functions of Several Variables
• The Contraction Principle
• The Inverse Function Theorem
• The Implicit Function Theorem
• Higher Order Derivatives