ANALYSIS II
Math 555
Spring 1998

Professor: Bob Sharpley
Office: 313D LeConte
Office Hours: MW 4 p.m. or appointment.

Course Materials:

• General Reference
1. Real Analysis, A First Course, by Russell A. Gordon, Addision-Wesley Higher Mathematics Series, Reading, MA, 1997.
• Supplementary materials
1. Principles of Real Analysis (3 ^rd ed.), by Walter Rudin, McGraw-Hill, 1976.
2. http://www.math.sc.edu/~sharpley/math555

Grading:

The course grade is computed from 3 Test grades (20% each), Homework (10%) and the Final Exam (30%).

Course Content

The course will cover the topics contained in the last three chapters of the text:

• Introduction to Metric Spaces
• Special Functions (exponential, logarithmic, trignometric functions, ...and their inverses)
• Infinite series (convergence tests)
• Sequences and Series of functions (for example, C[a,b] is a complete metric space.)
• Interchange of Limit Operations

Additional topics will be drawn from several sources (primarily Rudin and lecture notes) and will include:

• Riemann-Stieltjes Integration
• Weierstrass Approximation Theorem
• Picard Fixed Point Theorem
• Existence/Uniqueness of ODE
• Ascoli's Theorem

If time permits, we will also cover introductory material to

• Fourier Series and Existence/Uniqueness of solutions of elliptic and parabolic PDE.