Course Syllabus



The topics, presented in this class, are taught with an emphasis on their applicability. Topics covered include: linear spaces, normed spaces, Banach spaces, Hilbert spaces, linear operators on normed spaces, adjoint operators, compact operators, approximation theory, Fourier analysis, Banach fixed-point theorem, and Sobolev spaces.

This is a five (5) credit course.

An undergraduate course on real analysis or advanced calculus is required. Review of undergraduate material will be limited. Students are expected to be familiar with the contents in these books:
  • A. Taylor and W. Mann, Advanced calculus, Wiley, 3rd edition, 1983;
  • T. Apostol, Mathematical analysis, Addison Wesley, 2nd edition, 1974 (except Chapters 10, 11, and 15).


  • E. Kreyszig, Introductory functional analysis with applications, Wiley, 1st edition, 1989 (ISBN-13: 978-0471504597).


This class is a five (5) credit course. The average workload is 15 hours a week including class time (3 hours a week per credit hour). Class time amounts to 3 hours a week. Consequently, students are expected to spend, on average, 12 hours per week of outside contact with the material.