Purpose/Expectations: Graduate courses in functional analysis are extremely necessary. The main objective is to provide mathematics majors with an introduction to the theory of normed linear spaces, Hilbert spaces and linear operators through applications. Students will become knowledgeable about these spaces and some fundamental theorems of functional analysis. The course will also develop an understanding of the Open and Closed graph theorems.
Students are expected to attend every lecture. In order to fully benefit from the course, students should start doing homework and assignments. The entire syllabus will be covered approximately in 39 lectures as per schedule given below.
Text and References:
[Kreyszig] Erwin Kreyszig, Introductory Functional Analysis with Applications, Wiley, 2007.
[Kesavan] S. Kesavan, Functional Analysis, Hindustan Book Agency, 2014.
[Conway] John B. Conway, A course in Functional Analysis, Springer, 2nd edition, 1990.
Course Learning Outcomes (CLOs):
Upon completion of this course, the students will be able to:
understand the normed linear spaces, Banach space and Dual spaces.
Understand inner product spaces, orthogonality and Hillbert spaces.
distinguish between finite and infinite dimensional spaces.
apply linear operators in the formulation of differential and integral equations.