Instructor : Chandan Biswas
Office : 202 F, Mathematics Department
Office Phone : +91 2225767485
Email : cbiswas@iitb.ac.in (if you don't hear back within 48 hours please send a reminder)
Schedule : The class meets twice a week, Tuesday/Friday, 5:30 - 6:55 pm.
Office Hours : Tuesday and Friday, 5 - 5:30 pm.
TA office hours : Soumyadeb Samanta, Monday, 11:30 -12;30 pm, RS201, Table 12
Repana Devendra, Wednesday, 4 - 5pm, B2, Lower ground floor, Math dept.
Tutorial : Wednesday 2 - 3 pm.
Textbook : Functional Analysis (second edition) by Walter Rudin.
We will closely follow this book and many of the homework problems will be assigned from this book. You are also encouraged to refer to the following other standard books as well.
J.B. Conway, A Course in Functional Analysis, 2nd Edition, Springer, Berlin, 1990.
C. Goffman and G. Pedrick, A First Course in Functional Analysis, Prentice-Hall, 1974.
E. Kreyzig, Introduction to Functional Analysis with Applications, John Wiley & Sons, New York, 1978.
B.V. Limaye, Functional Analysis, 2nd Edition, New Age International, New Delhi, 1996.
A. Taylor and D. Lay, Introduction to Functional Analysis, Wiley, New York, 1980.
Syllabus :
Normed spaces, Continuity of linear maps, Hahn-Banach Extension and Separation Theorems, Banach spaces, Dual spaces and transposes, Uniform Boundedness Principle and its applications, Closed Graph Theorem, Open Mapping Theorem and their applications, Spectrum of a bounded operator, Examples of compact operators on normed spaces.Inner product spaces, Hilbert spaces, Orthonormal basis, Projection theorem, and Riesz Representation Theorem.
Optional Topics (if time permits) : Few applications such as boundedness of Hilbert transform, Existence of solutions of various model pdes, distribution theory.
Course Policy
You are encouraged to attend lectures regularly. You should try to read the book/ prepare class notes, and do all the assignment problems. Please feel free to ask questions during the class and office hours.
Please Note
The homework will be collected in the tutorial sections. Tutorials will be used to discuss the homework problems and any other questions that you may have. You are encouraged to attend these.
No late homework submission will be allowed. However we will drop the lowest two homework grades at the end of the semester.
No calculators are allowed in the exams.
Grading :
Homework : 40%
Midterm : 20%
Final exam : 40%.