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Functional Analysis and its Applications
Online
12 Weeks
Free Quick Facts
| Medium Of Instructions | Mode Of Learning | Mode Of Delivery |
|---|---|---|
| English | Self Study | Video and Text Based |
Courses and Certificate Fees
| Fees Informations | Certificate Availability | Certificate Providing Authority |
|---|---|---|
| INR 1000 | yes | IIT ISM Dhanbad |
The Syllabus
- Basic Analysis: Vector spaces, Linear transformation between vector spaces, Basic inequalities, Metric spaces and its properties. Convergence, Cauchy sequence, Completeness.
- Norms and Normed linear spaces: Definitions and properties, Convergence, Cauchy sequence, Completeness.
- Banach Spaces, Quotient spaces of Banach spaces, Illustrative examples.
- Bounded (continuous)linear operators, Bounded linear functionals, Dual spaces.
- Inner product spaces, Hilbert spaces,Illustrative examples of Hilbert spaces,Further properties of Inner product spaces, Schwartz’s inequality, Strong and Weak convergence, Applications of Polarization identity
- Orthogonality of vectors, Orthogonal complements, Gram- Schmidt orthonormalization process.
- Bessel’s inequality, The conjugate space H*, Riesz representation theorem
- Operators on Hilbert spaces: The adjoint operator, Self adjint operator
- Positive Operators, Normal Operators, Unitary Operators
- Partially ordered set, Zorn’s Lemma, Hahn-Banach Theorem (Normed spaces), Application to bounded linear functional on C[a,b].
- Baire’s category theorem, Uniform Boundedness principle and its applications.
- Open mapping theorem, Closed graph theorem. An application of the Banach’s theorem.
Instructors
Articles
31 Aug'25, 03:44 PM
17 Jun'25, 10:59 AM
28 Feb'24, 08:51 AM
28 Feb'24, 07:16 AM
31 Aug'25, 03:44 PM
17 Jun'25, 10:59 AM
28 Feb'24, 08:51 AM
28 Feb'24, 07:16 AM