This course will enable the students to -
Course Outcomes (COs):
Course |
Learning outcomes (at course level) |
Learning and teaching strategies |
Assessment Strategies |
|
---|---|---|---|---|
Paper Code |
Paper Title |
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MAT 321 |
Functional Analysis-I (Theory)
|
The students will be able to –
CO69: Explain the fundamental concepts of functional analysis in applied contexts. CO70: Use elementary properties of Banach space and Hilbert space. CO71: Identify normal, self adjoint or unitary operators. CO72: Communicate the spectrum of bounded linear operator. CO73: Construct orthonormal sets. CO74:Analyse various inequalities and their applications |
Approach in teaching:
Interactive Lectures, Discussion, Power Point Presentations, Informative videos
Learning activities for the students: Self learning assignments, Effective questions, presentations, Field trips |
Quiz, Poster Presentations, Power Point Presentations, Individual and group projects, Open Book Test, Semester End Examination
|
Normed linear space of bounded linear transformations, Equivalent norms, Basic properties of finite dimensional normed linear spaces and compactness, Riesz lemma.
Open mapping theorem, Closed graph theorem, Uniform boundness theorem, Continuous linear functional, Hahn-Banach theorem and its consequences.
Hilbert space and its properties, Orthogonality and functionals in Hilbert spaces, Phythagorean theorem, Projection theorem, Orthonormal sets.