FUNCTIONAL ANALYSIS-II (Compulsory Paper)
- Cover theoretical needs of Partial Differential Equations and Mathematical Analysis.
- Inter-relate the problems arising in Partial Differential Equations, Measure Theory and other branches of Mathematics.
- Know about various spaces such as Banach spaces, Hilbert Spaces.
- Use the operators on these spaces.
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Learning Outcomes |
Learning and teaching strategies |
Assessment |
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After the completion of the course the students will be able to: CLO107- Explain the fundamental concepts of functional analysis in applied contexts. CLO108- Use elementary properties of Banach space and Hilbert space. CLO109-Identify normal, self adjoint or unitary operators. CLO110- Communicate the spectrum of bounded linear operators. CLO111- Construct orthonormal sets.
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Approach in teaching: Interactive Lectures, Discussion, Tutorials, Reading assignments, Demonstration, Team teaching Learning activities for the students: Self learning assignments, Effective questions, Simulation, Seminar presentation, Giving tasks, Field practical
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Presentations by Individual Student Class Tests at Periodic Intervals. Written assignment(s) Semester End Examination |
Adjoint of an operator on a Hilbert space:Self-adjoint, positive, normal and unitary operators and their properties, Projection on a Hilbert space.
Derivatives of a continuous map from an open subset of Banach space to a Banach space, Rules of derivation, Derivative of a composite, Directional derivative.
Mean value theorem and its applications, Partial derivatives and Jacobian Matrix.
Continuously differentiable maps, Higher derivatives, Taylor’s formula, Inverse function theorem, Implicit function theorem.
Step function, Regulated function, Primitives and integrals, Differentiation under the integral sign, Riemann integral of function of real variable with values in normed linear space.
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- Barbara D. Maccluer, Elementary Functional Analysis, Springer, 2009.
