MA6220: Distribution Theory and Sobolev Spaces (Jan-Apr 2024)
Distributions: Test functions and Distributions, Convolution of Distributions, Fundamental solutions, The Fourier transforms, The Schwartz space S, Tempered Distributions. Sobolev spaces: Definition and basic properties, Approximations by smooth functions, Traces, Sobolev inequalities, Compactness, Dual spaces, Fractional order spaces, and trace spaces. Weak solutions of elliptic boundary value problems: Definitions of weak solutions, Existence, The Lax-Milgram theorem, Regularity, Galerkin method, Maximum principle, eigenvalue problems, Introduction to finite element methods.
Ref:
1. S. Kesavan, Topics in Functional Analysis and Applications
2. Robert A. Adams, John J. F. Fournier, Sobolev spaces
3. Haim Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations PDF
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MA 5030 Partial Differential Equations July-Nov 2023
Ref:
F. John, Partial Differential Equations, 3rd Edition, Narosa, 1979
L.C. Evans, Partial Differential Equations, Graduate Studies in Mathematics, Vol. 19, American Mathematical Society, 1998
A. K. Nandakumaran and P. S. Datti, Partial Differential Equations: Classical theory with a modern touch, 2020
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MA 4030 Ordinary Differential Equations Jan - April 2023
References: 1. Ordinary Differential Equations: Principles and Applications by A. K. Nandakumaran, P. S. Datti, Raju K. George
2. An Introduction to Ordinary Differential Equations by Earl A. Coddington
Assignment 1 Click here
Assignment 2 Click here
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MA 1220 Calculus II Dec 2022 - Jan 2023
Syllabus
Integral Calculus: Definite Integrals as a limit of sums, Applications of integration to the area, volume, surface area, and improper integrals. Functions of several variables: Continuity and differentiability, mixed partial derivatives, local maxima and minima for functions of two variables, Lagrange multipliers.
Textbook:
"Thomas' Calculus"
Homework: Click here
Assignment: Click here Please submit the assignment by Wednesday 21/12/2022 in the Class.
End sem : 3 rd January 2023, Tuesday 17:30 - 19:30
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MA 1000 Math foundation Oct 2022-Feb 2023
Syllabus
Statements, Logic, Proofs in Mathematics, Sets, Functions, Relations, Equivalence Relations, Partition of a Set, The Induction Principles, The Well ordering principles, Countability of Sets (finite and countable), Order Relations, Posets, Axioms of Choice
Textbook
"A Foundation Course in Mathematics" by Ajit Kumar, B. K. Sarma, and S. Kumaresan
MA 1230 Series of functions June-July 2022