Analysis and Partial differential equations (PDEs) are now the integral part of the curriculum in any postgraduate course in Mathematics. Advanced analysis like Measure Theory and Functional Analysis are playing a vital role in many mathematical disciplines including PDEs. PDEs naturally arise often in many mathematical modeling of physical phenomenon and engineering applications. Measure Theory and Functional analysis are the backbones for setting up the study of PDEs in the modern sense. Functional Analysis studies linear spaces provided with suitable topological structures and continuous linear transformations between such spaces. It has far-reaching applications in several disciplines. An introduction to the theory of measure and integration is helpful since the richest examples in functional analysis come from function spaces whose study demands such a knowledge. The topics in the school are designed in such a way that the participants get exposure to topics in Linear Algebra, Measure Theory, Functional analysis and Partial Differential Equations.

References:

1. Hoffman, K. and Kunze, R., Linear Algebra (2nd Ed.) ,Prentice-Hall of India, 1992.
2. Artin, M., Algebra, Prentice-Hall of India, 1994.
3. Terence Tao. An Introduction to Measure Theory.American Mathematical Society. Graduate Studies in Mathematics Vol. 126; 2011.
4. Elias M Stein and Rami Shakarchi. Real Analysis: Measure Theory, Integration, and Hilbert Spaces. Princeton University Press (2005).
5. Conway, J. B., A course in functional analysis, GTM 96, Springer.
6. Rudin, Walter., Functional Anaysis (2nd Ed.) ,McGraw-Hill, 2006.
7. Garabedian, P. R., Partial Differential Equations, John Wiley and Sons, 1964.
8. Renardy, M. and Rogers, R. C., An Introduction to Partial Differential Equations, Springer-Verlag, 1992.

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