Differential Equations is a basic topic of research and teaching in mathematics. The abstract theory behind this topic is also most important from the point of view of applications in large number of areas iin mathematics itself and, of course, in science and engineering. A few examples are geometry (including differential geometry), economics, hydrodynamics, elasticity, general relativity, geometric flows, biology etc. There are a few excellent research groups in India, especially in partial differential equations (PDE), but these are in a very small number of central institutes and the manpower available for teaching this topic in universities, and colleges is too small. In Indian curriculum, the topic “differential equations” is introduced to the students as a set of artificially created methods to solve differential equations. In the process, the whole beauty and importance is lost. Through this course, we will introduce the basics of differential equations through various aspects of mathematics, in particular analysis and linear algebra.

Syllabus to be covered:

References:

1. A.K. Nandakumaran, P.S. Datti and R.K. George, Ordinary Differential Equations: Principles and Applications, Cambridge, 2017.
2. Tyn Myint-U, \textit{Ordinary Differential Equations,} Elsevier North-Holland, 1978.
3. E.A. Coddington and N. Levinson,Theory of ODE's, Tata McGraw-Hill, 1972.
4. Prasad, P. and Ravindran, R, Partial Differential Equations, New Age, 2015.
5. Pinchover, Y. and Rubinstein, J. An Introduction to Partial Differential Equations, Cambridge, 2005.
6. Han, Q, A Basic Course in Partial Differential Equations, AMS, 2011.
7. McOwen, R. C, Partial Differential Equations: Methods and Applications}, Pearson, 2002.

Tentative time-table:

Ts = Tutors