IST Analysis and Differential Equations (2015)

The Instructional School for Teachers (IST) on Analysis and Differential Equations was conducted at TIFR Center for Applicable Mathematics (TIFR CAM), Bangalore during the period December 7-19, 2015. It was organized by Mythily Ramaswamy and Venkateswaran P. Krishnan from TIFR CAM. As we had a large number of requests from research scholars in addition to teachers, TIFR CAM, upon our request, had agreed to support some such candidates and NCM also had approved this. We had selected about 59 University/College teachers and research scholars. Eventually, we had 29 participants, out of which 15 were teachers and the rest were Ph. D. scholars.The aim of the school was to revisit the basics of Analysis and Differential equations, taught at the M.Sc level and also to go beyond to cover some advanced material.

The details of the topics covered in the 4 modules by the speakers from TIFR CAM are as follows :

1. Multivariable calculus: Functions of several variable : Continuity, Differentiability, Mean Value Theorems, Integration : line, surface and volume integrals, Integration Theorems, Inverse Function Theorem, Implicit Function Theorem; by Ujjwal Koley.

2. Linear algebra and Linear ordinary differential equations: Basics from Linear algebra, Matrices, Exponentials of operators, eigenvalues, Jordan Canonical form, ODE: first and second order linear ode, Linear System of ODE, Non-homogeneous system, asymptotic behaviour of solutions of linear systems; by Mythily Ramaswamy.

3. Nonlinear ODE and linear PDE:
(a) ODE: Existence, uniqueness, continuous dependence and stability of solutions of initial value problems.

(b) PDE: Method of characteristics for linear, quasilinear and fully nonlinear equations, notion of weak solutions: by K. Sandeep.

4. Differential Geometry and Differential Topology: Plane curves and space curves, Surfaces, Second Fundamental Form, Gaussian curvature, Mean curvature, Gausss Theorema Egregium, Sard’s Theorem; by Venkateswaran P. Krishnan.

 Each module consisted of 6 lectures, one per day from Monday to Saturday and 6 tutorials in the afternoon of each day. The tutorials were conducted in the afternoon, two per day for each of the morning topics. Eight of the senior students from TIFR CAM, helped as tutorial assistants. They had prepared an assignment sheet for each of 6 days for each module and in a few cases, even typed up the answers.The lectures started out from basic level and went up to an advanced level and were well received by the participants. The participants were enthusiastic in the lectures as well as in the tutorials. All the 4 modules were well appreciated and the participants were very impressed with the lectures. They felt that the lectures and tutorials were very useful to them in gaining insight into these basic topics and to see the inter-connections. They felt that this would strengthen their basics and help towards better research and teaching. The last session on December 19 was open to the participants to come forward and talk about their interests and research work or plans if any. Some of the participants came forward to tell us about their research work.

Registration:  7-Dec-2015 at 9.00 am.

Time Table

Speakers, Syllabus and Tutors   

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