IST Analysis and Differential Equations (2015) - Speakers and Syllabus

A brief Description of the school

The proposed Instructional School for Teachers (IST) is being organized for the University/College teachers. There will be 4 modules on (1) Multivariable calculus, (2) Linear algebra and Linear ordinary differential equations, (3) Nonlinear ODE and linear PDE, and (4) Differential Geometry and Differential Topology. The lectures will cover advanced topics in Analysis and Differential Equations taught at the M.Sc. Level and beyond. These schools are for teachers of age at most 35 years. Preference will be given to teachers who are pursuing a doctoral degree. Only NET/SET qualified teachers will be admitted into these schools.

Instructors:

• Ujjwal Koley, Reader, TIFR CAM
• Venky Krishnan, Reader, TIFR CAM
• K. Sandeep, Associate Professor, TIFR CAM
• Mythily Ramaswamy, Professor, TIFR CAM
 Speaker Lectures Detailed Syllabus Ujjwal Koley 6 Functions of several variable : Continuity, Differentiability, Mean ValueTheorems, Integration : line, surface and volume integrals, Integration Theorems, Inverse Function Theorem, Implicit Function Theorem Mythily Ramaswamy 6 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. K. Sandeep 6 ODE: Existence, uniqueness, continuous dependence and stability of solutions of initial value problems.PDE: Method of characteristics for linear, quasilinear and fully nonlinear equations, notion of weak solutions. Venky Krishnan 6 Basics of topology (1 lecture)Surfaces, Second Fundamental Form, Gaussian curvature, Integration on Surfaces, Gauss’s Theorema Egregium, Gauss-Bonnet Theorem (3 lectures)Manifolds, Sard’s Theorem, Tubular neighborhoods, Embedding Theorems (2 lectures)

References

1. Differential Equations, Theory, Technique and Practice by G.F.Simmons and S.G. Krantz, Tata McGraw Hill, 2003.

2. Differential Equations, Dynamical Systems and Linear Algebra by Hirsch and Smale, Academic Press

3. Partial differential equations by R. McOwen

4. Partial Differential Equations by Lawrence C.Evans, AMS, 2000.

5. Hoffman and Kunze, Linear Algebra

6. G. Strang, Linear Algebra and Applications

7. W. Rudin, Principles of Mathematical Analysis

8. T. Apostol, Mathematical Analysis

9. Topology by J. Munkres

10. Curves and Surfaces by S. Montiel and A. Ross

11. Differential Geometry of Curves and Surfaces by M. do Carmo

12. Introduction to Topological Manifolds by J. M. Lee

13. Introduction to Smooth Manifolds by J. M. Lee

14. Topics in Differential Topology by A. Mukherjee

LH111 (First floor)

Registration:  7-Dec-2015 at 9.00 am.

 Day Date Lecture 1 9.30 -11.00 Tea Lecture 211.30 -1.00 Lunch Tutorial 12.00 - 3.30 Tea & Snacks Tutorial 24.00 - 5.30 Tea & Snacks Mon 7-Dec-15 MR 11.00-11.30 UK 1.00-2.00 Tutorial 3.30-4.00 Tutorial 5.30-6.00 Tue 8-Dec-15 MR UK Tutorial Tutorial Wed 9-Dec-15 MR UK Tutorial Tutorial Thu 10-Dec-15 MR UK Tutorial Tutorial Fri 11-Dec-15 MR UK Tutorial Tutorial Sat 12-Dec-15 MR UK Tutorial Tutorial Mon 14-Dec-15 VK KS Tutorial Tutorial Tue 15-Dec-15 VK KS Tutorial Tutorial Wed 16-Dec-15 VK KS Tutorial Tutorial Thu 17-Dec-15 VK KS Tutorial Tutorial Fri 18-Dec-15 VK KS Tutorial Tutorial Sat 19-Dec-15 VK KS Tutorial Tutorial

• MR-Mythily Ramaswamy
• UK-Ujjwal Koley
• VK-Venkateswaran P Krishanan
• KS-K Sandeep

Tutorial Assistants :

 S.No. Name Affiliation 1 Dr. Prosenjit Roy Post-doc fellow, TIFR-CAM, Bangalore 2 3 research students from CAM