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 2
11.30 -1.00

Lunch

Tutorial 1
2.00 - 3.30

Tea & Snacks

Tutorial 2
4.00 - 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