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, GaussBonnet 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: 7Dec2015 at 9.00 am.
Day 
Date 
Lecture 1 9.30 11.00 
Tea 
Lecture 2 
Lunch 
Tutorial 1 
Tea & Snacks 
Tutorial 2 
Tea & Snacks 
Mon 
7Dec15 
MR 
11.0011.30

UK 
1.002.00 
Tutorial 
3.304.00 
Tutorial 
5.306.00 
Tue 
8Dec15 
MR 
UK 
Tutorial 
Tutorial 

Wed 
9Dec15 
MR 
UK 
Tutorial 
Tutorial 

Thu 
10Dec15 
MR 
UK 
Tutorial 
Tutorial 

Fri 
11Dec15 
MR 
UK 
Tutorial 
Tutorial 

Sat 
12Dec15 
MR 
UK 
Tutorial 
Tutorial 

Mon 
14Dec15 
VK 
KS 
Tutorial 
Tutorial 

Tue 
15Dec15 
VK 
KS 
Tutorial 
Tutorial 

Wed 
16Dec15 
VK 
KS 
Tutorial 
Tutorial 

Thu 
17Dec15 
VK 
KS 
Tutorial 
Tutorial 

Fri 
18Dec15 
VK 
KS 
Tutorial 
Tutorial 

Sat 
19Dec15 
VK 
KS 
Tutorial 
Tutorial 
 MRMythily Ramaswamy
 UKUjjwal Koley
 VKVenkateswaran P Krishanan
 KSK Sandeep
Tutorial Assistants :
S.No.  Name  Affiliation 
1  Dr. Prosenjit Roy  Postdoc fellow, TIFRCAM, Bangalore 
2  3 research students from CAM 