ISL Differential Equations and Computations (2012)

 Jaypee University of Information Technology, Waknaghat, Distt. Solan

School Convener(s)

Harinder Singh

 Mythily Ramaswamy

S. Sunder

Department of Mathematics,
Jaypee University of Information Technology, Waknaghat,
Distt Solan - 173234, Himachal Pradesh

TIFR Centre for Applicable Mathematics,
P. Bag No. 6503 Yelahanka,
Bangalore – 560 055

Department of Mathematics,
IIT Madras,
Chennai – 600 036

Speakers and Syllabus 

Speaker

Lectures

Detailed Syllabus

Harinder Singh

(HS)

JUIT, Waknaghat

4

Linear ODE: first and second order , Wronskian and linearly independent solutions, Characteristic equation :Complex roots, repeated roots, Non-homogeneous equations, method of variation of parameters, phase plane analysis, Examples of first and second order equation models, general nth order equations. (Chapters 1,2,3, 4 from Boyce and DiPrima)

Karanjeet Singh

(K Singh)

JUIT, Waknaghat

4

System of equations: First order linear system with constant coefficients, Solution of first order systems, Matrix algebra and exponentials of operators, Jordan Canonical form, Complex Eigenvalues, Repeated Eigenvalues, Non-homogeneous system, Existence and uniqueness of solutions: Picard's theorem Continuity of solutions with respect to initial conditions, Extending solutions to maximal domain of existence, global solutions, Flow of a differential equation ( Chapters 7, Boyce and Diprima; Chapters 4,5,6,8 from Hirsch and Smale )

A.S.Vasudeva Murthy

(ASV)

TIFR – CAM Bangalore

4

Autonomous systems, Types of critical points and stability, Critical points and stability of linear systems, Stability by Liapunov’s direct method, Critical points of non-linear systems, Conservation systems, Periodic solutions: Poincare’-Bendixson theorem ( Chapter 9, Boyce and DiPrima; Chapters 9,11 from Hirsch and Smale)

K. Sandeep

(KS)

TIFR – CAM Bangalore

4

Linear and quasi-linear first order PDE: solution by the method of Characteristics, Transport equation , Burgers equation (chapter from McOwen )

Mythily Ramaswamy

(MR)

TIFR – CAM Bangalore

4

Important second order linear PDE: Laplace equation, Heat equation, Wave equation, solution by separation of variables, Fourier series, Boundary value problems. (Chapters 10,11 of Boyce and DiPrima)

S. Sundar

(SS)

IIT, Madras

4

Solving IVP: RK methods, Multistep methods, Solving 1d BVP: Shooting method, finite difference method, convergence, Solving 2d BVP: Poisson Equation with Dirichlet data, Neumann data, Mixed data using finite difference method, convergence, Solving 2d Parabolic problem: Explicit schemes, implicit schemes, convergence, stability.