KUK - LMS

Syllabus

MODULE NO / UNIT	COURSE SYLLABUS CONTENTS OF MODULE	NOTES
Course Code: MMATH21-412 Course Name: Elective V) Boundary Value Problems
1	Applications to Ordinary Differential Equations; Initial value problems, Boundary Value Problems. Dirac Delta functions. Green’s function approach to reduce boundary value problems of a self-adjoint-differential equation with homogeneous boundary conditions to integral equation forms. Green’s function for N -order ordinary differential equation. Modified Green’s function. (Relevant portions from the Chapter 5 of the book “Linear Integral Equations, Theory and Techniques by R.P.Kanwal”).
2	Applications to partial differential equations: Integral representation formulas for the solution of the Laplace and Poisson Equations. The Newtonian, single-layer and double-layer potentials, Interior and Exterior Dirichlet problems, Interior and Exterior Neumann problems. Green’s function for Laplace’s equation in a free space as well as in a space bounded by a ground vessel. Integral equation formulation of boundary value prolems for Laplace’s equation. Poisson’s Integral formula. Green’s function for the space bounded by grounded two parallel plates or an infinite circular cylinder. The Helmholtz equation. (Relevant portions from the Chapter 6 of the book “Linear Integral Equations, Theory and Techniques by R.P.Kanwal”).
3	Integral Transform methods: Introduction, Fourier transform. Laplace transform. Convolution Integral. Application to Volterra Integral Equations with convolution-type Kernels. Hilbert transform. Applications to mixed Boundary Value Problems: Two-part Boundary Value problems, Three-part-Boundary Value Problems, Generalized Three-part Boundary Value problems. ( Relevant portions from the Chapter 9 & 10 of the book “Linear Integral Equations, Theory and Techniques by R.P. Kanwal”).
4	Integral equation perturbation methods: Basic procedure, Applications to Electrostatics, Low-Reynolds-Number Hydrodynamics: Steady stokes Flow, Boundary effects on Stokes flow, Longitudinal oscillations of solids in stokes Flow, Steady Rotary Stokes Flow, Rotary Oscillations in Stokes Flow, Rotary Oscillation in Stokes Flow, Oseen Flow-Translation Motion, Oseen Flow-Rotary motion Elasticity, Boundary effects, Rotation, Torsion and Rotary Oscillation problems in elasticity, crack problems in elasticity, Theory of Diffraction. ( Relevant portions from the Chapter 11 of the book “Linear Integral Equations, Theory and Techniques by R.P.Kanwal”).