MA 201: Finite Vibrating string Problem
Introduction to Fourier Series
Lecture - 8
MA201(2016):PDE
IBVP for Vibrating string with no external forces
We consider the problem in a computational domain
(x, t) [0, L] [0, )
The IBVP under consideration consi

MA 201: Convergence of Fourier Series
Lecture - 9
MA201(2016):PDE
Convergence of Fourier Series for Periodic Functions
Example
Recall that Fourier Series of the function f (x) = x for L x L is
given by
2L X
1
nx
(1)n+1 sin
.
n=1
n
L
Observe that value o

Surfaces orthogonal to a given system of surfaces
Nonlinear First-Order PDEs
Solving Cauchys problem for nonlinear PDEs
MA 201: Partial Differential Equations
Lecture - 4
IIT Guwahati
MA201(2016):PDE
Surfaces orthogonal to a given system of surfaces
Nonli

Quasi-linear First-Order PDEs
Formation of quasi-linear First-Order PDEs
General solution quasi-linear First-Order PDEs
The method of Lagrange
Solving a Cauchy Problem
MA 201: Partial Differential Equations
Lecture - 3
IIT Guwahati
MA201(2016):PDE
Quasi-l

MA 201: Second Order Linear PDE
Canonical Transformation
Lecture - 6
MA201(2016):PDE
A second order PDE with two independent variables x and y is
given by
F (x, y , u, ux , uy , uxy , uxx , uyy ) = 0.
(1)
What is the linear form?
The unknown function u(

Motivating Examples
Compatible Systems and Charpits Method
Charpits Method
Some Special Types of First-Order PDEs
MA 201: Partial Differential Equations
Lecture - 5
IIT Guwahati
MA201(2016):PDE
Motivating Examples
Compatible Systems and Charpits Method
Ch