Introduction to Partial Differential Equations

curves and surfaces

Genesis of First order p.d.e.

Elimination of parameter and arbitrary function to form p.d.e

Classification of Integrals (Solution)

Linear Equations of the First order

Pfaffian Differential equations

Examples on Pfaffian Differential equations

Compatible Systems of First Order P.D.E.

Charpit’s Method for First Order P.D.E

Examples on Charpit's Method

Some Standard type P.D.E based on Charpit's Method

Jacobi's method

The Cauchy Problem: Integral Surface Through a given Curve

Semi-Linear Equations : Geometry of Solution

Quasi-linear Equations: Geometry of Solution

The Cauchy Problem: Integral Surface Through a given Curve

Semi-Linear Equations : Geometry of Solution

Quasi-linear Equations: Geometry of Solution

Monge Cone

The Cauchy Problem for the non-linear p.d.f.

Example on Cauchy Problem for Non-linear first order Partial differential equations

Examples on Cauchy’s Problem for the Non-linear Partial Differential Equations

Uniqueness of the solution of Cauchy problem

Modeling of one dimensional wave equation

Genesis of Second Order P.D.E.

Classification of Second order P.D.E.

Examples on Classification of Second order P.D.E.

Solution of wave equation of an infinite String

Properties of Characteristics-Wave Equation

Vibration of semi infinite string

Vibration of a String of finite length

Method of separation of variables

Sol. of wave eq. using Method of Separation of variables

Uniqueness of Solution of Wave Equation

Fourier Transformation

Solution of Heat equation-infinite rod

Solution of Heat Equation for finite Rod

Uniqueness of Solution of Heat equation

In this lecture, we have discussed the Remain method.

Examples on Reimann's method

Boundary Value Problems based on Laplace equation

Maximum and minimum principles

Uniqueness Theorem of Dirichlet problem

The Cauchy Problem and Stability

The Dirichlet Problem for the Upper Half Plane

The Neumann Problem for the Upper Half Plane

Uniqueness and Necessary condition for Neumann Prob

Solution of the Dirichlet Problem for a circle

Poisson Integral formula

The Dirichlet Exterior Problem for a circle

The Neumann Problem for a Circle

The Dirichlet Problem for Rectangle

Harnack's Theorem

Laplace's Equation- Green function

Families of Equipotential Surfaces