$Partial$ $differential$ $equations$

Partial differential equation

Partial Differential Equations

Order

Degree

Derivation of partial differential equation

·        By elimination of arbitrary constants 

·        By elimination of arbitrary functions

Solution of partial differential equation

Types of solutions

IVP

BVP

Types of partial differential equations

• First order and first degree partial differential equations

Partial differential equations of first order first degree (Linear PDE)

• Non-linear partial differential equations 

Standard form I

Standard form II

Standard form III

Standard form IV

Charpit’s method

Cauchy method

Jacobi method

• Linear partial differential equations 

Lagrange’s linear partial differential equations of first order

Partial differential equations of 2^nd & higher order

Canonical form

Classification 

Linear partial differential equations with constant coefficients

Homogeneous linear partial differential equations with constant coefficient

Non-homogeneous equations with constant coefficient

Equations reducible to equation with constant coefficient

Methods for solving PDEs

Separation of variables

Laplace transformation method

Fourier series method 

Special partial differential equations

Laplace equation

Heat equation

Wave equation 

BVP

       Dirichlet BVP

       Neumann BVP

       Mixed BVP