Partial differential equations (PDEs) involve partial derivatives of dependent variables with respect to more than one independent variable. PDEs can be linear if the dependent variable and all its partial derivatives occur linearly, or non-linear. PDEs are used to model systems in fields like physics, engineering, and quantum mechanics, with examples being the Laplace, heat, and wave equations used in fluid dynamics, heat transfer, and quantum mechanics respectively. The heat equation specifically describes the distribution of heat over time in a given region.

1. Israt Zerin Tisha
Section-A
Roll- 16511013

2. 
A differential equation involving partial derivatives of
a dependent variable(one or more) with more than one
independent variable is called a partial differential
equation.
Example:
Definition
04
4
4
4






t
u
x
u
0
2
2
2
2


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


y
z
y
x
z
x

3. 
If the dependent variable and all its partial derivatives
occur linearly in any PDE then such an equation is
called linear PDE otherwise a non-linear PDE.
Example :
Linear:
Non linear :
Linear and Non Linear PDE

4. 
PDE are used to model many systems in different
fields of science and engineering such as –
 La place Equation
 Heat Equation
 Wave Equation
 Fluid dynamics
 Quantum mechanics
Application

5. 
The heat equation is a parabolic partial differential
equation that describes the distribution of heat (or
variation in temperature) in a given region over time.
Application