Partial differential equation & its application.
Download as PPTX, PDF6 likes9,453 views
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 of 5
Downloaded 46 times
Partial differential equation & its application.
- 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 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