applications of first order non linear partial differential equation
- 1. Advanced engineering mathematics Applications of first order non linear partial differential equation SY CE 1 Batch B 170410107026- Dhruv 170410107027 - Dhananjaysinh 170410107028 - Rajdeep 170410107029 - Atharva 170410107030 - Devam
- 2. Table of contents Partial differential equations Types of PDE Methods of solving diff types Applications
- 3. Partial differential equation An equation which involves function of two or more variable and partial derivatives of that function, then it is called partial differential equation. Notation
- 4. Partial differential equation A Differential equation which contains only p and q and no higher order derivatives is called of the first order. If the degree of p and q is unity throughout, it is called linear partial differential equation of first order. It is of the form Pp + Qq =R. P, Q and R are any functions of x,y,z. Nonlinear partial differential equation of first order is a PDE order 1 which is not linear.
- 5. Non linear PDE of 1st order Non linear PDE of 1st order can be of one of the four given forms.
- 13. Charpit’s method
- 15. Applications of 1st order non linear PDE
- 16. The equation is named for the 18th-century French mathematician and physicist Alexis-Claude Clairaut, who devised it. In 1736, together with Pierre-Louis de Maupertuis, he took part in an expedition to Lapland that was undertaken for the purpose of estimating a degree of the meridian, and on his return he published his treatise Théorie de la figure de la terre (1743; “Theory of the Shape of the Earth”). In this work he promulgated the theorem, which connects the gravity at points on the surface of a rotating ellipsoid with the compression and the centrifugal force at the Equator.
- 17. The following curves represent the solutions to two Clairaut's equations. In each case, the general solutions are depicted in black while the singular solution is in violet.