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.
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.
