**MA8353 TPDE** **Notes**

Anna University Regulation 2017 EEE **MA8353 ****TPDE**** Notes, TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS ****Lecture Handwritten Notes** for all 5 units are provided below. Download link for EEE **3rd Sem **TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS **Notes** are listed down for students to make perfect utilization and score maximum marks with our study materials.

**MA8353 TPDE TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS **

1 Partial Differential Equations(P.D.E.)Formation of partial differential equations – Lagrange’s Linear

equation Solution of standard types of first order partial differential equations – Linear partial differential equations of second and higher order with constant coefficients.

**1.1 Introduction**

In a differential equation if there are two or more independent variables and the derivatives are partial derivatives then it is called a partial differential equation.The order of a partial differential equation if the order of the highest

partial derivative occurring in the equation.The degree of a partial differential equation is the greatest exponent of

the highest order.In the above, e.g.1 is a second order & third degree equation, e.g.2 is a first order equation & first degree equation.Note : Throughout this chapter we use the following notations; z will be

taken as a dependent variable which depends on two independent variables x and y so that z = f(x, y).

1.2 Formation of Partial Differential Equation by Elimination of

Arbitrary Constants Let f(x, y, z, a, b) = 0. (1) be an equation which contains two arbitrary constants ‘a’ and ‘b’.

Partially differentiating (1) with respect to ‘x’ and ‘y’ we get two more equations.

Eliminating a and b from these three equations, we get φ(x, y, z, p, q) = 0 which is a partial differential equation of order 1. In this case the number of arbitrary constants to be eliminated is equal to the number of independent variables and we obtain a first order partial differential equation. If the number of arbitrary constants to be eliminated is more than the number of independent variables, we get partial differential equations of second or higher order.

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