First order partial differential equations
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The document discusses first-order partial differential equations (PDEs), defining them as equations involving a function of multiple independent variables and their partial derivatives. It explains the concepts of order and degree of a PDE, as well as the conditions for forming a PDE through the elimination of arbitrary constants or functions. General rules are provided regarding the relationship between the number of arbitrary constants and the independent variables in determining the order of the resulting PDE.
First order partial differential equations
- 1. By Dr. B.M.B.Krushna Sr. Asst. Professor Dept. Of Mathematics MVGR COLLEGE OF ENGINEERING (A) 1 FIRST ORDER PARTIAL DIFFERENTIAL EQUATIONS
- 2. A partial differential equation(shortly., PDE) is an equation for a function which depends on more than one independent variable which involves the independent variables, the function, and partial derivatives of the function.
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- 4. The order of a PDE is defined as the order of the highest order derivative occur in the equation. The degree of a PDE is defined as the +ve integral power to which the highest order derivative occur in the equation.
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- 6. We can form a PDE in Two ways Elimination of arbitrary constants from a relation f(x,y,z,a,b,…)=0 Elimination of arbitrary functions
- 7. General rules to remember. If the number of arbitrary constants to be eliminated is equal to the number of independent variables, then we get a PDE of first order. If the number of arbitrary constants to be eliminated is greater than the number of independent variables, then we get a PDE of 2nd or higher order. In this case we may get more than one PDE.
- 8. If the number of arbitrary constants to be eliminated is less than the number of independent variables, then we get a PDE of first order. In this case we may get more than one PDE. Note. In this chapter we use z=f(x,y), where x,y are independent variables and z is dependent variable.
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