Eulers theorem presentation and explanation

This ppt explains bout euler's theorem

1. Homogeneous functions Definition A function is said to be a homogeneous function of degree in two variables iff = (or) = = = =  

2. Examples : 1) ( ) is a homogeneous function of degree in and 2) , , and are homogeneous functions. is not a homogeneous function, but is a homogeneous function of deg. -1 4) Sum of two homogeneous functions is also homogeneous function.  

3. Note   If is a polynomial, i.e., an expression of the form in which every term is of degree, is called a homogeneous function of degree ‘ n ’. This can be rewritten as = = Thus, any function which can be expressed in the form of is called a homogeneous function of order, n in x & y.    

4. 2. In general, a function is said to be a homogeneous function of degree, ‘ n’ in x, y, z, t, ………., if it can be expressed in the form of  

5. EULER’S THEOREM ON HOMOGENEOUS FUNCTIONS : (Imp) If is homogeneous function of degree in and then NOTE : Euler’s theorem can be extended to a homogeneous function of any number of variables. I f ‘u’ is a homogeneous function of order ‘ n’ in x, y, z, t,…….., then by Euler’s theorem, we have  

6. EULER’S THEOREM ON HOMOGENEOUS FUNCTIONS FOR SECOND ORDER PARTIAL DERIVATIVES If be a homogeneous function of degree then Note : Some times will be given as a transcendental function. In such cases, we may use the following formula Special formulae : If is not a homogeneous function but f( ) is homogeneous function then 1) (say) 2) (