www.mathumatiks.com
Home home About Us home Submit Problem home Formulary home Contact Us
 
    Chapters
  #   Solutions of Equations and Curve-fitting
  #   Linear Algebra: Determinants, Matrices
  #   Fourier Series
  #   Vector and Solid Geometry
  #   Partial Differentation and its Applications
  #   Infinite Series
  #   Complex Number and their Applications
  #   Laplace Transformation
  #   Multiple Integrals and its Applications
  #   Integral Transformation
  #   Application of Differential Equation of First Order
  #   Differential Equation of First Order
  #   Function of Complex Variable
  #   Vector Calculus
  #   Difference Equation and Z-Transforms
  #   Finite Differences and Interpolation
  #   Statistical Methods
  #   Numerical Methods
  #   Numerical Solutions of ODE
  #   Numerical Solutions of PDE

Introduction

Exercise (Based on Homogeneous Functions)

 

Homogeneous Functions

An expression of the form  in which every term is of the nth degree, is called homogenous function of degree n, which can be also written as

This function further can be expressed in the form of  is called homogeneous function of degree n in  and . For example  is a homogeneous function of degree 4 in  and . In general, a function  is said to be homogeneous function of degree n in , if every term containing these variable combines to give degree of n, therefore can be expressed in the form .

Euler’s theorem of homogeneous functions

If u be a homogeneous function of degree n in  and , than

Proof:

Since u is a homogeneous functions of degree n in  and y, therefore

So, in general, if u is a homogeneous function of degree n in  then

Above expression represents the general form of Euler’s Theorem.

 

SEE ALSO:

Total Derivatives

 

 

Copyright © www.mathumatiks.com
Best Viewed: 1280x1024 IE 4 ,Netscape 4.7 and above.
Terms of Use :: Privacy Policy :: Site Map