Sec_2.3 - 2.3 Homogeneous Equations Definition 2.2...

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2.3 Homogeneous Equations Definition 2.2 Homogeneous Function If a function f has the property that ( 29 ( 29 , , n f tx ty t f x y = for some real number n , then f is said to be a homogeneous function of degree n . Ex1: Some Homogeneous Functions a. ( 29 2 2 , 3 5 f x y x xy y = - + The degree of each term is 2, therefore we can say that this function is a homogeneous function of degree 2. ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 2 2 2 2 2 2 2 2 2 2 2 , 3 5 3 5 3 5 , , . f tx ty tx tx ty ty t x t xy t y t x xy y f tx ty t f x y = - + = - + = - + = b. ( 29 2 2 3 , f x y x y = + ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 2 2 2 2 2 2 3 3 2 2 2 2/3 2 2 3 3 2/3 , , , , , . f x y x y f tx ty t x t y f tx ty t x y t x y f tx ty t f x y = + = + = + = + = This function is a homogeneous function of degree 2/3. c. ( 29 2 2 , 1 f x y x y = + + ( 29 ( 29 ( 29 ( 29 2 2 2 2 2 2 2 , 1 , 1 , , . f x y x y f tx ty t x t y f tx ty t f x y = + + = + + ° This function is not a homogeneous function. d. ( 29 , 4 2 x f x y y = + ( 29 ( 29 ( 29 ( 29 0 , 4 , 4 4 2 2 2 , , . x tx x f x y f tx ty y ty y f tx ty t f x y = + = + = + = This function is a homogeneous function of degree 0.
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If a function f
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  • Fall '06
  • EDeSturler
  • Equations, Trigraph, dx, homogeneous function

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