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175 bytes added ,  09:51, 22 August 2012
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==== Problem  ====
 
==== Problem  ====
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One sometimes needs to define a family of functions depending on a set of parameters, ''e.g.''
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One sometimes needs to define a family of functions depending on a set of parameters, e.g.,
<math>f (x, y, z; a, b, c)</math>  
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<math> f (x, y, z; a, b, c) </math>  
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where  
 
where  
<math>x, y, z</math>  
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<math> x, y, z </math>  
 
denote a the variables on which the function operates and  
 
denote a the variables on which the function operates and  
<math>a, b, c</math>  
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<math> a, b, c </math>  
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are the parameters used to chose one specific element of the family of functions.
 
are the parameters used to chose one specific element of the family of functions.
    
For example, let's say we want to implement a function that given the spring constant  
 
For example, let's say we want to implement a function that given the spring constant  
<math>k</math> and the initial elongation <math>x_0</math> of a  
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<math> k </math>  
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and the initial elongation  
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<math> x_0 </math>  
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of a spring, computes the time evolution of the elongation
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<math> x (t ; x_0, k) </math>
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by solving the Cauchy problem
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<math> x' = - k x\\ x(0) = x_0 </math>
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==== Solution ====
 
==== Solution ====
 
==== Discussion ====
 
==== Discussion ====
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