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==== Problem ==== | ==== Problem ==== | ||
One sometimes needs to define a family of functions depending on a set of parameters, | 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> | |||
<math> f (x, y, z; a, b, c) </math> | |||
where | where | ||
<math>x, y, z</math> | |||
<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> | |||
<math> a, b, c </math> | |||
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 | |||
<math> k </math> | |||
and the initial elongation | |||
<math> x_0 </math> | |||
of a spring, computes the time evolution of the elongation | |||
<math> x (t ; x_0, k) </math> | |||
by solving the Cauchy problem | |||
<math> x' = - k x\\ x(0) = x_0 </math> | |||
==== Solution ==== | ==== Solution ==== | ||
==== Discussion ==== | ==== Discussion ==== | ||