Illustrating Simple Variation Problem

Exercises

  1. Can you find another one-parameter family of functions f(x) (like f(x)=x^n which satisfies the boundary condition f(0)=0,f(1)=1? Try changing f(x)=SelectedElement(Functions) to the family of functions you chose – see what happens to the value of functional.
  2. Extremise the functional v[f(x)]=\int_0^{\pi\over2}[y'^2-y^2]dx; y(0)=0,y( {\pi\over2} )=1 using Euler-Lagrange Equation. Find a few families of functions that satisfies the boundary condition – illustrate it using GeoGebra.

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