Chapter 13.4, Problem 12P

In Sections 2, 3, 4, we have solved a number of physics problems which led to the expansion of a given $f(x)$ in a Fourier sine series. Look at (2.9) and (2.25) temperature in a plate; (3.12), heat flow; (3.26), wave function for a particle in a box; ( 4.7 ) and $(4.10),$ displacement of a vibrating string plucked or struck. If wehave expanded a given $f(x)$ in a Fourier sine series on $(0,1),$ we can immediately write the corresponding solutions for these six different physics problems on the same interval. Do this for $f(x)=x-x^2$ on $(0,1),$ that is with $l=1.$ Make computer plots of your results.