Consider the wave equation a2 uxx = utt in an infinite one-dimensional medium subject to the initial conditions u(x, 0) = 0, ut(x, 0) = g(x), < x < . (a) Using the form of the solution obtained in 13, show that(x) + (x) = 0,a(x) + a(x) = g(x).(b) Use the first equation of part (a) to show that (x) = (x). Then use the secondequation to show that 2a(x) = g(x) and therefore that(x) = 12a xx0g() d + (x0),where x0 is arbitrary. Finally, determine (x).(c) Show thatu(x, t) = 12a x+atxatg() d.

MATH 2010 - Multivariable Calculus & Matrix Algebra Professor Herron - Rensselaer Polytechnic Institute Week 6 (2/29/16 - 3/4/16) Important : These notes are in no way intended to replace attendance in lecture. For best results in this course, it is imperative that you attend lecture and take your own detailed notes. Please keep in mind that these notes are written...