Math 4163 - Assignment 9 1. Consider the following IBVP for the heat equation on the line: t1 = 50px u(z,0) = f(x) where

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Math 4163 Assignment 9 1 Consider The Following Ibvp For The Heat Equation On The Line T1 50px U Z 0 F X Where 1 (21.55 KiB) Viewed 66 times

Math 4163 - Assignment 9 1. Consider the following IBVP for the heat equation on the line: t1 = 50px u(z,0) = f(x) where f(x)=1 2. Find the solution of (-∞ <x<∞, t> 0) (-x<x<∞) a) Find the solution and express it in terms of error functions. b) Sketch the graph of u(x, t) when t=0,t=0.01, and t=0.1. e) Using the formula that you found in part a), check that lim u(3.5,1)=f(3.5), showing all work. (0,1)=0 u(z,0)=3-(³) u₁(x,0) = cos z for <3 for 3 ≤ x ≤4 for z> 4. (0<x<∞, f> 0) (120) (0<x<∞) (0 < x <∞) (Hint: this is the wave equation on the line. What formula should you use? By the way, I recommend graphing the answer on Desmos once you find it, and playing it as a video. It looks kind of neat, like a pair of rogue waves on a stormy ocean.)