MATH 264 Study Guide - Quiz Guide: Fourier Series, List Of Trigonometric Identities, Heat Equation

• School: McGill University
• Department: Mathematics and Statistics
• Course: MATH 264
• Professor: Sancho

Document Summary

This assignment will not be marked: let m and n be positive integers with m 6= n, and let l > 0. 0: consider a 40 cm long rod, whose ends are maintained at a temperature of 0 degrees. Celsius and whose constant of thermal di usivity is = 1. Solve the heat equation ut = uxx to nd an expression for the temperature u(x, t), if the initial temperature distribution is u(x, 0) =(x if 0 x < 20 cm, 40 x if 20 x 40 cm: solve the boundary value problem ut = uxx, 0 < x < 20, t > 0 ux(0, t) = 0, u(20, t) = 5, u(x, 0) =( x. 2 if 0 < x 10, if 10 < x < 20: consider a string of length 4cm, with xed ends. At time zero, the string is at rest, and its displacement is given by u(x, 0) =( x.