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Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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The Heat Equation is a particular partial differential equation that models how heat enters or exits a material over time. This means that the Heat Equation has two types of coordinates: space and time. For simplicity's sake, we will be assuming a rod of length L is being heated in only one dimension. This means that you will only have one space variable, x, and one time variable, t, (time always has one variable). Using Separation of Variables, solve the following Partial Differential Equation (picture)

With the initial/ boundary conditions,
U(x, 0)= f(x), u(0, t)= 0, u(L, t)=0

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