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du 4 0 < x < 2, t> 0, %D Ət Əx²* (0, t) : (2, t) = 0, t> 0 u(x, 0) = f(x) 0

du 4 0 < x < 2, t> 0, %D Ət Əx²* (0, t) : (2, t) = 0, t> 0 u(x, 0) = f(x) 0

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Consider the problem of heat flow in a uniform wire of length 2 described by ди 0 < x < 2, t> 0, 4. Əx²' du du Ôz (0, t). u(x, 0) = f(x) 0 <x < 2 (2, t) = 0, t > 0 a) If u(x, t) = X(x)T(t), derive and solve the eigenvalue problem obeyed by X(x). b) Find T(t), and write down the general solution for u(x, t) obeying the boundary conditions. Page 1 of 2 c) Find the formal solution for the temperature distribution in the wire at all times t > 0 if the initial temperature distribution in the wire is f (x) = g(x) + cos 3Tx with 1, 0< x < 1, g(x) = 2, 2 < x < 2, Write the solution in sigma notation.
Transcribed Image Text:Consider the problem of heat flow in a uniform wire of length 2 described by ди 0 < x < 2, t> 0, 4. Əx²' du du Ôz (0, t). u(x, 0) = f(x) 0 <x < 2 (2, t) = 0, t > 0 a) If u(x, t) = X(x)T(t), derive and solve the eigenvalue problem obeyed by X(x). b) Find T(t), and write down the general solution for u(x, t) obeying the boundary conditions. Page 1 of 2 c) Find the formal solution for the temperature distribution in the wire at all times t > 0 if the initial temperature distribution in the wire is f (x) = g(x) + cos 3Tx with 1, 0< x < 1, g(x) = 2, 2 < x < 2, Write the solution in sigma notation.
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