Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN: 9781337111348
Author: Bruce Crauder, Benny Evans, Alan Noell
Publisher: Cengage Learning
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4. (20 points) Consider a bar 30cm long that is made of a material for which a²
Assume both the sides and the ends of the bar are insulated. Suppose that the initial
temperature is given by f(x) = 4 cos (7x) - ½ cos (1) for x = (0,30).
(a) (5 points) According to the description in the problem, set up the corresponding
heat equation of the temperature u = u(x,t) with suitable initial and boundary
conditions.
(b) (15 points) Solve the heat equation to find the temperature u.
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Transcribed Image Text:= 1 4. (20 points) Consider a bar 30cm long that is made of a material for which a² Assume both the sides and the ends of the bar are insulated. Suppose that the initial temperature is given by f(x) = 4 cos (7x) - ½ cos (1) for x = (0,30). (a) (5 points) According to the description in the problem, set up the corresponding heat equation of the temperature u = u(x,t) with suitable initial and boundary conditions. (b) (15 points) Solve the heat equation to find the temperature u.
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