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Solve u t = k1 2u x2 + k2 2u y2 on a rectangle (0 < x < L, 0 <y

Applied Partial Differential Equations with Fourier Series and Boundary Value Problems | 5th Edition | ISBN: 9780321797056 | Authors: Richard Haberman ISBN: 9780321797056 284

Solution for problem 7.3.3 Chapter 7.3

Applied Partial Differential Equations with Fourier Series and Boundary Value Problems | 5th Edition

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Applied Partial Differential Equations with Fourier Series and Boundary Value Problems | 5th Edition | ISBN: 9780321797056 | Authors: Richard Haberman

Applied Partial Differential Equations with Fourier Series and Boundary Value Problems | 5th Edition

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Problem 7.3.3

Solve u t = k1 2u x2 + k2 2u y2 on a rectangle (0 < x < L, 0

Step-by-Step Solution:
Step 1 of 3

The Definite Integral To find the area under f(x) from x=a to x=b Divide the interval [a, b] into n subintervals of equal width. Let X0, X1, X2, ….Xn, be the endpoints of these subintervals and X*1, X*2, X*3, ….X*n be any sample point in our subintervals, so that X*i is in the ith subinterval. The area of the ith rectangle is height * width =f(xi*)Δx where Δx= (b-a)/n The total area of all the rectangles is f(x*1)Δx + f(x*2)Δx + f(x*3)Δx + …… f(x*n)Δx n =​ Σ​f(xi*)Δx i=1 This is called a​ iemann Sum​ n b The definite integral of f(x) from x = a to x= b if(x)dx = lim (Σf(xi )Δx) ∫ *

Step 2 of 3

Chapter 7.3, Problem 7.3.3 is Solved
Step 3 of 3

Textbook: Applied Partial Differential Equations with Fourier Series and Boundary Value Problems
Edition: 5
Author: Richard Haberman
ISBN: 9780321797056

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Solve u t = k1 2u x2 + k2 2u y2 on a rectangle (0 < x < L, 0 <y