Use the solution given in Problem 20 to rewrite the solution of Example 1 in an alternative
Question:
Use the solution given in Problem 20 to rewrite the solution of Example 1 in an alternative integral form. Then use the change of variables v = 7)/2vra and the results of Problem 11 in Exercises 14.1 to show that the solution of Example 1 can be expressed as
(reference problem 20)
In Problem use the Fourier integral transforms of this to solve the given boundary-value problem. Make assumptions about boundedness where necessary.
If
then the convolution theorem for the Fourier transform is given by
Use this result and
Show that a solution of the boundary-value problem
(reference example 2)
Example 2 Using the Cosine Transform
The steady-state temperature in a semi-infinite plate is determined from
Solve for u (x, y).
(Reference problem 11 of section 14.1)
Modeling the Dynamics of Life Calculus and Probability for Life Scientists
ISBN: 978-0840064189
3rd edition
Authors: Frederick R. Adler