Exercise 2. Consider the following heat equation on the upper half-space u₁(x,t) = uxx(x, t) + 2u(x, t) for xЄR, t> 0 u(x, 0) = f(x) for x = R. where f is a given continuously differentiable function such that f is integrable on R. Obtain a general solution for this pde by using the "Fourier transform &" and justifying all the development as done in the Lecture classes. 元 Hint: if g(x) = ¸¯x²/41 e², then F (81)(x) = e²x²+1+21.) t

Exercise 2. Consider the following heat equation on the upper half-space u₁(x,t) = uxx(x, t) + 2u(x, t) for xЄR, t> 0 u(x, 0) = f(x) for x = R. where f is a given continuously differentiable function such that f is integrable on R. Obtain a general solution for this pde by using the "Fourier transform &" and justifying all the development as done in the Lecture classes. 元 Hint: if g(x) = ¸¯x²/41 e², then F (81)(x) = e²x²+1+21.) t

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section6.6: Additional Trigonometric Graphs

Problem 78E

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