Find the best L1 linear approximation of ex on [0,1]... see attachment
Locate and classify all isolated singularities (see attached). No calculator or computer allowed.
Use Fourier transform to solve the following differential equation: g" + 2g' + 5g = delta(x) Where delta is the dirac delta function (impulse).
Solve the Schrodinger equation with different potentials using the Fourier transform.
Laplace transform and the heat equation
Solve the heat equation for a semi-infinite long thin rod kept initially at zero degrees using Laplace transfrom
What is the solution to Y’’(x) + 2y’(x) + 5y(x) = f(x) Where f(x) is a given forcing function, and y and f both decay to 0 as x ---> + or - INF Note: should read “as x approaches plus or minus infinity”
f(x)= {0 -2
Application of Fourier Transfors to Diffusion
Using Fourier Transforms, solve the one-dimensional equation for a point source located at x=xo, i.e., at time zero, c(x,0) = (delta)(x-xo).
Please see the attached file for the fully formatted problems. The problem is number 8 on page 989 of the 2nd Edition of Greenberg's Advanced Engineering Mathematics book, PART C ONLY. This is in section 18.4 (Chapter 18 is the Diffusion Equation), in the exercises at the end of the section. PLEASE NOTE: I have scanned th ...continues
Yinon, If you do not wish to work on the Laplace diffusion problem anymore, I would like to see the solution you have formulated thus far and will pay you some credits even though it is not entirely correct. Please leave me a note. Thank you!
