Dr. Faisal Fairag


(30 points Bonus Quiz)

(30 points Extra Quiz)

Please read this before your start

*Use MATLAB or Mathematica to solve these problems.

*You will receive your code number by email

*Submit your answers any time before 11:55PM Wed December 20, 2006

*Here is a  quick start to MATLAB

*Here is a  quick start to MATHEMATICA

*Let    w = ( last four digits of your ID number ) / 1000

*Be aware that each student has  different answers.
*To submit    3.567 X 10^(-33)    type     3.567e-33
*First solve all the 6 problems then enter all the 6 answers in the left page then click on submit button.
*In Matlab before you start the computaions type the command "format long" to display the result in 15 digits for double.

*In Mathematica use  the command N[----,10]  This gives the numerical value of the computation to a 10 number of significant digits. Try N[Pi,10]

* Here is an example of submission
*After you click on Submit button, wait until you receive the confirmation page.


[Hint: use Matlab command laplace or Mathematica command LaplaceTransform]

[Hint: use Matlab command ilaplace or Mathematica command InverseLaplaceTransform]


The temperature u(x,t) of the BVP (1-3) page 697 with f(x)=100, L=π, k=1 is given in equation(13) page 699. Find the temperature of the rod at the center of the rod after (w-1) seconds.

[Hint: use Mathematica command Sum[----]  ]



The Fourier series of f(x) is given in equation (13) page 659. Let S100(x) be the 100-th partial sum of the Fourier series of f(x). Find  S100(0.0005*w)

[Hint: use Mathematica command Sum[----]  ]


Expand f(x)=sin(x^w), where -2<x<2, in a complex Fourier series as in section 12.4 equation (7). 

Find  | c100 |

[Hint: use Mathematica command NIntegrate[----]  and ABS[---]   ]


Consider the exercise 5 in page 708 ( solve Laplace's Equation ). The solution of the problem is given in page A-59. Use Mathematica command Plot3D to graph the solution in [0,1]x[0,1] square. then from graph find the maximum value for u(x,y) and this maximum occurs at (x0,y0). Find x0 and y0