MATLAB MATHEMATICA MATH-301-061 Dr. Faisal Fairag |
||
QUIZ (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. | ||
PROBLEM 1 [Hint: use Matlab command laplace or Mathematica command LaplaceTransform] |
||
[Hint: use Matlab command ilaplace or Mathematica command InverseLaplaceTransform] |
||
PROBLEM 3 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[----] ] |
||
PROBLEM 4 Let 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[----] ] |
||
PROBLEM 5 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[---] ] |
||
PROBLEM 6 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 |
||