Sample Exercises for Matlab

• Write a subroutine to calculate the binomial factor:

  $$\left( \begin{array} {c} a\\ b \end{array}\right)= \frac{a!}{b!(a-b!)}$$

• Write a subroutine which returns the first n Fibonacci numbers F_i, i=1,..,n, where F₁=F₂=1, and

  F_i+1=F_i+F_i-1

• Write a subroutine which prints out the first n rows of Pascal's triangle. An element in a row is defined by the addition of neighbouring elements in the previous row: 1
  1 1
  1 2 1
  1 3 3 1
  1 4 6 4 1
  
• Write a subroutine which returns the value of the Laguerre Polynomial. The Laguerre Polynomial requires two parameters, $\alpha$ and n both nonnegative integers and

  $$L_n^\alpha(x)=\sum_{m=0}^n\,(-1)^m\left( \begin{array} {c} n+\alpha\\ n-m\end{array}\right)\frac{x^m}{m!}$$

• Obtain the help for the commands surf, contour, meshgrid, real, and create a 3d plot the real part of the function z² where z=x+iy, on a grid where x=[-2,+2] and y=[-2,+2]. Choose a suitable number of grid points to plot.
• Create a 3d plot of sin(r)/r, where $r=\sqrt{x^2+y^2}$, $x\in [-10,+10]$ and $y\in [-10,+10]$ with a suitable number of gridpoints. Try a contour plot, surf plot and a waterfall plot. Get the help of the command view and type view(0,90);shading flat.

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