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Next: More damn exercises Up: Mma Previous: Runaway calculations

Exercises

  1. Fire up the Help Browser as the first order of business.
  2. If you are unfamiliar with Mathematica , check the Getting Started/Demos section of the Help Browser
  3. Look here for scads of Notebooks which illustrate various tasks-look at the Notebook names. Try running at least a couple (some may require an ancillary data or image file you'll need to download too).
  4. Plot $\sin^2 x \coth x$ over the range $0\leq x \leq 1$.
  5. Evaluate the indefinite integral of $\frac{(x-1)^2 (x+2)}{(x-3)^3 (x+1)}$ and verify your result by differentiating and reducing it to the starting form. Hint: use Apart
  6. Make a table of the numerical values of $\sqrt{x+3 i x^2}$ for $x=0,1,2,3,4$. Warning: Don't use $()^{0.5}$-this forces things to be treated numerically. Ugh!
  7. What are the first 50 places of $e^{\pi}-\pi^{e}$?
  8. Find the first four terms in the Taylor series for the functions
    1. $\sin(\exp(-x))$ about $x=1$
    2. $\exp(-a/x))$ about $x=0$
  9. Define the function $f(x,y)=\sin^{2}(x^2 y)$ and use the ContourPlot to plot it over the range $-2\pi\leq x\leq +2\pi$ and $0\leq y \leq 4\pi$. What options could you use to make the contours smoother?
  10. Same function, but plotted with Plot3D Can you suppress the surface mesh? Play with the viewpoint using Input$\rightarrow$ 3D Viewpoint Selector
  11. Find the eigenvalues and eigenvectors of a $3 \times 3$ symmetric real matrix.
  12. Practice saving EPS graphics files from your notebook by selecting the graphic (only), then using Edit$\rightarrow$Save Selection As.
  13. Solve the ordinary differential equation

    \begin{displaymath} x y'' -2 x y' +y = 0 \end{displaymath}

next up previous
Next: More damn exercises Up: Mma Previous: Runaway calculations
David Wood 2007-06-25