1. Solve and NSolve.
2. Plotting functions.
3. Defining your own functions.
4. Tutorial questions.

1. Solve and NSolve:
   • We'll look at various equations. A quadratic, a cubic and a quartic(a fourth order polynomial so will have x⁴ terms in it). The first 2 you are more familiar with and can do by hand, the quartic is that bit trickier. Of course using mathematica it's all the same. So just type in:
     

     Solve[x3+2x2+4x-7 = = 0, x]

     or
     

     NSolve[x3+2x2+4x-7 = = 0, x]

     and your done.

2. Plotting functions:
   • This too is easy enough. Exactly what you would have guessed in fact. It is Plot with a capital P. The arguements are then given in square brackets and the range of x's which you plot are given in curly ones as in the Integrate command. So to plot x² from -10 to 10 we type:
     

     Plot[f,{x,-10,10}]

   • You can specify the y-range too by specifiying the PlotRange. From the notes we have:
     

     Plot[(x+1)/(x2+x-2),{x,-5,5}, PlotRange- > {-5,5}]

     We use this because the function goes to infinity between -5 and +5 so by limiting y to between +5 and -5 we get a more sensible graph.

3. Defining your own functions:
   • We can define our own constants. So we can say that interest=0.1.
   • To define a function f(x) = x²+1 say we type
     

     f[x_] = x2+1

     then we can type f(5) and mathematica will work that out to be
     

     52+1 = 26

     .
   • Once we have this we can perform calulations using f(x). Then the calculations can be repeated easily for different cases by changing f(x)'s definition.

4. Tutorial questions(need to do the last two on mathematica before the tutorial!):
   • Express 5,7,13,21 in binary, octal and hex.
   • What is (341)₅ and (211)₁₆ in base 10.
   • Express [41/3] in binary.
   • Determine
     

     ó õ xcos(x) dx

     and
     

     ó õ 2 0  3x 4x3+2 dx.

   • Solve x⁴-x³+4x²+3 = 0.

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File translated from T_EX by T_TH, version 2.70.
On 1 Nov 2002, 11:08.