# A brief introduction to Mathematica by Moretti C.

By Moretti C.

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Use tick marks 0, π2 , π, 3π 2 , 2π on the x-axis and 0, 2 , 1 on the y-axis. Label the plot “y=cos(x)”. 4) Plot y= x31−x from x=-5 to 5. Restrict the range of y-values displayed to -5 to 5. √ 5) Create a plot of y= 9 − x2 as x goes from -3 to 3. Use AspectRatio->Automatic and label both axes. 6) Create a plot of the parametric curve defined by x=t cos(t), y=t sin(t) as t goes from 0 to 10. Use AspectRatio->Automatic, and have Mathematica sample the functions 50 times to create the plot. 7) Create a plot of the curve defined by x=sin(2t), y=sin(t) as t goes from 0 to 20.

You should see the following graphic: The format for Plot3D[ ] is exactly the same as for the Plot[ ] command, except you have to add the second list for the variable y and its range. Another way to plot this function would to first define f=xˆ2-yˆ2, and then enter Plot3D[f,{x,-2,2},{y,-3,3}]. This approach would be useful if you are going to work with x2 − y 2 - taking derivatives, plugging in numbers with the /. notation, and so on. Unlike the Plot[ ] command, you cannot use Plot3D[ ] to plot more than one surface in the same 3-dimensional box.

Solve[ Det[ x*IdentityMatrix[Length[mat1]]-mat1]==0,x]. In practice you always use the Eigenvalues[ ] command, but this shows how you can combine other functions to do complex calculations. Finding Eigenvectors: If mat1 is a square matrix, the Eigenvalues[mat1] will return a list of the eigenvalues of mat1 (remember, if mat1 is an n-by-n matrix, this will be a list of at most n vectors). Eigenvectors may involve complex numbers in their components, as Mathematica always works over the complex numbers.