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Section Three - Parametric Plots Mathematica can generate plots parametrically using the command ParametricPlot[ ]. If the x-coordinate of a point is given by f(t) and the y-coordinate is given by g(t), then the parametric plot from t=a to t=b is generated by ParametricPlot[{f[t],g[t]},{t,a,b}]. For example, to plot the curve defined by x=t*cos(t) and y=sin(t) as t goes from t=0 to 2π, use the command ParametricPlot[{t Cos[t],Sin[t]},{t,0,2Pi}]. This parametric plot should look like this: The options for ParametricPlot[ ] are the same as for Plot[ ] and entered in exactly the same fashion (including the use of Show[ ] to change options or combine plots).

Transposing Matrices: Transpose[mat1] will return the transpose of mat1 (mat1 with its rows and columns interchanged). Determinants: If mat1 is a square matrix, then Det[mat1] is the determinant of mat1. Minors of matrices: If mat1 is any matrix and k is a positive integer, Minors[mat1,k] will return a list of the k-by-k minors of mat1; that is, a list of the determinants of all k-by-k submatrices of mat1. Inverses: If mat1 is a square matrix and if Det[mat1] is not 0, then Inverse[mat1] will be the matrix inverse of mat1.

Mathematica creates graph by plotting a lot of points and then trying to connect them cleverly. The number of points it uses is PlotPoints. The default value is 25. If a graph has very rapid changes in it (like y=sin(1/x) does near x=0) or the range of x-values is large, 25 points may not be enough to capture the true behavior of the graph. Using more points by using the option PlotPoints->50 or PlotPoints->100 may make the picture a bit better. 2},PlotPoints->100]. Of course, the more points you plot the longer it takes to graph and the more memory Mathematica may need.

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