By Moretti C.

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**Additional info for A brief introduction to Mathematica**

**Example text**

This scale will make it impossible to see any local details on the graph. The graph may have a local maximum at (2,3), but you’ll never see it on that scale. Restricting the range of y-values will allow you to see more features of the graph. An example of this option would be Plot[Sin[x],{x,0,2Pi},PlotRange->{0,1}], which generates the graphic You can also force Mathematica to try to plot all y-values that occur in a graph (sometimes a graph might be “beheaded” by the edges of the plot) - to do this, use PlotRange->All.

8) Find the critical points of x4 − 4x3 + 2x2 − 9. 9) Find all of the first and second order partial derivatives of x2 y−y 2 x2 +y 2 . 10) Find the Taylor polynomials of tan(x) at 0 of orders 3, 5, and 10. Use these to estimate tan( 12 ). 11) Find an antiderivative of x2 sin(x). 12) Find an antiderivative of 13) Find an antiderivative of 14) Find 1 0 15) Find ∞ x2 dx. 1 ex 1 x3 −1 . ∞ xn n=2 n2 . x3 ex dx. 16) Numerically estimate ∞ n+1 n=2 n4 . 17) Solve the differential equation y − y = 0. 18) Solve the initial value problem y + y = 0, y(0) = 3, y (0) = 2.

DSolve[{y [x]+y[x]==0,y[0]==3,y’[0]==2},y[x],x])[[1]] The y[x]/. command tells Mathematica to replace y[x] with the solution from DSolve[ ] - but this is a list, so the [[1]] at the end returns the first (and only) element of the list. {-2,1,0,3} For 3-8, define a={{1,2,3},{4,5,6},{2,1,5}} and b={{3,2,1},{0,-6,5},{1,2,3}}. To view the results as matrices, put the commands inside a MatrixForm[ ] command. a 6) Transpose[a] 7) Det[a] 8) Inverse[a] 9) Define c={{1,2,1},{2,6,1},{1,1,0}}, then evaluate Eigenvalues[c] and Eigenvectors[c] 53 Chapter Eight Exercises 1) Plot[xˆ3,{x,-2,3}] 2) Plot[{Sin[x],Cos[2x]},{x,0,10Pi}] 3) Plot[Cos[x],{x,0,2Pi},Ticks->{{0,Pi/2,Pi,3Pi/2,2Pi},{0,1/2,1} },PlotLabel->“y=cos(x)”] 4) Plot[1/(xˆ3-x),{x,-5,5},PlotRange->{-5,5}] 5) Plot[Sqrt[9-xˆ2],{x,-3,3},AspectRatio->Automatic, AxesLabel->{“x-axis”,“y-axis”}] 6) ParametricPlot[{t Cos[t], t Sin[t]},{t,0,10},AspectRatio->Automatic, PlotPoints->50] 7) ParametricPlot[{Sin[2t],Sin[t]},{t,0,20}] 8) After loading in the ImplicitPlot package (see solutions to Chapter One Exercises), use ImplicitPlot[xˆ2/9+yˆ2/4==1,{x,-4,4}].

### A brief introduction to Mathematica by Moretti C.

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