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Introduction to Mathematica

# Introduction to Mathematica - Introduction to Mathematica...

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Introduction to Mathematica Seth F. Oppenheimer The purpose of this handout is to familiarize you with Mathematica. The Mathematics and Statistics Department computer lab is on the fourth floor of Allen Hall and is open most afternoons and evenings. You will need your netID and password to log on. What you will now see is a printout of an actual Mathematica session. Mathematica can act as a scientific calculator as in the examples below: 2+3.6 In order to evaluate this, you must hold the shift key and while holding the shift key, press enter or return. 5.6 Sin[Pi/4] 1 ------- ------ Sqrt[2] Now that is an exact answer! We can use the notation %25 to indicate output 25. The command N[ ] yields a numerical approxi- mation for what is in the square brackets. N[ , 100] would give that approximation to 100 places. %25 1 ------- ------ Sqrt[2] N[%25] 0.707107 N[%25,100] 0.707106781186547524400844362104849039284835937688474\ 0365883398689953662392310535194251937671638207864 N[Pi] 3.14159

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N[Pi,30] 3.14159265358979323846264338328 Cool, huh? Case matters in Mathematica. All built in functions such as Sin, Cos, Exp, Sqrt, and so on are started with upper case letters. When you define your own functions, make sure you spell them with lower case letters. Let us define a function f that takes a number squares it and adds three to that square. f[x_]:= x^2 + 3 We may now evaluate f at a variety of numbers: f[2] 7 f[47] 2212 f[-32] 1027 We can now plot f, differentiate it with respect to x, find the indefinite integral of f with respect to x. Plot[f[x],{x,-3,4}] -3 -2 -1 1 2 3 4 2.5 5 7.5 10 12.5 15 17.5 -Graphics- D[f[x],x] 2 x 2 intro1c.nb
Integrate[f[x],x] 3 x 3 x + -- - 3 Notice that you have to provide the arbitrary constant. Now we can take definite integrals as well, say from 1 to 3: Integrate[f[x],{x,1,3}] 44 -- - 3 We can even do three dimensional graphs and parametric plots in one and two dimensions: g[x_,y_] := x^2 - y^2 Plot3D[g[x,y],{x,-2,2},{y,-2,2}] -2 -1 0 1 2 -2 -1 0 1 2 -4 -2 0 2 4 -SurfaceGraphics- Now let us plot the parametric curve of (Sin[t],t Cos[t]) as t goes from 0 to 4 Pi. intro1c.nb 3

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ParametricPlot[{Sin[t], t Cos[t]},{t,0,4 Pi}] -1 -0.5 0.5 1 -10 -5 5 10 -Graphics- Or how about the helix in three dimensions given by (Cos[4 t],Sin[4 t],t) for t from 0 to Pi?
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Introduction to Mathematica - Introduction to Mathematica...

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