Mathematica Commands for Calculus

Mathematica is a powerful tool, but we are only going to need a few of it's capabilities. Below I have listed what should be all the Mathematica commands you may want for a calculus course. Mathematica preforms a command after you hit the 'enter' key, not the 'return' key. Mathematica is very picky about capitalization and about the difference between () and {} and [], so be careful.

1. This command clears any previous value of the function F which Mathematica may have stored.

Clear[F] 

2. This command defines a new function called F[x], not F(x). Notice that Mathematica requires you to put an underscore after the x when defining a function.

F[x_]=x^3

3. This command draws a graph of the function F[x]. The list {x, -2, 3} tells Mathematica to graph from x=-2 to x=3.

Plot[F[x],{x,-2,3}]

To specify the dimensions of your window along the y-axis you need to use

Plot[F[x], {x, -2, 3}, PlotRange->{-10,10}]

4. Mathematica knows how to find derivatives provided you tell it the function and the variable.

D[F[x],x]

5. Mathematica knows the two most useful constants.

Pi   E

6. Mathematica knows many popular functions. Log[x] means the natural log, which we often call ln.

Sin[x]   Cos[x]   Log[x]   E^(x)

You can find more functions in the function browser under the help menu.

7. You can get decimal approximations by using the N command

N[Pi]    N[Cos[34]]  N[Sqrt[2]]

8. Mathematica can do summation.

Sum[x^2, {x, -3, 1.9, .12}]

The list {x, -3 ,1.9, .12} gives the lower and upper limits for x, and tells Mathematica to increment each step by .12. In the Mathematica 3.0 you can use

9. Mathematica does symbolic integration of indefinite integrals

Integrate[F[x],x]

as well as definite integrals. Here the list {t, 2, Pi} tells Mathematica to integrate from t=2 to t=Pi.

Integrate[F[t],{t, 2, Pi}]

In Mathematica 3.0 you can use the symbols

10. If you prefer decimal approximations, you can use this command

NIntegrate[Log[x], {x, 1, 10}]

11. Mathematica can find limits.

Limit[(1+1/x)^x, x->Infinity]

Limit[((3+h)^2-3^2)/(h), h->0]

The arrow "->" is just the minus sign followed by the greater than sign.

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