During the semester, we will ask you to use some Mathematica applets
for exploration. You will not need to know Mathematica
to use the applets.
Installing Mathematica on your computer
If you would like to install Mathematica on your computer, download it
here,
and follow the instructions on that page. When you request your
activation key (do that
here), be sure to use your
Harvard email
address.
If you prefer not to install Mathematica yourself, it is available on
computers in many computer labs on
campus.
Applets
Here are some applets for you to use. When you use an applet,
Mathematica may ask whether you want to "Enable Dynamic"; you do.
Please right-click and save the applets to your
computer before using them;
alternatively, download all applets
as a zip file.
- FunctionGrapher.nb allows
you to graph up to 6 functions.
- FunctionPlotterEvaluator.nb
allows you to graph up to 6 functions and evaluate them at a
particular number.
- FiniteSumTable.nb looks at
sums where you're summing from something to n. The applet
will evaluate the sum for all values of n up to 100.
- TaylorPolynomialGrapher.nb
allows you to enter a function, together with its general Taylor
polynomial approximation, and see graphs of the function together with
the Taylor polynomial approximations.
- FiniteSum.nb will give you a
decimal approximation of any finite sum that you enter in summation
notation.
- RearrangeAlternatingHarmonic.nb
- One of the odd features of conditionally convergent series (such as
the alternating harmonic series) is that you can rearrange the terms
to get a series with a different sum. This applet shows how that
happens.
- SlopeFieldAndFunctionGrapher.nb
- This applet graphs a slope field and a function.
Mathematica is picky about how you enter functions. Here are some
useful references:
In our applets, once you're done entering an expression, Mathematica
will try to reformat it, which should help you find any mistakes.