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- Since Newt will plot any function you can think of, it's the perfect
way to check yourself. The most obvious case is when you are
required to plot functions yourself. This is useful at school, when
you're introduced to quadratics, or trigonometric functions. Newt
is equally useful for university students, when you encounter
functions of two variables, and begin a more in depth study
of the calculus.
- Familiarise yourself with the principles behind differentiation and
integration by using Newt's animation features for some of the
calculus modules. When you understand the principles behind the methods, you can start
to do the calculations with confidence.
- Newt has a built-in library of special functions,
Some of these functions, such as Bessel functions and Fourier
summations, are defined in terms of infinite series - which
makes them very difficult to plot. Luckily, it's as simple as
looking up the expressions for these functions in the help,
and entering them with the arguments you want. Since
Newt will plot these summations for a range of different
orders, you can easily obtain a visual understanding of
convergence. This is an easy way to see how these
summations converge to the functions defined
by their infinite counterparts.
- For applied maths students: when you encounter dynamical systems
in a modeling course, you will undoubtedly be required to plot
these systems by hand. Far from suggesting that you use Newt
to do these for you, we recommend that you use Newt to check
yourself. If you later do a more advanced course and start to
look at non-linear systems, Newt will be even more valuable,
and is a good way of visualising linearisation.
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- Use Newt's printing features to print out graphs for
project write-ups and other handins. You can label and caption
these graphs easily using Newt's special features.
- Check your calculations when integrating complex expressions by
getting Newt to quickly approximate the numerical value of an integral. In this
way you'll be able to tell if you're far off the mark.
- Get together with a friend and test each other's knowledge of
calculus before a maths test by using the hidden functions to plot
mystery graphs for your friend to identify.
- Stepping constants will allow you to explore just how the constants
in a graph's standard form affect the shape of the graph. Try something
like sinax and see how a affects the period.
- Use Newt to explore the idea of beats in waves in science.
Try plotting something like 3sinx+cos10x.
- Use the Functions of two variables module to explore contours
for geography. Try plotting
e^-2(xx+yy) (a small hill, if you like) and then use the Contour
Plot function to plot contours from 0 to 1 in steps of 0.2.
- Biology students can explore the predator-prey relationship. In
the 2D Dynamical Systems module, set dx/dt to x-xy and
set dy/dt to -y+xy. Then plot curves using the Twin Graphs
option, to see how the two populations interact.
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