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Entering and evaluating Mathematica Expressions
All Mathematica functions begin with a capital letter and the
argument list is delimited by square brackets [ ], thus
sin( x2 ) is entered as Sin[xÙ2]
| (x - y)/z |
is entered as Abs[(x-y)/z]
3Ö{e7x}
is entered as Exp[7x/3].
Other items such as q or p have to be entered with special keystrokes or can be typeset using the palettes. Follow the menus File -> Pallettes -> Basic Typesetting. Mathematica expressions are evaluated on MS Windows machines with the keystroke Shift-Enter.
| Function | Range | Mathematica |
| y = f(x) | a £ x £ b | Plot2D[f(x), {x, a, b}] |
| y = f(x) | a £ x £ b, c £ y £ d | Plot2D[f(x),{x,a,b},PlotRange->{c,d}] |
| y = f(x) and y = g(x) | a £ x £ b | Plot2D[{f(x),g(x)},{x, a, b}] |
| z = f(x,y) | a £ x £ b, c £ y £ d | Plot3D[f(x,y), {x, a, b}, {y, c, d}] |
| x = f(t), y = g(t) | a £ t £ b | ParametricPlot[{f(t), g(t)}, {t, a, b}] |
| (x1,y1), (x2, y2), ¼, (xn, yn) | ListPlot[{{x1,y1},{x2,y2}, ¼,{xn,yn}},PlotJoined->True] | |
Algebraic and Numeric manipulations
Any expression can be numerically approximated by using the N
command, so the expression N[Pi] gives the approximation
of p to a default number of significant digits
places and
N[E,100] gives the approximation of e to 100
significant digits.
Equations such as f(x,y) = C can be solved algebraically for x with the command Solve[f(x,y)==C,x] and can be solved numerically with the command NSolve[f(x,y)==C,x]. This can be used for substitutions as well, so to solve f(x,y) = C for x, given that y = D, we can use Solve[{f(x,y)==C, y==D},x}].
In a similar manner, systems f(x,y) = C and g(x,y) = D can be solved algebraically with the command Solve[{f(x,y)==C, g(x,y)==D}, {x,y}] and numerically with the command NSolve[{f(x,y)==C, g(x,y)==D}, {x,y}].
Evaluation of limits
The expression limx® af(x)
can be evaluated as Limit[f(x), x->a] with the Side
variable controlling the one sided limits. Thus, limx®
a+ f(x) is entered as Limit[f(x), x->a, Direction->-1]
and limx® a-f(x) is
entered as Limit[f(x), x->a, Direction->1].
Expansion of series
The expansion of the first n terms of the Taylor series for f(x) about
the point x = a, including a ``Big O'' order term, is calculated using
the command Series[f(x), {x, a, n}]. The order term can
be removed with the command Normal[Series[f(x), {x, a, n}]].
Evaluation of derivatives
The first derivative with respect to x of the function f(x) can be
generated with the command D[f(x),x]. The n'th derivative
with repsect to x can be generated with the command D[f(x),{x,n}].
Evaluation of integrals
The indefinite integral òf(x) dx
can be generated with the command
Integrate[f(x),x]. The
definite integral òab
f(x) dx is generated by the command Integrate[f(x),{x, a, b}].
Loading application packages
Many of the packages that are added on must be loaded separately before
being used. You can browse for these packages by following the menus to
Help
-> Add-ons -> Standard Packages -> Package Family ->
Package.
For instance, the Combinatoria package of the DiscreteMath
package family is loaded with the command
<<DiscreteMath`Combinatorica`
Printing a notebook
Choose the File menu and then the Print sub-menu to print
the current notebook.
Shutting down Mathematica and logging
out of the OCCNet
Use the mouse to click on the File menu and take the Exit
command. Then, click on the Start menu followed by the Shut Down
command. Finally, click on the Shut down the computer option followed
by the Yes button.