TJM's Mathematica Reference Sheet
(adapted from works by Trisha Bergthold, Andy Miller, and Jon White)
-
Capitalize all commands and use square brackets around their arguments.
-
Use only parentheses as grouping symbols in your expressions -- Mathematica
reserves brackets and braces for other purposes.
-
Press SHIFT-ENTER, not just Enter, when you want Mathematica to
evaluate an expression.
Arithmetic
Algebra
Calculus
Graphing
two dimensional
gives the graph of
on the interval
three dimensional
gives the graph of z=sin(x)sin(y)
for x values from -6 to 6 and y values from -8 to 8
contour plot
gives the graph of z=sin(x)sin(y)
for x values from -6 to 6 and y values from -8 to 8
More advanced options
These are given for the Plot3D but have analogues for the Plot and ContourPlot commands.
(These options can be included just within the final bracket of the Plot3D
or other command)
-
Axes->None eliminates the axes from the plot.
-
AxesLabel->{"x","y","z"} labels the three axes with the names given.
-
BoxRatios->{1,1,1} changes the ratios of length, width, and height
from the squished default.
-
Framed->False eliminates the box normally plotted around the graph.
-
Mesh->False eliminates the trace lines Mathematica normally
includes on the surface.
-
PlotPoints->30 samples 30 points along each axis, rather than the
default of 15. This can produce a much smoother graph.
-
PlotRange->{-.3,.3} specifies the vertical range to be plotted.
-
Shading->False produces a graph without any shading of the surface.
-
Ticks->{Automatic,None,{0,Pi/2,Pi,3Pi/2,2Pi}} puts the tick marks
on the x axis in the default locations, puts no tick marks on the y axis,
and forces the tick marks on the z axis to take the specified locations.
-
ViewPoint->{2,2,2} specifies the point from which to view the surface.
or 
(or a blank space between variables: 
)
,
,
,
,
,
,
,
gives the square root of 2 to 20 decimal places.
produces 
,
meaning 
,
,
, and 541 are the factors of 2434500.
gives 
because 5757 is not prime
defines f to be the function
produces 
produces 
gives 
solves the equation
for x
gives 
computes the derivative of the function
f(x)=ln(x)sin(x) with respect to x.
computes the third derivative of the function
f(x)=ln(x)sin(x) with respect to x.
computes the antiderivative with respect to x
of the function 
computes the integral with respect to x
from 0 to 1 of the function 
computes a numerical approximation of the
integral with respect to x from 0 to 1 of the function