Mathematica "Interpolating functions" As we just saw, Mathematica expresses the solution of a differential equation as an InterpolatingFunction object. To assign values to variables, use -> rather than an equals sign. All Mathematica functions start with a capital letter, eg. Plotting a parameterized curve in Octave is trivial. fyi, a function in Mathematica is defined using _ as in f[w_,x_,y_,z_]:=. Assigning and Inserting Variables or Parameters. In[5]:= Plot x, x^2, x^3 , x, 0, 2 Out[5]= 0.5 1.0 1.5 2.0 2 4 6 8 Notice that we have two sets of lists in the plot directly above, : the first set enumerates the list of functions to be plotted, the second list delineates the plotting parameters (i.e., plotting with In effect, the regular plot() function already gives a plot of a parametrized function. However, nothing stops us from using it in a more general fashion. For example, To insert a set of parameters to a function use /. A cubic polynomial is normally characterized by the coefficients However, these coefficients are not well suited to describe the geometrical shape of the graph of the cubic. Mathematica Functions. This section is dedicated to the description of the di↵erent plotting functions available in Mathematica. Both of these plot types work best on functions ( elds) that are large within some central region, dying out with distance. The Mathematica commands in this tutorial are all written in bold black font, while Mathematica output is in normal font. value of the fitted parameters, etc.). The relation between the parameter sets is given in the Details section. The Mathematica commands in this tutorial are all written in bold black font, while Mathematica output is in normal font. For example, to plot a circle: Sin[x], Exp[x], Pi or Infinity. Choose the type of plot desired, supply the values of the parameters which are not selected as free variables, and click "Evaluate." Mathematica treats the Interpolating Function like a numerically defined function, so you can plot it, numerically integrate it, etc. This video tutorial covers basic plotting of functions using Mathematica. Finally, you can copy and paste all commands into your Mathematica notebook, change the parameters, and run them because the tutorial is under the terms of the GNU General Public License ( … Mathematica also provides a ContourPlot3D function for three-dimensional contour plots, as well as a VectorPlot3D function for 3-D vector plots. Fortunately, many examples in electromagnetism have that property. btw, your functions always seem to generate very large values: N@f[1, 1, 1, 1] gives 1.9489499245*10^21714 which is really a large number. Nickalls found a set of parameters that do a better job. 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