Thursday, September 16, 2010

Plot the zeros of transcendental equations in Mathematica

  • A transcendental equation is defined as function f.
  • It is solved not by the usual Solve routine but by the new Refine routine because it includes all the different possibilities of the unknown variables the equation has. 
  • Assuming is used to tell the kernel that the variables XX and YY  are always positive. Note the way the two conditions are clubbed. With an &&.
  • Now, we have to set XX and YY to some value, otherwise Mathematica would not be able to Plot it. 
  • Then to evaluate at what point the zeros of the function f occurs using the {v,f(v)} and setting v= {the solution}.
  • Now, we can inject this point into the Plot by the Epilog command.  Epilog command is an option for graphics functions which gives a list of graphics primitives to be rendered after the main part of the graphics is rendered. 
  • The options used for the point size / color are standard commands.
  • Now mathematics plots the function f. Then renders the points of its zeros directly into the plot. So, the end effect is that we see the points where the function crosses the x-axis highlighted in RED.

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