Visualizing the long run behaviors of solutions to differential equations. Some typical solution curves that are needed to determine some otherįeatures of streamlines, such as the bounds (or fences), sepatratrix,Īnd other similar properties within varying domains.

$mathematica command line$

A phase portrait is a graphical tool that consists of Theĭetailed features can only be obtained if we observe the phase Shows arrows on a plot indicating the direction of streamlines. Is not detailed on the behavior of specific solutions, as it only Plotting either a list of vectors or lines. Previously we discussed direction fields that could be visualized by Return to the main page for the course APMA0340 Return to the main page for the course APMA0330 Return to Mathematica tutorial for the second course APMA0340 Return to computing page for the second course APMA0340 Return to computing page for the first course APMA0330 Laplace transform of discontinuous functions.Picard iterations for the second order ODEs.Series solutions for the second order equations.Part IV: Second and Higher Order Differential Equations.Numerical solution using DSolve and NDSolve.Part III: Numerical Methods and Applications.Equations reducible to the separable equations.(* Convert Mathematica notebooks to PDFs *) #!/usr/local/bin/MathematicaScript -script Save the following code as nb2pdf, make it executable and place it the directory with the files you want to convert or somewhere in your path. Here's a solution in the form of a Mathematica script - it can easily be turned into a Notebook or package file. This means that you could either make a notebook to do the conversion or call the frontend from the command line. To print or convert it, you first need to open it andĪ naive attempt to open a notebook from the Mathematica command line yields the error FrontEndObject::notavail In:= NotebookOpenĪ front end is not available certain operations require a front end. Basically, there is no way to convert Mathematica notebooks into PDFs without invoking the frontend.