![]() ![]() Show how to create a set of variables that act like “phi sub i”.Ĭompute the coexistence curve for the van der Waals equation of state by numerically solving the Maxwell construction using FindRoot. Solve the Lorenz equations, three coupled nonlinear ODEs that give rise to chaotic motion and sensitive dependence on initial conditions an example of how to solve ODEs using NDSolve.įind the optimum shape of an extended object (here, a chain of beads connected by springs, crossing over a potential “hill”), using FindMinimum to minimize the potential energy. Generate a random permutation of n integers, using the technique of sorting a list of random numbers. Draw in 3D and in projection construct histograms.Ĭode Newton’s method for rootfinding, using traditional “procedural” programming style, and then more compact “functional” programming style of Mathematica using NestList and FixedPoint. Generate a “cloud” of fake data points rotate randomly in space then analyze, to find the principal axes of the cloud, and characteristic widths in each direction. ![]() Each consists of a video and a corresponding Mathematica notebook. The following are examples of problem-solving in Mathematica, which demonstrate various techniques that are generally useful for advanced undergraduates and graduate students in science and engineering. This notebook presents the capabilities of Mathematica at a higher level, suitable for graduate students and postdocs, with an emphasis on list manipulation, defining functions, and programming techniques.Īdvanced Mathematica tutorial.nb.zip Example Problems One-hour intro notebook.nb.zip second hour intro notebook.nb.zip Advanced Mathematica tutorial The Mathematica documents or “notebooks” corresponding to these three lectures can be downloaded, so that a student can follow along with the examples in the lectures, and experiment on her own: These two one-hour lectures introduce the main analytical, numerical, graphical, and programming capabilities of Mathematica relevant to advanced undergraduate or graduate students in science and engineering: The following 30-minute lecture (developed for ChE 230, Computational Tools for Chemical Engineering) introduces Mathematica at the level of beginning undergraduates: ![]()
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