Mathematica Notebooks

This page provides some Mathematica Notebooks (and occasionally lecture notes) from a few courses that I have taught. The Notebooks were updated to Mathematica 8.01 in June 2011. My Mathematica notebooks are not necessarily useful to anybody else but me.

Last modified Sunday, 19-Jun-2011 14:27:29 CDT
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Mathematica Information Center

Fall 2002, METR 6803

Here are a few notebooks from an interdepartmental applied math course I taught.

series_sol.nb (html). Series solution of an ODE.
algebra_pert.nb (html). Real simple application of a regular perturbation method to an quadratic equation with a known solution.
regulart_pert.nb (html) Regular perturbation method applied to an ODE.
nonosc_pert.nb (html) Regular perturbation method applied to an ODE, with a secular term.
matched_pert.nb (html) Matched asymptotic expansion applied to an ODE boundary value problem.
coupled_osc.nb (html) Eigenvalue, eigenvector method applied to linear coupled oscillators.

Spring 1998, METR 5123

After becoming familiar with Mathematica and reviewing the elementary theory of water waves, look at the following notebooks:

waterwave.nb The theory of surface gravity waves. Some bugs fixed Jan. 16 (Thanks to Ted Mansell).
waterwave2.nb Two-layer internal waves. Notation repaired Jan 23, layers were reversed. Thanks to John Mewes

prob01.nb Your first assignment! It's about Kelvin-Helmholtz instability. Enjoy! (Review Kundu).

Anelastic Equations for the Atmosphere (postscript file).

After reading the above, enjoy the following notebooks:

plotinternalwave.nb Make a colorful plot of the cross-section of an internal wave.
internalwaveshoot.nb A shooting scheme applied to solving the boundary value problem for internal waves.
wavepackets.nb Animating dispersive wave packets.
animator.nb Dumps sequences of gif images that can be animated or put on a web page.

prob02.nb Unleash your creative powers!

The Shallow Water Canon geostrophic adjustment, Rossby waves (postscript file).

After reading the above, enjoy the following notebooks:

hatadjust.nb Examine how a "top hat" profile in surface displacement undergoes conversion to a geostrophic state.
shallowshoot.nb A shooting scheme applied to the boundary value problem for Rossby waves and other waves with strongly varying f. This notebook is not complete, and a prob03b.nb may appear here, asking you to complete it.

prob03.nb Try your hand at geostrophic adjustment!

An Unstable Parallel Flow (postscript file)

Now enjoy the following notebooks:

ezm.tar.gz A directory with data files. Download into your mathematica directory, then:
```
gunzip ezm.tar.gz
tar xvf ezm.tar
```
You should find a directory ezm with 11 files inside.
ezmplot.nb Plot the pretty figures in An Unstable Parallel Flow.
shearshoot.nb.gz Solves the eigenvalue problem in An Unstable Parallel Flow.

prob04.nb Now it is your turn to analyze the "data"!

Dynamical Equations in the ARPS and COAMPS Coordinate System

After reading the above, enjoy the following notebooks:

lambert.nb.gz Makes the nice plots seen in Dynamical Equations in the ARPS and COAMPS Coordinate System
UDelU.nb Derives the acceleration terms as in Dynamical Equations in the ARPS and COAMPS Coordinate System

prob05.nb Acceleration terms in cylindrical coordinates.

Symmetric Instability (postscript file)

prob06.nb A collection of problems about symmetric instability.

Thermal convection (postscript file) A few more typos fixed on April 8

After reading the above, enjoy the following notebooks:

convstab.nb makes the stability plot seen in convect.ps.gz
spect.nb functions used by the following notebooks:
chaos.nb.gz Explore the chaos of the Lorenz equations.
compare.nb.gz Compares solutions from the spectral model, with various levels of truncation.

prob07.nb.gz A couple of fun things to try with thermal convection.

Baroclinic instability (postscript file)

prob08.nb.gz Make the plots in the above manuscript.