How to do it in Mathematica

This page will be used to accumulate short Mathematica notebooks with examples that we encounter in Physics 834. It is not intended to be exhaustive!
URL: http://www.physics.ohio-state.edu/~ntg/834/mathematica.php
The notebooks here were written assuming Mathematica version 7 or later (you may get an advisory with later versions).

Recent changes to this page:

Integrals

Date Revised	Notebook	Comments
25-Sep-2011	Spherical coordinates volume integrals	Sample integrals for doing a three-dimensional volume integral in spherical coordinates.
15-Oct-2011	Checking PS#3 integrals	Getting answers for the contour integrals in PS#3, including using Assumptions.
15-Oct-2011	Checking PS#2 problems	Checking answers for PS#2 (still in progress --- the first problem is done).
23-Nov-2011	Gaussian quadrature tests, Part 1	Some sample tests of gaussian quadrature (Gauss-Legendre and Gauss-Laguerre with N=3).

Complex Numbers and Functions

Date Revised	Notebook	Comments
29-Sep-2011	Finding Residues	Using the Residue command in Mathematica.
29-Sep-2011	Complex Series	Examples of expanding complex functions in series and determining the radius of convergence.
29-Sep-2011	Complex Roots	Examples of how to solve zⁿ = a.
29-Sep-2011	Complex Trigonometry	Examples of trig functions with complex arguments and also converting back and forth from expoential to trig.

Differential Equations

Date Revised	Notebook	Comments
23-Nov-2011	Green's functions, Part 1	A look at Green's functions for a sample Helmholtz equation example.
04-Nov-2011	Diffusion Part 1	Animated solution to a diffusion problem (not derived; just plotted).
17-Oct-2011	PS#4 checks	Checking answers for (some of) the differential equations in PS#4.
15-Oct-2011	Checking PS#3 differential equations	Getting answers for the differential equations in PS#3, including using extracting the equations in convenient form.
25-Sep-2011	Nonlinear Diff Eq	Mathematica notebook solving the nonlinear Duffing differential equation, looking at the time dependence, phase space plots, Poincare sections, and the power spectrum.
25-Sep-2011	Nonlinear Pendulum	Mathematica notebook solving the nonlinear pendulum differential equation for various initial conditions, looking at the time dependence, phase space plots, Poincare sections, and the power spectrum.

Special Functions

Date Revised	Notebook	Comments
13-Nov-2011	Legendre polynomials	Plots of polynomials and checks of orthogonality.
13-Nov-2011	Laguerre polynomials	Plots of polynomials and checks of orthogonality.
23-Nov-2011	Spherical harmonics	Plots of spherical harmonics. 3D!!

Fourier Series and Transforms

Date Revised	Notebook	Comments
16-Oct-2011	Fourier Series	Basic integrals and plots of Fourier Series.
24-Oct-2011	Fourier Series 2	Comparing full, sine, and cosine Fourier Series.
26-Oct-2011	Fourier Series 3	Generalized string plucking and harmonics. Includes animation!
30-Oct-2011	Checks of PS#5	Solutions to Fourier series problems from PS#5.
07-Nov-2011	Checks of PS#7	Solutions to Fourier transform problems from PS#7.

Dirac Delta Functions

Date Revised	Notebook	Comments
04-Nov-2011	Checks of PS#6	Solutions to Dirac delta function and Fourier series problems from PS#6.
31-Oct-2011	Dirac Delta function	Basics of using the built-in delta function in Mathematica.

Simplification

Date Revised	Notebook	Comments
07-Nov-2011	Defining Simplication Rules	Simplication rules for logarithms are defined for a private function.
29-Sep-2011	Trig Simplification	Simplifying cos[3θ] and simplifying cos[nπ] enforcing the assumption that n is an integer.

Formatting

Sample Mathematica notebooks

On some machines clicking the link will start Mathematica directly. If not, "right click" to save the file and then read it into Mathematica separately.

Date Added	Notebook	Comments
23-Sep-2011	Calculate area	A simple Mathematica notebook defining a function to calculate the area of a circle, including forcing numerical output and multiple definitions of a function with different numbers of arguments. Also, making it into a program.
23-Sep-2011	Defining n!	Mathematica notebook with many ways to define n!.
23-Sep-2011	Rolling dice	Mathematica notebook that simulates the rolling of dice, where the outcome is a random integer from 1 to 6. Histograms are generated for different numbers of "trials" (i.e., throws of the dice), providing visualization of how the fluctuations scale with the number of trials.
25-Sep-2011	3D Square Well	Mathematica notebook to find the eigenvalues of a spherical three-dimensional square well by matching solutions.