This page will be used to accumulate short Mathematica notebooks with
examples that we encounter in Physics 7701. It is not intended to be
exhaustive!

URL: http://www.physics.ohio-state.edu/~ntg/7701/mathematica.php

The notebooks here were written assuming Mathematica version 7 or later
(you may get an advisory with later versions but this is not likely to
cause problems).

- 14-Oct-2013 --- Added a Fourier Transform examples notebook
- 11-Sep-2013 --- Fourier scribble from Mario Carneiro added.
- 02-Sep-2013 --- Upgraded "Finding Residues" notebook and added one on "Complex Integration Examples".
- 22-Aug-2013 --- The notebooks already linked here are from the last two years. New ones will be added (or old ones upgraded) as we proceed this year.

- Integrals
- Dirac Delta Function
- Complex Numbers and Functions
- Differential Equations
- Special Functions
- Fourier Series and Transforms
- Dirac Delta Function
- Simplification
- Formatting
- Sample Mathematica notebooks

Date Revised | Notebook | Comments |
---|---|---|

02-Sep-2013 | Complex integration examples | Some sample integrals that can also be done as contour integrals. |

25-Sep-2011 | Spherical coordinates volume integrals | Sample integrals for doing a three-dimensional volume integral in spherical coordinates. |

23-Nov-2011 | Gaussian quadrature tests, Part 1 | Some sample tests of gaussian quadrature (Gauss-Legendre and Gauss-Laguerre with N=3). |

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Date Revised | Notebook | Comments |
---|---|---|

02-Sep-2013 | Finding Residues | Using the Residue command in Mathematica. |

05-Sep-2012 | Complex Series | Examples of expanding complex functions in series and determining the radius of convergence. |

29-Aug-2012 | Complex Roots | Examples of how to solve z.^{n} = a |

29-Sep-2011 | Complex Trigonometry | Examples of trig functions with complex arguments and also converting back and forth from expoential to trig. |

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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). |

04-Sep-2013 | Solving some PS#3 differential equations | Examples of 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. |

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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!! |

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Date Revised | Notebook | Comments |
---|---|---|

14-Oct-2013 | Fourier Transforms 1 | Basic examples of taking Fourier transforms and inverses. Also a bit on the implementation of the theta (step) function. |

15-Sep-2013 | Fourier scribble | Created by Mario Carneiro, with revisions by Dick Furnstahl. [Original version] Build up a mouse-drawn curve in a Fourier series. |

11-Sep-2013 | 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! |

18-Sep-2013 | Gibb's overshoot | A physics-style analysis. |

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Date Revised | Notebook | Comments |
---|---|---|

31-Oct-2011 | Dirac Delta function | Basics of using the built-in delta function in Mathematica. |

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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. |

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Date Revised | Notebook | Comments |
---|

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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. |

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Your comments and suggestions are appreciated.

[OSU Physics] [Math and Physical Sciences] [Ohio State University]

Last modified: 09:01 am, October 14, 2013.

furnstahl.1@osu.edu