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).

- 23-Nov-2011 --- Added spherical harmonics, gaussian quadrature, and Green's function (under differential equations) example notebooks
- 13-Nov-2011 --- Added Legendre and Laguerre example notebooks

- 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 |
---|---|---|

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). |

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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 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). |

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. |

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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 |
---|---|---|

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. |

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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. |

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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: 07:08 am, November 28, 2011.

furnstahl.1@osu.edu