gibson:teaching:fall-2016:math753

Lecture: MWF 12:40-2:00pm Kingsbury N129

Instructor: John Gibson. Office hours t.b.d.

Prerequisite: Math 426; Math 445 or CS 410 or IAM 550.

- 09/15/2016: HW1 due date has been revised to Friday 9/16 at midnight. I have also added some clarifications and fixes to HW1.
- 08/30/2016: Please bring your laptop to class on Wednesday 8/30 if you have one. Otherwise please bring a USB drive.

Numerics for this course will be done in the Julia programming language. Here are links to a few key resources.

- Julia docs. Extensive, detailed documentation of the Julia language
- Julia by Example, Samuel Colvin. A compact set of examples of Julia syntax.
- "Hands on Julia" notebooks, David Sanders. An interactive tutorial in a set of Julia notebooks.

Introduction, Julia | ||
---|---|---|

date | topic | exercises/homework |

M 08/29 | Why numerics? Why Julia? | |

W 08/31 | Installing Julia, Starting a Julia notebook | ex1 |

F 09/02 | Working with Julia notebooks | ex2 |

Floating-point numbers & arithmetic | ||

date | topic | exercises/homework |

M 09/05 | (Labor Day, no class) | |

W 09/07 | Floating point numbers | ex3 |

F 09/09 | Floating point arithmetic | hw1 due Fri 9/16 Solutions |

Nonlinear equations, 1d | ||

date | topic | exercises/homework |

M 09/12 | Bisection | hw2 due Sun 9/25. Hints, solutions |

W 09/14 | Newton's method | |

F 09/16 | ||

M 09/19 | convergence of Newton and bisection | |

Numerical linear algebra | ||

date | topic | homework |

W 09/21 | Gaussian elimination | |

F 09/23 | LU decomp, without pivoting | |

M 09/26 | ||

W 09/28 | Solving Ax=b with LU, forward/backward substitution | HW3 due Sun 10/9. Solutions. |

F 09/30 | LU with pivoting | |

M 10/03 | ||

W 10/05 | Norms and orthogonality | |

F 10/07 | QR decomposition, Gram-Schmidt algorithm | |

M 10/10 | QR and the least-squares problem | |

W 10/12 | ||

F 10/14 | exam 1 Topics | |

Interpolation and modeling | ||

date | topic | homework |

M 10/17 | Horner's method | |

W 10/19 | Lagrange interpolating polynomial | |

F 10/21 | Newton's divided differences | HW4 due Sun 10/30 solutions |

M 10/24 | Chebyshev interpolating polynomial | |

W 10/26 | Least-squares polynomial models | |

F 10/28 | ||

M 10/31 | Least-squares nonlinear models | HW5 due Sun 11/13 solutions |

Numerical differentiation and integration | ||

date | topic | homework |

W 11/02 | Finite differencing | |

F 11/04 | ||

M 11/07 | Finite differences application: the heat equation | |

W 11/09 | ||

F 11/11 | (Veteran's Day, UNH closed) | |

M 11/14 | Quadrature | HW6 quadrature, ungraded |

W 11/16 | ||

F 11/18 | exam 2 | |

Ordinary differential equations | ||

date | topic | homework |

M 11/21 | ||

T 11/22 | ||

W 11/23 | (Thanksgiving, UNH closed) | |

F 11/25 | (Thanksgiving, UNH closed) | |

M 11/28 | ||

W 11/30 | ||

F 12/02 | Forward Euler, Midpoint methods | HW7 due Sun 12/11 midnight |

M 12/05 | ||

W 12/07 | ||

F 12/09 | ||

W 12/14 | Final exam, 10:30am-12:30pm Kingsbury N343 | topics |

gibson/teaching/fall-2016/math753.txt · Last modified: 2016/12/12 18:12 by gibson