gibson:teaching:fall-2016:math753
Table of Contents
MATH 753/853 Numerical Methods
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.
Syllabus
Notices
- 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.
Julia resources
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.
Course outline and schedule
| 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
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