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====== 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 =====

  * [[gibson:teaching:fall-2016:math753:description| Description and objectives]] 
  * [[gibson:teaching:fall-2016:math753:policies| Policies on grades, homeworks, exams, etc.]]
  * [[gibson:teaching:fall-2016:math753:resources| Resources: books and online material.]]



===== Notices =====

  * 09/15/2016: HW1 due date has been revised to Friday 9/16 at midnight. I have also added [[gibson:teaching:fall-2016:math753:hw1| 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. 

  * [[http://julialang.org/downloads/ | Julia download]]
  * [[http://docs.julialang.org/en/release-0.5/ | Julia docs]]. Extensive, detailed documentation of the Julia language
  * [[http://samuelcolvin.github.io/JuliaByExample/ | Julia by Example]], Samuel Colvin. A compact set of examples of Julia syntax.
  * [[https://github.com/dpsanders/hands_on_julia/find/master| "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? [[gibson:teaching:fall-2016:math753:why-julia|Why Julia?]] |  |  
| W 08/31 | [[gibson:teaching:fall-2016:math753:installing-julia|Installing Julia]],  [[gibson:teaching:fall-2016:math753:julia-notebooks|Starting a Julia notebook]] | [[gibson:teaching:fall-2016:math753:ex1|ex1]] | 
| F 09/02 | [[gibson:teaching:fall-2016:math753:notebook-workflow|Working with Julia notebooks]] | [[gibson:teaching:fall-2016:math753:ex2]] | 
^Floating-point numbers & arithmetic ^^^
| date      | topic | exercises/homework | 
| M 09/05 | (Labor Day, no class) | |  
| W 09/07 | [[gibson:teaching:fall-2016:math753:floating-point| Floating point numbers]] | [[gibson:teaching:fall-2016:math753:ex3| ex3]] | 
| F 09/09 | [[gibson:teaching:fall-2016:math753:floating-point| Floating point arithmetic]] | [[gibson:teaching:fall-2016:math753:hw1| hw1]] due Fri 9/16   [[http://nbviewer.jupyter.org/url/channelflow.org/math753/math753-hw1-solutions.ipynb|Solutions]] |
^Nonlinear equations, 1d ^^^
| date      | topic | exercises/homework | 
| M 09/12 | [[gibson:teaching:fall-2016:math753:bisection| Bisection ]] | [[gibson:teaching:fall-2016:math753:hw2| hw2 ]] due Sun 9/25. [[gibson:teaching:fall-2016:math753:hw2-hints| Hints,]] [[http://nbviewer.jupyter.org/url/www.channelflow.org/math753/math753-hw2-solutions.ipynb|solutions]] |
| W 09/14 | [[gibson:teaching:fall-2016:math753:newtonmethod| Newton's method]] | |
| F 09/16 |  | | 
| M 09/19 | convergence of Newton and bisection | | 
^Numerical linear algebra ^^^
| date    | topic | homework | 
| W 09/21 | [[gibson:teaching:fall-2016:math753:gaussian-elimination| Gaussian elimination]] | 
| F 09/23 | [[http://nbviewer.jupyter.org/url/www.channelflow.org/math753/math753-lu-nopivot.ipynb| LU decomp, without pivoting]] | 
| M 09/26 | | 
| W 09/28 | [[http://nbviewer.jupyter.org/url/www.channelflow.org/math753/math753-forwardsub.ipynb| Solving Ax=b with LU, forward/backward substitution]] | [[http://nbviewer.jupyter.org/url/www.channelflow.org/math753/math753-hw3-lu-nopivot.ipynb|HW3]] due Sun 10/9. [[http://nbviewer.jupyter.org/url/www.channelflow.org/math753/math753-hw3-solutions.ipynb|Solutions.]]|
| F 09/30 | [[gibson:teaching:fall-2016:math753:lu-pivoting|LU with pivoting]] | 
| M 10/03 |  | | 
| W 10/05 | [[gibson:teaching:fall-2016:math753:norms-orthogonality| Norms and orthogonality]] | 
| F 10/07 | [[http://nbviewer.jupyter.org/url/www.channelflow.org/math753/math753-gramschmidt.ipynb|QR decomposition, Gram-Schmidt algorithm]]| |
| M 10/10 | [[gibson:teaching:fall-2016:math753:qr-leastsquares|QR and the least-squares problem]]  | 
| W 10/12 | | |
| F 10/14 | **exam 1** [[gibson:teaching:fall-2016:math753:exam1topics| Topics ]]| |
^ Interpolation and modeling ^^^
| date  | topic | homework | 
| M 10/17 | [[gibson:teaching:fall-2016:math753:horner|Horner's method]] |  |
| W 10/19 | [[gibson:teaching:fall-2016:math753:lagrangepoly|Lagrange interpolating polynomial]] |  |
| F 10/21 | [[gibson:teaching:fall-2016:math753:newtondivdiff|Newton's divided differences]] | [[http://nbviewer.jupyter.org/url/www.channelflow.org/math753/math753-hw4-polyinterp.ipynb|HW4]] due Sun 10/30 [[http://nbviewer.jupyter.org/url/www.channelflow.org/math753/math753-hw4-solns.ipynb|solutions]] | 
| M 10/24 | [[http://nbviewer.jupyter.org/url/www.channelflow.org/math753/lecture-chebyshev-interp.ipynb|Chebyshev interpolating polynomial]] | 
| W 10/26 | [[http://nbviewer.jupyter.org/url/www.channelflow.org/math753/lecture-10-26-leastsquares.ipynb| Least-squares polynomial models]] | 
| F 10/28 |  | 
| M 10/31 | [[http://nbviewer.jupyter.org/url/www.channelflow.org/math753/lecture-10-31-leastsquares.ipynb| Least-squares nonlinear models]] | [[http://nbviewer.jupyter.org/url/www.channelflow.org/math753/math753-hw5-leastsquares.ipynb|HW5]] due Sun 11/13 [[http://nbviewer.jupyter.org/url/www.channelflow.org/math753/math753-hw5-solns.ipynb|solutions]] |
^ Numerical differentiation and integration ^^^
| date  | topic | homework | 
| W 11/02 | [[gibson:teaching:fall-2016:math753:finitediff|Finite differencing]] | 
| F 11/04 | |
| M 11/07 | [[http://nbviewer.jupyter.org/url/www.channelflow.org/math753/lecture-heateqn.ipynb| Finite differences application: the heat equation]] | 
| W 11/09 | | 
| F 11/11 | (Veteran's Day, UNH closed) | 
| M 11/14 | [[gibson:teaching:fall-2016:math753:quadrature|Quadrature]] | [[http://nbviewer.jupyter.org/url/www.channelflow.org/math753/math753-hw6-quadrature.ipynb|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 | [[http://nbviewer.jupyter.org/url/www.channelflow.org/math753/math753-lecture-forwardeuler.ipynb|Forward Euler, Midpoint methods]] | [[http://nbviewer.jupyter.org/url/www.channelflow.org/math753/math753-hw7-ode.ipynb|HW7]] due Sun 12/11 midnight |
| M 12/05 | | 
| W 12/07 | | 
| F 12/09 | |
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