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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-2.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 | |
