Applied Numerical Methods I, Kreider, Summer 2017


Policy sheet
Course outline
Anticipated schedule

Homework Sets

Homework Set 1, due on Thursday 16 June
Homework Set 2, due on Tuesday 20 June
Homework Set 3, due on Thursday 29 June
Homework Set 4, due on Thursday 6 July
Homework Set 5, due on Monday 17 July
Homework Set 6, due on Thursday 20 July
Homework Set 7, due on Monday 24 July
Homework Set 8, due on Thursday 27 July
Homework Set 9, due on Monday 1 August

Exam Preparation

Sample Exam 1
Answer key for Sample Exam 1
Preparation Sheet for Exam 1
Sample Exam 2
Answer key for Sample 2
Preparation Sheet for Exam 2
An example of Pade Approximation

Topics

There are thousands of web sites that offer information on the topics we cover in class. Here are just a few samples. If you find a good resource, please send me the link.

Mathworks Academy
Mathworks Examples
 
Floating point representation:
from Cornell University
from Wikipedia

Computer Arithmetic:
from Internet Archive

Root finding:
from California State University

Numerical Linear Algebra:
from Vrije Universiteit Brussel
from MIT

Interpolation:
from University of Connecticut

Curve Fitting:
from GraphPad Software

Quadrature:
from University of Michigan

Sundries

MATLAB Overview
Links to information about IEEE floating point representations (thanks to Jon Hafner):
    http://www.psc.edu/general/software/packages/ieee/ieee.html
    http://en.wikipedia.org/wiki/IEEE_floating-point_standard

Downloads

Ex1forwarddifferences.m: cancellation error in computing derivatives
Ex1polyeval.m: polynomial evaluation
Ex1signdigits.m: significant digits
FPS.pdf: introduction to floating point systems
Ex1binarylist.m: machine numbers are not evenly spaced
Ex1machineepsilon.m: computing machine epsilon
Ex1errors.m: absolute and relative errors
Ex1cancellation.m: cancellation error
quad.pdf: machine arithmetic for the quadratic formula
Ex1money.m: not all calculations are problematic
Ex1stability.m: a sequence of calculations may be stable or unstable
Ex1overflow.m: calculations using large numbers must avoid overflow
Ex1series.m: Using series
Ex1ODE.m: Numerical convergence illustrated by Euler's method for an ODE

Introduction to rootfinding
Order of convergence
MATLAB code for fixed point iteration
Notes on Newton's method
Notes on stopping criteria
usebisect.m
Ex2convergence.m: Linear vs quadratic convergence
Ex2fixedpoint.m: Fixed point iteration example
Ex2newtonlinquad.m: Newton's Method linear versus quadratic convergence
Ex2FPvsStef.m: Fixed point versus Steffensen
Ex2FPvsStef2.m: Fixed point versus Steffensen (alternate implementation)
Ex2comparison.m: Comparison of methods
Ex2snell.m: Using bisection to illustrate Snell's Law
Ex2boundary.m: Using the secant method to match derivatives of 2 functions
Ex2ATV.m: Plot for the ATV-in-a-ditch problem
Ex2Cheby.m: Plot of Chebyshev Polynomial T_4(x)
Ex2abstractrootfinding.m: Shooting Method for 2x2 IVP
Ex2embeddedfunction.m: Using embedded functions
Ex2separatebisect.m: Bisection script file; you'll need to create a bisect.m to use this
Ex2separatesecant.m: Secant script file; you'll need to create a secant.m to use this
Ex2embeddedbisect.m: Embedded bisection
Ex2embeddedsecant.m: Embedded secant
Ex2publish.m: Using the publish feature

Vectors and Matrices in MATLAB
partpivot.pdf: Partial pivoting example
illcond.pdf: Ill Conditioning example
Ex3illcond.m: Ill conditioning of the Hilbert matrix
Ex3conditioning.m: A structured matrix is better conditioned than a random matrix
Ex3jacobi.m: Jacobi iteration requires diagonal dominance
uptrbk.m: Gauss elimination with partial pivoting
tridiag.m: Tridiagonal solver tridiag.m (from Numerical Recipes text)
Using the tridiagonal solver

Ex4goodbad.m: good versus bad polynomial approximation
  Ex4goodbad.m graph
Ex4TaylorExample.m: Examples of Taylor series and their errors
Ex4LIP.m: LIPs for n=2
Ex4LIPvsTaylor.m: LIPs versus Taylor
Ex4badpoly.m: examples of bad polynomial approximation
Ex4pade.m: example of Pade approximation
Ex4cheby.m: Chebyshev Approximation
Ex4divdiff.m: Divided difference example
Hermitetransition.pdf: using Hermite interpolation to build a transition function

lspoly.m
Ex5linear.m: Linear Curve Fitting
Ex5shapeLS.m: Shape of S(A,B)
Ex5NMRtitr.m: NMR Titration Example
Ex5windchill.m: Windchill Example
vel.dat: Windchill data
Ex5spline.m: Splines

Ex7integrationexample.m: Compare Newton-Cotes rules
Ex7compare.m: Compare errors for various rules
Ex7composite.m: Compare errors for composite rules
compositegauss5.pdf: building a composite Gaussian rule