Policy sheet

Course outline

Anticipated schedule

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

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

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

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

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