Math 310 Numerical Analysis (Bueler)

Fall 2019, UAF

Ed Bueler
elbueler@alaska.edu

Office: Chapman 306C (hours)

Class times and room:
TTh 11:30 am -- 1:00 pm
Gruening 412

CRN: 74440

Syllabus

Required text:
A. Greenbaum & T. Chartier, Numerical Methods, Princeton U. Press 2012 (ISBN-13: 978-0691151229)

Alternate texts which could be used for this course (not required):

J. F. Epperson, An Introduction to Numerical Methods and Analysis 2nd ed., Wiley 2013
R. Burden, J. Faires, & A. Burden, Numerical Analysis, 10th ed., Brooks Cole 2015

Links:

the "MATLAB Student" version ($49) works fine for Math 310
UA students should be able to get Matlab for Windows or Mac through OIT
Octave will also work fine
Octave Online means you can use Octave without installing it.
Free "Getting Started with Matlab" from MathWorks
Free online book by Cleve Moler: introductory numerical methods course using Matlab
Nick Trefethen's 11 page essay, which defines what it means: Numerical Analysis
drawing irregular curves with an actual wooden spline (video)

Matlab/Octave codes:

gaussint.m (see this PDF)
bis.m (see this PDF)

Schedule: (version 5 December 2019; final)

Day	Week/ Chapter	Topic	Assigned/ Due
T 8/27	1 Chapter 2	introduction-by-example getting started with Matlab class27aug.m	Assignment #1
Th 8/29	Chapter 4	bisection bisect.m
T 9/3	2	Newton's method more Matlab bisection0.m	A#1 Due Assignment #2
Th 9/5		class starts at 12 noon! programming using functions bisection.m newton.m class5sept.m
T 9/10	3	Taylor's theorem analysis of Newton's method	A#2 Due
Th 9/12		cont. programming worksheet	A#2 Due Assignment #3
T 9/17	4	secant method, fixed points coastline.m class17sept.m
Th 9/19	Chapter 5	fixed points, cont. newtonfractal.m and results: figure 1, figure 2 floating-point scientific notation worksheet	A#3 Due Assignment #4
T 9/24	5	floating-point cont. binary12 (notional) worksheet
Th 9/26	Chapter 7	Gauss elimination
T 10/1	6	matrices	A#4 Due Assignment #5
Th 10/3		GE and LU decomposition class3oct.m bad-determinants worksheet mydet.m absdet.m
T 10/8	7	cont. operation counting	A#5 Due
Th 10/10		partial pivoting tridiagonal systems worksheet tridiag.m	A#5 Due
T 10/15	8	a bit of review mylu.m myslash.m showmat.m least squares review guide for Midterm Exam
Th 10/17		Midterm Exam	Midterm Exam
T 10/22	9 Chapter 8	least squares polynomial interpolation class22oct.m	Assignment #6
Th 10/24		Lagrange form lagrangeform.m integrating-by-polynomial worksheet deg4int.m
T 10/29	10	Newton form computing square roots worksheet ieeeparts.m mysqrt.m mysqrttay.m
Th 10/31		polynomial interpolation error theorem worksheet: using the theorem Chebyshev points	A#6 Due
T 11/5	11	piecewise interpolation cubic interpolation summary class5nov.m review: slides on polynomial interpolation newt4.m	A#6 Due Assignment #7
Th 11/7	Chapter 10	trapezoid rule computing sine worksheet mysin.m
T 11/12	12	Newton-Cotes rules order-of-accuracy worksheet	A#7 Due Assignment #8
Th 11/14		worksheet: orthogonal functions Gauss quadrature
T 11/19	13	Clenshaw-Curtis integration compareint.m mytrap.m Romberg integration
Th 11/21	Chapter 11	ordinary differential equations nearasteroid.m narhs.m worksheet: easy ODE problems	A#8 Due Assignment #9
T 11/26	14	Euler's method slides on Euler's method Taylor methods explicit midpoint method worksheet: using ODE methods
Th 11/28		no class: Thanksgiving
T 12/3	15	implicit methods (trapezoid rule) classical RK4 rk4.m worksheet: using Matlab's ODE solvers review guide for Final Exam SAMPLE Final Exam
Th 12/5		existence, uniqueness, well-posedness stiff equations review worksheet: big ideas for review	A#9 Due
T 12/10		Final Exam 10:15 am -- 12:15 pm	Final Exam