MTH 132 (sec 104) Syllabus Fall 2004



MTH 443/643 (sec 101) Syllabus Fall 2009

CRN 3072/3092

Prerequisites: Completion of MTH 331 ( linear algebra )

Course Objectives: To understand computer arithmetic, error analysis, methods of finding roots to equations,

methods of interpolation, solving linear systems, numerical methods of differentiation and

integration, and convergence properties of algorithms, as well as computer

programming for executing methods.

Meeting time : Lectures T R 6:30 -7:45 pm Smith Hall Rm 511

Instructor : Dr. Alan Horwitz Office : Room 741 Smith Hall

Phone : (304)696-3046 Email : horwitz@marshall.edu

Text : Numerical Analysis, Timothy Sauer, Pearson/Addison Wesley

Software : Matlab, Mathematica

Grading : homework 27.8% (125 points)

2 major exams 44.4% (200 points)

( if there’s a 3rd exam, I’ll use the highest two grades )

final( semi- comprehensive ) exam 27.8% (125 points)

450 points total

Final exam date : Wednesday December 9, 2009 from 6:30-8:30 pm

General Policies :

Attendance is required . You are responsible for reading the text, working the exercises, coming to office hours for help when you’re stuck, and being aware of the dates for homework assignments and major exams as they are announced. Late homework will be penalized. Graduate students will have slightly more challenging homework questions.

Exam dates will be announced at least one week in advance. Makeup exams will be given only if you have an acceptable written excuse with evidence and/or you have obtained my prior permission. On exam days, we may have a shortened lecture period followed by the exam. Graduate students will have slightly more challenging exam questions.

Makeups are likely to be more difficult than the original exam and must be taken within one calendar week of the original exam date. You can’t make up a makeup exam: if you miss your appointment for a makeup exam, then you’ll get a score of 0 on the exam.

If you anticipate being absent from an exam due to a prior commitment, let me know in advance so we can schedule a makeup. If you cannot take an exam due to sudden circumstances, you must call my office and leave a message or email me on or before the day of the exam! Makeups may be more difficult than the original exam and must be taken within one calendar week of the original exam date. You can't make up a makeup exam: if you miss your appointment for the makeup exam, then you

get a score of 0 on the exam.

In borderline cases, your final grade can be influenced by factors such as your record of attendance, whether or not

your exam scores have been improving during the semester, and your class participation. For example, if your course point total is at the very top of the C range or at the bottom of the B range , then a strong performance on the final exam can result in getting a course grade of B, while a weak performance can result in a grade of C.

Attendance Policy : This is NOT a distance learning course !

Regular attendance is expected ! Attendance will be checked daily with a sign-in sheet. If your grade is borderline, then good attendance can result in attaining a higher grade. Likewise, poor attendance can result in a lower grade.

Having more than 3 weeks worth of unexcused absences (i.e., 6 of 29 lectures ) will automatically result in a course grade of F! Being habitually late to class will count as an unexcused absence for each occurrence. Carrying on conversations with your neighbor could be counted as being absent. Walking out in the middle of lecture is rude and a distraction to the class ; each occurrence will count as an unexcused absence. If you must leave class early for a doctor’s appointment , etc., let me know at the beginning and I’ll usually be happy to give permission. Absences which can be excused include illness, emergencies, or official participation in another university activity.

Documentation from an outside source ( eg. coach, doctor, court clerk…) must be provided to ME directly. If you lack documentation, then I can choose whether or not to excuse your absence.

MTH 443/643 (sec 101) Syllabus Fall 2009

CRN 3072/3092

(continued)

HEED THIS WARNING:

Previously excused absences without documentation can always, later, instantly change into the

unexcused  type if you accumulate an excessive number ( eg. more than 2 weeks worth ) of absences of any kind ,

both documented and undocumented .

You are responsible for keeping track of the number of times you've been absent and whether or not the absence was excused.

I tally this information up at the end of the semester, so don't count on me to give you a warning when you've reached the threshold of failing from being excessively absent.

.

Cell-Phone and Pager Policy: Shut off those damned things !

Unless you are a secret service agent, fireman, or paramedic on call, all electronic communication devices such as pagers and cell phones should be shut off during class. Violation of this policy can result in confiscation of your device and forced participation in a study of the deleterious health consequences of frequent cell phone use.

Sleeping in Class:

Habitual sleeping during lectures will be considered as an unexcused absence for each occurrence. If you are that tired,

go home and take a real nap! You might want to change your sleeping schedule, so that you can be awake for class.

____________________________________________________________________________________________________

The major exams will be roughly on the 6th and 11th weeks, plus or minus one week.

Their precise dates will be announced at least one week in advance and the topics will be specified.

We may not have the time to cover all the topics listed on the Topics sheet, and we won(t necessarily

cover the sections in order. In some chapters, we will focus on specific topics, rather than covering everything.

Come regularly and you(ll know where we are.

|Week |Dates | Approximate schedule : Sections covered and topics |

| |Fall | |

| |2009 | |

|1 |8/24- | |

| |8/28 | |

| | | |

| | | |

|2 |8/31- | |

| |9/4 | |

| | | |

|3 |9/8- | |

| |9/11 | |

| |Labor | |

| |Day on 9/7 | |

|4 |9/14- | |

| |9/18 | |

| | | |

| | | |

| | | |

| | | |

| | | |

|Week |Dates | Approximate schedule : Sections covered and topics |

| |Fall | |

| |2009 | |

|5 |9/21-9/25 | |

| | | |

| | | |

| | | |

|6 |9/28- | |

| |10/2 | |

|7 |10/5- | |

| |10/9 | |

| | | |

| | | |

| | | |

|8 |10/12- | |

| |10/16 | |

|9 |10/19- | |

| |10/23 | |

|10 |10/26- | |

| |10/30 | |

| |(Last day | |

| |to drop | |

| |on 10/30) | |

|11 |11/2- | |

| |11/6 | |

| | | |

|12 |11/9- | |

| |11/13 | |

| | | |

| | | |

|Week |Dates | Approximate schedule : Sections covered and topics |

| |Fall | |

| |2009 | |

|13 |11/16- | |

| |11/20 | |

| |Thanks-giving | |

| | | |

| |Break | |

| |next week | |

|14 |11/30-12/4 | |

| |Week | |

| |of thee | |

| |Dead | |

| |(12/2-12/8) | |

|15 |12/7- | |

| |12/8 | |

| | | |

MTH 443/643 Topics( through end of Chapter 2)

0.1 Horner's Method for efficiently evaluating polynomials

0.2 converting decimal to binary representation

0.3 floating point binary numbers:sign, mantissa, exponent

machine epsilon

chopping vs. rounding

"rounding to the nearest...."

absolute vs. relative error

single vs. double precision

bytes vs. bits

machine representation of a double precision floating point number

adding floating point numbers

0.4 how significant digits are lost when subtracting

using a conjugation trick to preserve significant digits

0.5 Intermediate Value Theorem

Mean Value Theorem

Taylor's Theorem with Remainder

1.1 root of a function

using the Intermediate Value Theorem and Bisection Method to bracket a root

estimating maximum error from Bisection Method

making estimates correct up to p decimal places

1.2 using iteration to try to find the fixed point of a continuous function

different ways to set up fixed point iteration for the same polynomial function

illustrating fixed point iteration with a cob-web diagram

linear convergence with rate S

a sufficient condition for linear convergence of a fixed point iteration

local convergence

MTH 443/643(sec 101) Topics( through end of Chapter 2)

8/25/09

1.3 using derivatives to find multiplicity of roots

computing forward and backward error and using them as criteria for

stopping an algorithm

Wilkinson polynomials

error magnification factor

sensitivity formula for magnification of input errors in computing roots

estimating how much a root changes when the formula changes

condition number: well conditioned vs. ill conditioned problem

1.4 iterative formula for Newton-Raphson Method for finding roots

quadratically convergent errors

sufficient conditions for Newton's Method to be

linearly or quadratically convergent

conditions for Modified Newton's Method to be quadratically convergent

how Newton's Method can fail to converge

1.5 Secant Method for finding roots requires 2 initial guesses

Secant Method has super-linear convergence

Method of False Position

variations of Muller's Method, Inverse Quadratic Interpolation, Secant Method

and Brent's Method

2.1 naive Gaussian elimination and back substitution

2.2 lower and upper triangular matrices

using row reduction steps to construct the lower triangular matrix of an

LU factorization

using an LU factorization to solve a system by back substitution

not all matrices have an LU factorization

LU factorization requires fewer steps than naive Gaussian elimination for solving

several linear systems with the same coefficient matrix

2.3 calculating maximum norm of a vector

calculating backward error and forward error

error magnification for a linear system

condition number of a square matrix

using matrix norms to compute condition number

using MATLAB "backslash" command to solve a linear system

using condition number to compute error magnification number

and to predict the number of digits of accuracy in an approximation

properties of vector norms, 1-norms and operator norms

swamping as a source of error in doing Gaussian elimination

2.4 Method of Partial Pivoting by swapping rows to get the largest entry of

the pivot column into the pivot row position before doing pivoting

constructing permutation matrices to exchange two rows and multiplying on the

left by a permutation matrix to do the row exchange

using zeros as storage locations to perform PA=LU factorization

using PA=LU factorization and back substitution to solve a system Ax=b

PA=LU method is used in order to avoid swamping

2.5 Gaussian elimination is a direct method, iterative methods are not

Jacobi Method of iteration works on strictly diagonally dominant matrices

writing recursive formula for Jacobi iteration to solve Ax=b system in terms of

the diagonal, the lower and upper triangles for A

Gauss-Seidel iteration uses the most recent values of unknowns at each step

using Gauss-Seidel iteration to find an approximate solution to Ax=b when

A is strictly diagonally dominant

using successive over-relaxation and a relaxation parameter

iterative method saves steps in solving a system with a sparse coefficient matrix

MTH 443/643(sec 101) Topics( through end of Chapter 2)

8/25/09

2.6 symmetric matrices, positive definite matrices

Conjugate Gradient Method "loop" program for solving systems with a

symmetric positive definite coefficient matrix

preconditioning an ill-conditioned matrix to solve a

better-conditioned matrix system

geometric interpretation of Conjugate Gradient Method

2.7 Jacobian matrix of a multivariate function

generalizing one-variable into Multivariate Newton's Method

applying Multivariate Newton's Method to solve a non-linear system

no "secant method" generalization of Multivariate Newton's Method

using Broyden's Methods when the Jacobian matrix is not defined

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