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
................
................
In order to avoid copyright disputes, this page is only a partial summary.
To fulfill the demand for quickly locating and searching documents.
It is intelligent file search solution for home and business.