AMSC 466 (Fall 2009)
AMSC 466 (fall 2009)– Introduction to
Numerical Analysis
o Prerequisites: MATH240; and MATH241; and CMSC106 or
CMSC114 or ENEE114.
o Also offered as CMSC466.
Who
Professor: Manuel Tiglio
o Office: 4129 CSIC Building.
o Phone: (301) 405-0667
o email: tiglio AT umd.edu
TA and grader: Rongrong Wang
o email: rongwang AT math.umd.edu
Topics (this list will be
expanded during the semester, depending on the pace of the class):
o Interpolation theory
1.
The
interpolation problem
2.
Existence and
uniqueness. The Lagrange form.
3.
Newton’s form.
4.
The Vandermonde form.
5.
Error
estimates.
6.
Interpolation at the Chebyshev points, convergence of the interpolant.
o Approximations, Least squares
1. Orthogonal polynomials.
o Numerical integration
1. Quadratures, integration through interpolation.
2.
Gauss quadratures.
3.
Gauss-Lobatto quadratures.
o Numerical differentiation
1. Finite differences.
2.
Differentiation through interpolation.
3.
Differentiation through orthogonal polynomials.
o Methods for solving systems of linear equations
1. Solving triangular systems.
2.
Gaussian elimination.
3.
LU decomposition.
4. The condition number, stability.
o Roots of non-linear equations
o Numerical methods for ordinary differential
equations
Homework
1. HWK1, due September 10 2009.
2.
HWK2, due September 23 2009.
3. HWK3, due October 5 2009.
4. HWK4, due October 13 2009.
5. HWK5, due October 26 2009.
6. HWK6, due November 9 2009.
7. HWK7, due November 24 2009.
When and where
Lectures
o Tuesday and Thursday: 9:30AM-10:45AM.
CSIC 4122. Exceptions: Sep 22
and Sep 24 lectures will take place in Room 4102 of the Physics department building.
o Office hours: Tuesday and Thursday: 11:00pm-12:00pm,
CSIC 4129. Use these office hours for questions regarding the lectures.
o TA’s office hours: Monday and Friday 4pm-5pm (2117 Math
Building). Use these office hours for questions regarding the homework.
o Directions to the CSIC building can be found here: http://www.cscamm.umd.edu/visitors/directions/index.htm
Midterm
o CSIC 4122, October 29 2009, 9:30AM-10:45AM. Topics to be included: Interpolation theory, Approximations and Least squares, Numerical integration. You can bring books, notes, etc. Laptops will not be necesssary and, in fact, will not be allowed.
Final exam
o CSIC 4122, date TBA
Webpage
The webpage of the course is
o http://www.cscamm.umd.edu/people/faculty/tiglio/AMSC466_09.html.
Check it regularly for notifications, homework, deadlines and other, especially
if you do miss lectures.
Texts
Please
notice: no particular text will be
followed and, as such, there is no required textbook.
Instead, you are encouraged to attend the lectures, which will provide you with
all the theory that you need for the homework and exams (attendance to the
lectures will not be enforced, though). During the semester I will be writing
and posting my class notes here (last updated: Nov 16 2009, 4:28PM EST).
Please check the link often, since I will be cleaning, embelishing and
rewriting them. I would strongly encourage everybody to provide me feedback and
constructive criticism to improve them.
Understand at the same time, though, that I am writing them for your
convenience and so that you do not have to spend on a textbook. So be patient
as they get improved (and please, again, do provide feedback about them!).
The following texts might be of help and are suggested:
o An Introduction to Numerical Analysis, by K. E.
Atkinson (Wiley)
o Afternotes on Numerical Analysis, by G. W. Stewart (SIM)
o Doron
Levy’s notes on Numerical Analysis (free)
o MATLAB: Quick Reference
(free), a
Primer (by K. Sigmon, free)
Computing
About 1/3 of the homework will consist on programming
exercises in MATLAB. You can access MATLAB in some of the Computer Labs on campus (check http://www.oit.umd.edu/wheretogo/allSoftware.cfm
to see which ones have MATLAB), or on your PC, if you have the Student Version
(which can be obtained from OIT here).
I have also granted you access to the GRACE
cluster at UMD, a set of machines devoted 100% to instructional support;
the relatively bad news is that the maximum disk quota per class is 4Gb....
Grading Policy
40% of the final grade will be based on homework (note: the one with the lowest grade will be dropped), 10% on class participation,
20% on a midterm exam, and 30% on a final exam.
For an A you will need 90%-100% of points, for a B 80%-89%, for a C 70%-79%,
and for a D 50%-69%.
Homework policy
o Homework assignments and their deadlines will be
given in class and posted on this webpage.
o Notice change: Please turn in the homework by the specified
deadline by placing it in the appropriate envelope that you will find in her office door in the Math Department (room 2117). You will
usually have around one week to work in your homework. The dates on which your
next homework is due, the previous one (graded) will be ready to pick up from
the same door.
o Solutions to some of the problems
will be presented by the TA either during some lectures or her office hours.
o Not all
problems might be graded--- if so a representative, random sample will be.
o In grading the turned in assignments your work
for reasoning, logic, completeness and clear explanations will be considered.
Points will be deducted if your answer is hard to read or difficult to
understand (for example, due to incomplete sentences), or the logic not clearly
explained, even if the final result is correct.
o If some homework includes some programming, please
do not turn it in as the package/language spreadsheet or source code. Instead,
use the program to find the results that are asked for and write down
everything that the problem asks for, along with printing any plots that are
needed, etc.
o Late homework will be accepted under the exceptional
circumstances stipulated by UMD (see below).
o Please make sure you include your name and collect
the pages together with a clip.
o You are encouraged to discuss the homework with others, however the work you turn in should be your own
formulation and reflect your own understanding.
Exams policies
In order to get a make up for a missed exam you need to provide in written the
reason, which has to be one of allowed by the university: religious holiday,
illness, or an official university event. Students who cannot attend a test due
to religious reasons should contact me in advance to discuss an alternative.
Students with disabilities
Students with disabilities should contact
me as soon as possible so that appropriate arrangements can be made to
accommodate the student's needs.
Academic integrity
The University of Maryland, College Park has a nationally recognized Code of
Academic Integrity, administered by the Student Honor Council. This Code sets
standards for academic integrity at Maryland for all undergraduate and graduate
students. As a student you are responsible for upholding these standards for
this course. It is very important for you to be aware of the consequences of
cheating, fabrication, facilitation, and plagiarism. For more information on
the Code of Academic Integrity or the Student Honor Council, please visit
http://www.shc.umd.edu.
To further exhibit your commitment to
academic integrity, remember to sign the Honor Pledge on all examinations and
assignments: "I pledge on my honor that I have not given or received any
unauthorized assistance on this examination (assignment)."