Math 441 - Introduction to Numerical Analysis
Fall 2009 - Matthias K. Gobbert
This page can be reached via my homepage at
http://www.math.umbc.edu/~gobbert.
Basic Information
- Matthias K. Gobbert,
Math/Psyc 416, (410) 455-2404, gobbert@math.umbc.edu,
office hours: MW 04:00-05:00 or by appointment
- Classes: SOND 206, MW 01:00-02:15;
see the detailed schedule for more information.
- Prerequisites: Math 221, Math 225, Math 251, Math 301, CMSC 201,
or instructor approval
- Copies of the following books are on reserve in the library.
These books are highly recommended as reference, but are not required.
The intention is to cover the material of the course sufficiently well
by the lectures, possibly complemented by specific reading assignments,
for which you can use the reserve copies in the library.
- Grading policy:
Homework and Quizzes
| Participation
| Midterm Exam
| Final Exam or Project
|
30%
| 10%
| 30%
| 30%
|
-
The homework is weighted so heavily, because it includes
the computer assignments that are vital to understanding
the course material.
A late assignment accrues a deduction of 10% of the possible score
for each day late until my receiving it;
I reserve the right to exclude any problem from scoring
on late homework, for instance, if we discuss it in class.
The quizzes will generally be unannounced and brief and
will include the use of learning groups assigned by the instructor.
For instance, they may be designed to initiate class discussion
or to give me feedback on your learning.
They may be technical or non-technical in nature.
-
The graded participation component rewards
your professional behavior and active involvement
in all aspects of the course.
Examples of expected professional behavior include
attending class regularly,
reading assigned material when requested,
cooperating with formal issues such as
submitting requested material on time, and
participating actively in class, specifically in group work.
-
The midterm and final exams are traditional
in-class exams.
See the detailed schedule for the dates
of the exams.
-
It is increasingly important
at this point in your education to learn
how to work on a larger project on your own
(with guidance by the instructor)
and to present your results in the form of a
professional-grade type-set
report (e.g., using LaTeX).
To allow interested students to develop the necessary skills,
you may choose to replace
the final exam by a project;
since I assume here that this is a new experience for you and
not suitable for all students, you must talk to me for approval.
I want to mention that a class project is a great way to start
on a research project,
in case that is something you are interested in.
Additional details or changes will be announced as necessary.
See also general policies and procedures
for more information.
-
Blackboard
is a course management system that allows for posting
and communicating among registered participants of a course.
To log in, I suggest to go to myUMBC
and then use the Blackboard link on the left.
Then look for this course under "My Courses".
We will actively only use the "Course Documents" area.
I will post PDF files of the lectures for each class and
possibly appropriate additional notes in this area.
I will also use Blackboard to send e-mail to the class,
which goes to your UMBC account by default.
Therefore, you must either check your UMBC e-mail regularly
or have the mail forwarded to an account that you check frequently.
Course Description
Numerical Analysis is concerned with the approximation of
mathematical objects, the analysis of the errors incurred in
this approximation, and the development and implementation
of computer algorithms for the computation of these approximations.
The approximations take various forms including the approximation of a function
by a series with finitely many terms or the approximation of a derivative
by a finite difference.
These approximations incur numerical error, in the examples above
known as truncation error and discretization error, respectively.
The methods covered include polynomial interpolation, numerical
differentiation and integration,
the solution of non-linear systems of equations, and
an introduction to numerical methods for ordinary differential equations.
Additionally, we will discuss Gaussian elimination for the
solution of systems of linear equations and other selected topics
such as the representation of real numbers
in computers according to the IEEE-standard for floating-point numbers.
This course will also include computational work to gain practical
experience with the numerical methods discussed.
I recommend the professional software package Matlab
as platform of choice, because it is a very popular package
and knowing it thoroughly is itself a marketable skill.
To read about Matlab,
you can read its expansive and well-written documentation or
you may consider the book recommended above.
For hands-on training in Matlab,
you can consider the 2-credit class Math 426 on Matlab or
for a brief initial overview the software workshops
offered by CIRC.
Learning Goals
By the end of this course, you should:
-
understand and remember the key ideas, concepts, definitions,
and theorems of the subject.
Examples include computational algorithms, sources of error,
convergence theorems, and implementations of these algorithms.
More broadly, you should also understand the purpose of
numerical analysis.
--> This information will be discussed in the lecture.
You will apply and use them on homework and tests.
-
have experience using a professional software package,
writing code in it, and understanding how some of its functions work.
We will focus on the package Matlab in this course,
which is the most popular package in mathematics and many application areas.
Writing code in this context includes the requirements to deliver code
in a form required, such as writing code to stated specifications,
using a requested method, complying with a required function header, etc.
The knowledge and skills in this item are valuable job skills,
which justifies the emphasis here.
--> This is one of the purposes of the homework and most
learning will take place here.
-
have some foundational experience in writing a professional-grade report
in Mathematics.
We will discuss issues of outline and approach in class
as well as privately in connection with revisions of the project report.
--> This is the purpose of the project.
-
have experience working with peers in a group.
Group work requiring communication for effective collaboration
with peers and supervisors is a vital professional skill,
and the development of professional skills including this networking
is a declared learning goal of this course.
Additionally, getting to know other students as part of learning groups
will prove invaluable for homework and tests.
--> The groups will be assigned by the instructor and used
for group quizzes in class.
Other Information
UMBC Academic Integrity Policy
By enrolling in this course, each student assumes the responsibilities of
an active participant in UMBC's scholarly community in which everyone's
academic work and behavior are held to the highest standards of honesty.
Cheating, fabrication, plagiarism, and helping others to commit these acts
are all forms of academic dishonesty, and they are wrong.
Academic misconduct could result in disciplinary action that may include,
but is not limited to, suspension or dismissal.
To read the full Student Academic Conduct Policy, consult the
UMBC Student Handbook, the Faculty Handbook, the UMBC Integrity
webpage www.umbc.edu/integrity,
or the Graduate School website
www.umbc.edu/gradschool.
Copyright © 1999-2009 by Matthias K. Gobbert. All Rights Reserved.
This page version 1.0, April 2009.