Math 441 - Introduction to Numerical Analysis
Fall 2019 - Syllabus - Matthias K. Gobbert
This page can be reached via my homepage at
- Matthias K. Gobbert,
Math/Psyc 416, (410) 455-2404, firstname.lastname@example.org,
office hours: TuTh 11:30-12:30 or by appointment
- Classes: SOND 109, TuTh 10:00-11:15;
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.
Kendall E. Atkinson, An Introduction to Numerical Analysis,
second edition, Wiley, 1989.
An analytical introduction to the subject, comprehensive and timeless.
Recommended book on Matlab:
Desmond J. Higham and Nicholas J. Higham,
Matlab Guide, third edition, SIAM, 2017.
Webpage of the book
including list of errors.
Matlab's documentation is excellent, but along with its functionality
has reached a scale that requires a lot of sophistication to fully
understand. Moreover, there is a definite role for a book that
is organized by chapter on topics such as all types of functions
(inline, anonymous, etc.), efficient Matlab programming
(vectorization, pre-allocation, etc.), Tips and Tricks, and more.
- Grading rule:
| Homework and Quizzes
|| Midterm Exam
|| Final Exam or Project
Additional details or changes will be announced as necessary.
See also general rules and procedures
for more information.
Announcements may be made in class, by e-mail, or in Blackboard.
You are responsible for checking
your UMBC e-mail address sufficiently frequently.
The homework assignments will be posted in
the Blackboard site of our course; see below.
The detailed schedule indicates
the due date of each homework.
The homework includes
the computer assignments that are vital to understanding
the course material,
and you are expected to work all problems.
Submit each homework as one PDF file in the Assignments area
of our Blackboard site.
A late assignment accrues a deduction of
up to 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 online quizzes on the lecture tapings
are administered in Blackboard and are due before class.
The in-class quizzes
will include the use of learning groups formed by the instructor.
They are 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 constructively in class, specifically in group work.
The midterm and final exams are traditional
To help you focus on what is relevant,
they are closed-book and closed-notes, but
you should bring a scientific calculator.
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.
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.
We will use the course management system
for posting of all material
(including homework, class summaries, PDF transcripts, handouts),
for links (to tapings of lectures), and
for submission of homeworks and online quizzes.
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.
Do not use Blackboard to message me,
since I may not find it in a timely fashion;
rather use conventional e-mail to my UMBC address listed above.
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 systems of non-linear 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
equivalently the free and nearly fully compatible package
as platform of choice, because they are very popular packages
and knowing them thoroughly is itself a marketable skill.
For both packages,
you can read its expansive and well-written documentation or
you may consider the book recommended above.
For hands-on training in Matlab and Octave,
you can consider the 2-credit class Math 426 on Matlab or
for a brief initial overview the software workshops
offered by CIRC.
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
--> This information will be discussed in the lecture.
You will apply and use them on homeworks, quizzes, 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 professional-grade reports
This is explained more in the syllabus portion on
How to Report on Computer Results.
--> This is included in the homeworks and is also
one of the reasons for offering a project option.
have experience working actively with peers in a group,
both on the scale of the class and in a smaller team.
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. Their formal evaluation is
included in the participation category of the grading rule.
UMBC Statement of Values for Academic Integrity
Academic integrity is an important value at UMBC.
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 webpage on Academic Integtrity at
UMBC Undergraduate Student Academic Conduct Policy
for undergraduate students,
UMBC Graduate School Policy and Procedures for Student Academic Misconduct
for graduate students.
Copyright © 1999-2019 by Matthias K. Gobbert. All Rights Reserved.
This page version 1.3, September 2019.