MATH 308 – Numerical Analysis
Welcome to Numerical Analysis! The techniques you will learn in this course form the bedrock of what is
generically called scientiﬁc computing. At the heart of most computational problems in industry, engineering,
or science lies a basic question: what is the relation between the computer’s answer and the true answer?
If computers had inﬁnite precision, and if programers never made errors, and if mathematical models were
perfect, one might reasonably hope the two answers to be identical. The world being as it is, however, we
are reduced to seeking bounds on the extent to which the two answers can diverge. The purpose of this
course is thus twofold: on the one hand, to develop a body of techniques for solving applied problems, and
on the other, to formally estimate the accuracy of the solutions.
This is a math course. As such, it will focus on proofs and logical arguments. But the purpose of the
mathematical results is to provide rigorous performance guarantees for computer implementations, and in
this sense the course is also a computer course. Much of the beauty of this subject lies in the way the
formalism of the mathematics captures the awesome computational power of the modern desktop. Expect
to both prove and program in this course.
Text: Numerical Analysis, 8th Edition, by Richard Burden and Douglas Faires.
Class Hours: MWF, 10:00-10:50, ColH 446.
Week 1-2 Error Analysis
Weeks 3-4 Solutions to Equations in One Variable
Weeks 5-6 Solutions to Linear Systems
Weeks 7-8 Solutions to Nonlinear Systems
Weeks 9-10 Interpolation
Weeks 11-12 Integration and Diﬀerentiation
Weeks 13-14 Solving Diﬀerential Equations
The prerequisites for this course are solid coursework in calculus, linear algebra, and ordinary diﬀerential
equations. (Though as the mathematician Paul Halmos says, “The beginner should not be discouraged if he
ﬁnds he does not have the prerequisites for the prerequisites”–be bold, take the plunge.)
Homework, Quizzes, and Participation (20%)
You learn mathematics by solving problems: the importance of doing homework cannot be overstated. In
general, I will assign homework on Monday, and it will be due the following Monday. You are encouraged to
work with other students, but must write up your own solutions. Grading will be purely cursory, so it will
be easy to get all the homework points. However, tests and quizzes will largely follow the homework, so it
behooves you to have a thorough understanding of the problems.
The project is a paper of about ﬁve pages in which you analyze a problem of your choice. It will be due the
last day of class–more information will be distributed later in the semester.
There will be two cumulative in-class exams, spaced at roughly equal intervals throughout the semester.
As with quizzes, exams will be based on homework problems, so the best preparation is to thoroughly
understand the homework. Tentatively, the exams will be on February 14 and March 27.
A comprehensive closed-book exam to be administered Thursday, April 24th, from 8:45 a.m. to 10:45 a.m.
in 446 College Hall.
Final grades will be weighted as per above, with letter grades roughly as follows:
F < 60
Pluses and minuses will be assigned to scores on the high or low ends of the scale, respectively.
Since this is a rather high level class, ﬁnding tutors is not easy. But your peers are a good substitute: a group
of minds is generally a better problem solver than a mind working alone. You are encouraged to discuss the
material with your classmates, and to work on the homework in groups. (Caveat: homework can be solved
in groups, but should be written up independently.) You should also feel free to drop by my oﬃce, even if
it’s just to say hello or ask a quick question. If my oﬃce hours don’t work for you, drop in some other time,
shoot me an email, or give me a call. (Contact information below.)
Statement on Disabilities
Students with documented disabilities are entitled to reasonable accommodations if needed. If you need
accommodations, please contact the Oﬃce of Freshman Development and Special Student Services in 309
Duquesne Union (412-396-6657) as soon as possible.
College Hall 418
Tel: (412) 396-4851
Oﬃce Hours : MW 11-12, T 10-10:50, or by appointment
“A scientist worthy of his name, above all a mathematician, experiences in his work the same impression
as an artist; his pleasure is as great and of the same nature.” –Henri Poincar´ e