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\centerline{Mathematics 172--Numerical Analysis II}
\centerline{Course Information--Spring 1999}
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\leftline{{\bf Professor:}  John Little}
\leftline{{\bf Office:} Swords 335}
\leftline{{\bf Office Phone:}  793-2274}
\leftline{{\bf Office Hours:}  MWF 10 - 12, TR 1 - 3, and by appointment}
\leftline{{\bf Course Homepage:} {\tt http://math.holycross.edu/\~{}little/Num299.html}}
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{\bf Course Description}
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As we said at the start of the fall semester, 
the subject matter of numerical analysis is the mathematics of computation
of:
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\item{1.}  approximate solutions of algebraic (linear and polynomial)
and transcendental equations,
\item{2.}  numerical approximations to values of functions, their
derivatives and integrals, 
\item{3.}  approximate solutions of differential equations, and
\item{4.}  eigenvalues and eigenvectors of matrices and other quantities
from linear algebra
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We covered (most of!) the topics we will discuss from 
points 1 and 2 in the fall; this semester we will concentrate
on topics from points 3 and 4.  In somewhat more detail, 
the topics we will study and the projected schedule this semester are:
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\itemitem{Unit I:}  Additional numerical integration methods -- 
adaptive quadrature and Gaussian quadrature (about 3 class
days; January 19, 21, 26; Sections 4.6 and 4.7 in Burden and Faires)
\itemitem{Unit II:}  Numerical techniques for ordinary differential
equation initial value problems -- Euler, Taylor, and Runge-Kutta methods
(about 5 class days; January 28, February 2,4,9,11; Sections 5.1-5.5 and 
5.9 in Burden and Faires)
\itemitem{Unit III:}  Direct methods for systems of linear equations -- 
Gaussian Elimination interpreted as matrix factorization, pivoting strategies, 
techniques for special classes of matrices (about 4 class days; February
16,18,23,25; Sections 6.1-6.2,6.5-6.6 in Burden and Faires)
\itemitem{Unit IV:}  Iterative techniques for systems of linear
equations -- Jacobi and Gauss-Seidel iteration, their analysis via
matrix and vector norms, the spectral radius of a matrix 
(about 8 class days; March 2, 16, 18, 23, 25, 30, April 6, 8; Sections
7.1-7.4 in Burden and Faires)
\itemitem{Unit V:}  Numerical eigenvalue techniques -- the basic
and shifted inverse power methods, Householder matrices and the 
QR algorithm  (about 6 class days; April 13, 15, 20, 22, 27, 29; 
Chapter 9 in Burden and Faires)
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The remaining day will be devoted to an in-class exam.  See below.  As
always, some additions, deletions, or rearrangement of topics may
become necessary as we
progress through the course.  Any changes will be announced in class
and on the class homepage.
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{\bf Text}
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The text for the course is the same as last semester -- {\bf Numerical Analysis, 6th ed.}
by R.~Burden and J.~D.~Faires. We will cover most of the material in
Chapters 5,6,7,9 this term. 
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{\bf Course Format}
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To get you more directly involved in the subject matter of this course,
periodically during the semester, the class will break down into groups
of 3 or 4 students for one or more days, and each group will work together
for a portion of those class periods on a group discussion exercise.
The exercises will be made up by me.  I will be present and available for questions
and other help during these periods.  At the conclusion of some
of these discussions,
groups, the class as a whole will reconvene to talk about what has
been done, to sum up the results, to hear short oral reports from each group,
etc.  Each group will be responsible for a write-up of solutions for 
the questions from each discussion day, and those will be graded and
and returned with comments.
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Other meetings of the class will be structured as 
lectures or computer laboratory days when that seems appropriate.
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{\bf Computer Work}
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We will again be using {\it Maple\/} on the departmental Sun workstation network
quite extensively throughout the course
to implement the techniques we discuss and to generate numerical 
solutions to problems.  Several class meetings will take place in 
the SW 219 computer lab and some of the individual problem sets will
include problems for which you will need to use Maple.  
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{\bf Grading}
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The assignments for the course will consist of:
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\item{1.} One midterm in-class exam   
worth $20\%$ of the course grade.  Tentative date:
\itemitem{a.}  Thursday, March 4.
\item{2.} Final exam worth $30\%$ of the course grade.  The final exam for 
this course will be held at 8:30 a.m. Thursday, May 13.
\item{3.} Group final project, worth $20\%$ of the course grade.
\item{4.} Individual problem sets and lab reports, worth $15\%$ of the course grade.
\item{5.} Group reports from discussion
days, worth $15\%$ of the course grade.  
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The final projects will give you the chance to explore additional topics
extending what we do in class, implement some
of the algorithms involved, and apply them to realistic problems.
This should be an interesting way to see how numerical analysis is
used ``in the real world''.
More information about the projects, including some suggested topics
and sources to consult as you work on them, will be distributed later 
in the semester in class and on the course homepage.
If you ever have a question about the grading policy, or about your 
standing in the course, please feel free to consult with me.
\bye
   
