Syllabus for Math 481/581 (Spring 2005)
Basic Information
Description
This class is devoted to the basic scientific computing and it will be useful to most science and engineering students. The most useful knowledge that you will acquire in this class includes:
 Tools for writing scientific papers with mathematical formulas and figures
 Scientific problem solving using standard scientific software (MATLAB, Octave, Mathematica, Maxima, R)
 Setting up of the Linux operating system
The selection of topics includes:
 Monte Carlo simulations. Generating random walks. Computing frequencies in the game of poker. Finding areas, volumes and multiple integrals too complicated for exact calculations.
 Modeling mechanical systems with differential equation. The motion of planets and satellites under the action of the gravity forces (the nbody problem). Periodically forced mechanical systems (Hill's equation).
 Modeling with Markov chains. Computing the age structure of a population
 Modeling with systems of linear equations. Electrical circuits. Springmass systems. Eigenvalue problems.
In the past, the course has met with an enthusiastic reception by
its students, reflected both in the student comments and the teaching
evaluations (see Prof. Rychlik's teaching evaluations for Fall
2003). Many students commented that this was one of the most ueful
classes they have taken.
Prerequisites
This class addresses the computing needs for a variety of science
majors and it does not require computer background. The mathematical
subjects involving linear algebra, differential equations and
statistics will be preceeded by a brief summary of the mathematics
involved, and will be accessible to students who took two semesters of
calculus. A course in differential equations, linear algebra or
engineering math is a plus.
Textbooks
There will be one main textbook and several optional texts
available at the bookstore ordered
throughout the semester. In addition, there will be an ample amount of supplementary
material available through the class Web site.
Software
The software used in this class is predominantly highquality free
scientific software (Octave, Maxima, R, the Linux operating system,
LaTeX).
It will be distributed to students on CDROMS and/or downloadable over the Internet.
The commercial software (MATLAB, Mathematica) is available on the University of Arizona student cluster
and it can be accessed from either the public computer labs or over the Internet.
Exams
The course will not have inclass exams, but there will be three midterm projects
and a final project, on which the grading will be based. Each midterm project is worth 25%
or the grade, and the final project is worth the remaining 25%.
Homework
Small homework assignments with the purpose of helping with the midtrem and final projects
will be assigned regularly in class. The homework will be submitted electronically, in required
formats. Typically a LaTeX file with PostScript figures, small pieces of computer
code written in Matlab, Octave or Mathematica, and packaged into a zip archive.
The homework does not earn credit directly, but it will be considered as measure
of progress towards a project. If necessary, the instructor may provide feedback to the
student and make suggestions towards successful completion of the homework assignments.
Attendance
Students are expected to attend classes regularly, and to be
familiar with the University Class Attendance policy as it appears in
the General Catalog. Missing 4 lectures will be considered an
excessive absence will result in a
failing grade. Missing a deadline on a class project will automatically
result in a zero score for it. The students have the responsible
for keeping informed of any announcements, syllabus adjustments or
policy changes made during scheduled classes.
The grade of I
The grade of I will be awarded if all the
following conditions are met:

The student has completed all but a small
portion of the required work.

The student has scored at least 50% on the
work completed.

The student has a valid reason for not
completing the course on time.

The student agrees to make up the material in
a short period of time.

The student asks for the incomplete before
the final exam.