Mathematical
Models (in Science and Engineering),
and their Analysis
Prerequisites: Calculus I -- III for Engineers & Scientists; (Applied) Linear Algebra
and a course that has given you knowledge of separable differential equations.
Some light
programming work is expected,
so basic
experience with programming will be helpful.
The willingness to learn a
few simple commands in Matlab,
following provided guidelines, is
required.
Expected
audience:
Upper-class undergraduate and beginning
graduate students.
Note:
This is an exciting, but difficult class.
Its difficulty rating by the students has consistently been above 4.5
(out of 5).
While I do not expect that the students will remember most of the
material from the prerequisite courses, I do expect - and will enforce
-
that the students be prepared to review any of the material which they
do not remember, on their own.
Background information from Algebra, Precalculus, Calculus, and Linear Algebra whose knowledge I will assume (and hence will not review in class).
My motivation for teaching this
course is two-fold:
- Demonstrate that the knowledge of Calculus,
Linear Algebra, and elementary Differential Equations is already sufficient to tackle a wide
variety of problems in sciences and engineering.
- Develop the concepts (e.g., Taylor series) which the
students learned in their undergarduate mathematics courses but never
used, into
practical "tools of trade" by showing how to apply those concepts to research
problems.
Consistent with the above motivation, I will pursue two
main
goals:
- Bring the students to a level where they can read and understand textbooks and papers written at the advanced undergraduate level, which use basic applied
mathematical techniques
(e.g., linearization and eigenvector expansion).
- Teach the
students to present their
results (or the
results they read about in a textbook/paper) to the audience.
An expanded
catalogue
description
of this course is found here.
Another important goal
of the course is to promote active
learning.
To that end,
this course will differ from standard mathematics courses in two
ways:
- More than half of the class time will be dedicated not to my giving a lecture, but to
answering students' questions about:
- (a) the assigned reading
material (from the posted Notes) and
- (b) any difficulties that
the students encounter when doing Homework problems.
Although Homework
will be collected only once a week or so, the students will be
expected to attempt a
couple (and sometimes more) of the Homework
problems before every class. Thus, the willingness to ask questions is
an important skill that I will foster in this class.
- Instead of taking midterm and
final tests, the students will
have to present
to the class their report on two mathematics-related
paper(s) or book chapter(s). The first (midterm)
paper will be assigned by the instructor. For the final project, the students will be
required to select a paper or book chapter of their choice from a list provided by the instructor and give a short
presentation about it to the class.
If you have any questions
about whether this course may be right for you, please do not hesitate
to contact me.