Math 577: Mathematical Modeling (Spring 2019)
"You cannot understand the physical world in any deep or
satisfying way without using mathematical reasoning." -- R. P. Feynman
This course will present an introduction and survey of mathematical models
for problems in the applied sciences and engineering. The real-world problems,
coming from areas like mechanical systems, control theory, bio-chemical
reactions, and heat transfer will be formulated as idealized mathematical
models. Equations will be derived from first principles in geometry, physics
and the calculus of variations. Mathematical techniques such as
nondimensionalization, perturbation analysis, and self-similar solutions
will then be introduced to simplify the models and yield insight into
the underlying problems.
Prerequisites
Some background in solving ordinary and partial differential equations
[Math 353 or Math 356],
basic physics/mechanics, multivariable calculus [Math 212].
Math 577-01 (5947) Mathematical Modeling
Tu/Th, 10:05-11:20am, Room 259 Physics Building
- First class meeting: Thurs, Jan 10 --
see Academic Calendar
- Lectures end: Tues, April 23
Instructor
Thomas Witelski, Professor, Dept of Math
Office: Room 295 Physics Building
Office hours
TBA, Room 295 Physics,
or by email request
for an appointment for other times.
Textbook
Problem sets
Course materials and web links
- Course outline/syllabus
- Lecture notes and Review sheets
- (See the resources folders on Sakai)
- Tests
-
Test 1: Tuesday Feb 26,
in class, HWs 1--4, Logan 1,3, Lectures 1-9:
scaling and
nondimensionalization, similarity solutions, perturbation problems and
boundary layers. No books, no calculators allowed. You will be
given the 'basic math summary' sheet and you can bring ONE sheet
handwritten notes.
-
Test 2: Thursday, April 11th,
in class, HWs 5,7,8,9 (NOT #6) and associated lectures and sections from Logan:
weakly nonlinear oscillators, Poincare-Lindstedt, method of multiple scales,
calculus of variations and transport models.
No books, no calculators allowed. You will be
given the 'basic math summary' sheet and you can bring ONE sheet
handwritten notes.
Reference books