Math 229: Mathematical Modeling (Spring 2012)
(4587)
"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 104 and 131) or (Math 107 and 108)],
basic physics/mechanics, multivariable calculus [Math 103].
Schedule
Wed/Fri, 2:50-4:05pm, Room 119 Physics Building
- First class meeting: "Classes meeting in a Wednesday/Friday
meeting pattern begin January 13" -- see Academic Calendar
Instructor
Thomas Witelski, Associate Professor, Dept of Math
Office: Room 295 Physics Building
Office hours
(Tentative)
Tuesdays, 10:00am-1:00pm, Room 295 Physics,
or by email request
for an appointment for other times.
Textbook
Problem sets
Course materials and web links
- Course outline/syllabus
- Review sheets
- Lecture notes
- Tests
- Test 1: Friday, Feb 24, in class, 2:50-4:05 pm, HWs 1--4, Logan 1--2:
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: Friday, Apr 13, in class, 2:50-4:05 pm,
HWs 5,6,8,9, lectures and sections from Logan Chapters 2 and 3:
weakly nonlinear
oscillators, Poincare-Lindstedt, multiple timescales, phase plane, fast/slow
systems, chemical reaction systems, calculus of variations.
No books, no calculators allowed. You will be
given the 'basic math summary' sheet and you can bring ONE sheet
handwritten notes.
Computer access: Duke OIT VPN (set Dept to "Library Resources Only")
Reference books