Vito Volterra (1860-1940), mathematician interested in integral equations and predator-prey models.
Info concerning the Lotka-Volterra model. Some other models of populations can be found here and here.
- Wednesday, April 24, 8:00 am - 10:00 am, A115
Problem 1
page 2
Problem 2
page 2
Problem 3
(There's a typo in the definition of effective potential)
Wednesday, April 17 : project presentations!! (and project due date)
Exam #3
on Monday, April 15
Topics covered: Lagrange undetermined
multipliers, Hamiltonian & Hamilton's equations of motion, motion under
a central force
Formulas to be memorized:
Exam #3 review page
2
Homework due Friday, April 12
In addition to the homework
problems assigned, here are more
Practice problems
for Exam #2
See below for Exam schedule and material
Exam #2
on Monday, March 25
Topics covered: Green functions, Calculus
of variations, Lagrange equations of Motion
Sections in Marion
(updated 3/18/02)
Exam #1A
Advice: 1) work through derivations in
the text
2) solve problems 1, 2, 3, 10, 11, 18
(and any others that are relevant)
More
practice problems
Text:
Classical Dynamics of Particles
and Fields, 4th edition, by Marion and Thornton.
See the syllabus for more detailed information.
This is the first semester in which you really apply the mathematics you have learned, and in which really begin to discover some of the more sophisticated concepts in physics. Your first taste of this was in PS 303 - Modern Physics, and now your "physical education" begins in earnest.
We will cover:
Fundamentals of mechanics, oscillatory
motion, systems of particles, varying mass, motion under central forces,
motion in three dimensions, gyroscopic motion, generalized coordinates,
normal coordinates, Lagrangian and Hamiltonian formulations, and numerical
projects.
Prerequisites: MA 345 (Differential Equations
and Matrix Methods), ES 204 (Dynamics), PS 219 (Physics III).
Corequisites: PS 303 (Modern Physics)
First Exam:
Jan 7 - Jan 30 [Exam Friday, Feb 8]
Repeat FIrst Exam:
Feb 11 - Feb 15 [Exam Wednesday, Feb 20]
Second Exam:
Feb 1 - Mar 8 [Exam Monday, Mar 25]
Third Exam:
Mar 18 - Apr 10 [Exam Monday, Apr 15]
Some links to nonlinear dynamics and chaos are listed here to give you some starting ideas for your project. I have several good books in my office that you can check out for other ideas.
Nonlinear
math archive
Chaos
at Maryland
Nonlinear
Glossary
newsgroup:
sci.nonlinear
Nonlinear
aspects of the life sciences
If you absolutely have no ideas, choose one of the following systems to analyze
van
der Pol 1
van
der Pol 2
van
der Pol 3
Belousov-Zhabotinsky reaction:
George Green (1793-1841), baker and mathematician. More information can be found here.
Vito
Volterra (1860-1940), mathematician interested in integral equations
and predator-prey models.
Info concerning the Lotka-Volterra
model. Some other models of populations can be found here
and here.
Jocopo Riccati, physicist and mathematician who worked on nonlinear differential equations.
FRICTION
Information about tribology can be found
at Robert
Carpick's web site.
Two papers on friction -
Scratching
the surface: Fundamental investigations of tribology with atomic force
microscopy
A general
equation for fitting contact area and friction vs. load measurements
On reserve
at the Jack R. Hunt Library are the following items:
Mechanics,
by Keith Symon - another text at about the same level as Marion.
(The following items are on reserve for
my PS 150 course. They can be, however, useful for you if you feel
that you need some review. Do not hesitate to read through them,
if only to realize how far you have come in two years!)
Lectures on Physics,
by Richard Feynman - a Nobel Prize winner deeply explains the why of physics.
Understanding
Physics, by Isaac Asimov - a great science fiction writer explains
physics.
Cartoon Guide
to Physics, by Huffman - physical principles in a visual format.
3000 Physics
Problems - lots and lots of practice quantitative problems.
Practice at problem solving is an important part of learning physics, especially for engineers. I suggest that you work as many problems as possible. I will post solutions to certain problems from the text below. However, you are not required to hand in your solutions.
http://www.indiana.edu/~wts/wts/plagiarism.html
http://www.rbs2.com/plag.htm
http://www.rbs0.com/tw.htm
http://www.rbs0.com/tw2.htm
(There are lots of links on this site)