Math 485 - 13 Jan 11
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Semester long project:
-Midterm time: written progress and presentation on progress
-End of semester: poster session and nal report
-Assigned a graduate student mentor
Must keep him apprised of progress
Math 485 24 Feb 11
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Project midterm report format
1) initial stage of investigation
list of papers
few sentence description of each paper
A paragraph explaining why we chose the paper to
follow
2) Model
Variables, conside
Math 485 - 1 March 11
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We are presenting 31 March 11
Predator-Prey (last lecture)
Competing species (two species competing for the same natural
resource)
Math 485 - 1 March 11
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Math 485 - 1 March 11
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Math 485 - 3 Ma
Math 485 - 8 March 11
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Math 485 - 10 March 11
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Stability of xed points
1) nd the xed points
2) stability of xed point
x0 is a stable xed point if for an
Math 485 - 21 April 11
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Connect between dynamic systems and ordinary differential equations
For a given equation
Math 485 - 21 April 11
2) poincare return map
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Math 485 - 21 April 11
3)
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REPORT ABOUT A MLS MODEL
1. Introduction to the model
The proposed player index is represented by the following:
Where:
GS: number of games started (determines how many games a player started in a
season)
MINsperGP: minutes played per game (how many min
At this point in the presentation, one of the major questions one could ask
is: what are the applications of these models? Essentially, how can we use these
models to demonstrate viral dynamics so that we can more effectively eradicate
the hepatitis C vir
Math 485 - 8 Feb 11
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soln: curves tangent to v = ( f(x,y) , g(x,y) ) for all t
1) what kind of solution curve is allowed by v(x,y) (vector)
2) How do solution curves t together in phase space
(phase portrait)
Analysis:
1) f(x,y)
Math 485 - 22 Feb 11
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Math 485 - 22 Feb 11
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when a stone hits, it goes
down and comes back up
with the same magnitude
and opposite direction
rigid body, so assume forces act at center of mass
Math 485 -
Math 485 - 18 Jan 11
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One of the Greatest Modeling Project in Human History: Solar System
Over time:
Circular orbits
Circles within circles
Kepler: elliptical: equal area -> equal time
Newton: Gravity effects the orbit
Vectors:
M
Math 485 - 27 Jan 11
Page 1 of 5 - Jan 27, 2011
Projects:
In about a week
Need to decide which paper to work on
Do a strict imitation and repeat the results, unless we don't have the
same resources and can't do the same as the original paper, then
expl
Math 485 - 20 Jan 11
Direction vector
mixed product
Triple (?) product
N body problem
1) calculus
2) Newton'sGravitational Law
3) Force
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Math 485 - 20 Jan 11
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1 is pulling 2 closer to 1
now we have six 2
Math 485 - 25 Jan 11
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Two body problem:
= integral of angular momentum
Math 485 - 25 Jan 11
Integral of energy:
be a solution to the two body problem
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Math 485 - 25 Jan 11
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ecce
Math 485 - 1 Feb 11
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The wave traveling around a stadium
Objective: model the stadium wave
Set up principles and rules that dictate when and how the
wave happens
Elements:
Individual behavior
Collective behavior
Properties
Ind
Math 485 - 17 Feb 11
Page 1 of 3 - Feb 17, 2011
Stone Skipping
Assume the stone is a round disk and the mass is evenly distributed
S_inside =
contact area, is a
function of time
rho_water =
density
C = constant of
proportionality
Assumptions:
Math 485 -
Math 485 - 15 Feb 11
multi-scale analysis
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Math 485 - 15 Feb 11
Observations:
1) f = Pi, - Pi are again equilibrium solutions
2) f = Pi is now stable (condition to come)
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Math 485 - 15 Feb 11
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Math 485 - 3 Feb 11
assume a solution does exist
therefore no equilibrium state
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Math 485 - 3 Feb 11
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Examples in Classical Mechanics
Review on second order ODE's
Autonomous equation
since we can't solve i
Future directions:
It is important to take into account that our model considers the effectiveness of ribavirin and
interferon alone, an older treatment option, rather than newer, more effective treatments.
Consider for instance, that newer treatments usi