math 110, fall 2007 occidental college an introduction to mathematical modeling friday september 14,...
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![Page 1: Math 110, Fall 2007 Occidental College An introduction to Mathematical Modeling Friday September 14, 2007 (adapted from a presentation by Prof Angela Gallegos)](https://reader035.vdocuments.us/reader035/viewer/2022070410/56649ef35503460f94c04f81/html5/thumbnails/1.jpg)
Math 110, Fall 2007Math 110, Fall 2007Occidental CollegeOccidental College
An introduction to Mathematical An introduction to Mathematical ModelingModeling
Friday September 14, 2007Friday September 14, 2007
(adapted from a presentation by (adapted from a presentation by ProfProf Angela GallegosAngela Gallegos))
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How Are You Feeling Today?How Are You Feeling Today?
11 22 33 4 4
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What do the following What do the following have in common?have in common?
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www.digbysystems.com/emtlist/images/human_heart.jpg
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www.lao.ca.gov/2004/budget_overview/04-05_1.gif
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two.ucdavis.edu/spartina
Spartina alterniflora
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www.nlm.nih.gov/medlineplus/ency/images/ency/fullsize/19263.jpg
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Image provided courtesy of Alex Mogilner
Ascaris suum sperm
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www.caddigest.com/subjects.mcad/select/alias_wavefront_lance.htm (2003)
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cmgm.stanford.edu/devbio/kaiserlab/about_myxo/about_myxococcus.html
Myxococcus xanthus
adventurousmutants
non-motile cells
socialmutants
wild type
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www2.kenyon.edu/People/holdenerj/
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www.channelopathies.com/health/neuron2.jpg
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LORD OF THE LORD OF THE RINGS: THE TWO RINGS: THE TWO
TOWERSTOWERS
%error: 1.24%%error: 1.24%
302,660,08302,660,0833
454,725,92454,725,9233
19-May-0419-May-04111,343,38111,343,385589%89%92%92%52,620,00052,620,00073,668,00073,668,000
dom grdom grorordom grdom grrel daterel dateopen gropen grcrit ratecrit ratepub ratepub ratemark budmark budprod budprod bud
εεgrpgrpDDgrpgrpH%H%grpgrp
0.10.11.11.10.0350.035
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Again, what do these all Again, what do these all have in common?have in common?
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1. Mathematical Modeling!1. Mathematical Modeling!
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1.1. Mathematical Mathematical Modeling! Modeling!
2. Differential Calculus!2. Differential Calculus!
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Navier-Stokes Equations
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predator-prey
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elasticity equations
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reaction-diffusion equations
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)~(~
)~(~~
~)~(~
)~(~
~~
)~(~
tAtGtS
tS
td
tAd
A system of three coupled, A system of three coupled, non-linear ordinary non-linear ordinary differential equations:differential equations:
))~(~
)~(~
(~)~(
~tAtS
td
tSd
)~(~
)~(~
~)~(
~tAtS
td
tGd
Where the parameters Where the parameters are given by:are given by:
max
~S
M
DS
A
)1(
1~
SP
ASH
maxmax2
%~
Edwards-Buckmire-Shah Edwards-Buckmire-Shah Model Model
for Cinematic Box-Office for Cinematic Box-Office DynamicsDynamics
http://faculty.oxy.edu/ron/research/
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climate models(diffusion, convection, reaction equations)
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parametric equations
www2.kenyon.edu/People/holdenerj/Projects/CalculusProjects.htm
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marginal cost
units of pollution
$ v
alu
e
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nVnVdt
dn
hVhVdt
dh
mVmVdt
dm
VVngVVhmgVVgdt
dVC
nn
hh
mm
KKNaNaLLm
)1(
)1(
)1(
)()()( 43
Hodgkin-Huxley Equations
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WELCOME!WELCOME!
Differential Calculus and Differential Calculus and Scientific ModelingScientific Modeling
We’ll begin in the next class by We’ll begin in the next class by studying Limits…studying Limits…
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EXIT SURVEYEXIT SURVEY
Math 110 is movingMath 110 is moving
1.1. Too Fast for MeToo Fast for Me
2.2. A Little Fast for MeA Little Fast for Me
3.3. A Little Slow for MeA Little Slow for Me
4.4. Too Slow for MeToo Slow for Me