Math 110, Fall 2007 Occidental College
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Math 110, Fall 2007 Math 110, Fall 2007 Occidental College Occidental College An introduction to Mathematical An introduction to Mathematical Modeling Modeling Friday September 14, 2007 Friday September 14, 2007 (adapted from a presentation by (adapted from a presentation by Prof Prof Angela Angela Gallegos Gallegos)
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Math 110, Fall 2007 Occidental College. An introduction to Mathematical Modeling Friday September 14, 2007 (adapted from a presentation by Prof Angela Gallegos ). How Are You Feeling Today?. 1 2 3 4. What do the following have in common?. - PowerPoint PPT Presentation
Transcript of Math 110, Fall 2007 Occidental College
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))
How Are You Feeling Today?How Are You Feeling Today?
11 22 33 4 4
What do the following What do the following have in common?have in common?
www.digbysystems.com/emtlist/images/human_heart.jpg
www.lao.ca.gov/2004/budget_overview/04-05_1.gif
two.ucdavis.edu/spartina
Spartina alterniflora
www.nlm.nih.gov/medlineplus/ency/images/ency/fullsize/19263.jpg
Image provided courtesy of Alex Mogilner
Ascaris suum sperm
www.caddigest.com/subjects.mcad/select/alias_wavefront_lance.htm (2003)
cmgm.stanford.edu/devbio/kaiserlab/about_myxo/about_myxococcus.html
Myxococcus xanthus
adventurousmutants
non-motile cells
socialmutants
wild type
www2.kenyon.edu/People/holdenerj/
www.channelopathies.com/health/neuron2.jpg
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
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0.10.11.11.10.0350.035
Again, what do these all Again, what do these all have in common?have in common?
1. Mathematical Modeling!1. Mathematical Modeling!
1.1. Mathematical Mathematical Modeling! Modeling!
2. Differential Calculus!2. Differential Calculus!
Navier-Stokes Equations
predator-prey
elasticity equations
reaction-diffusion equations
)~(~
)~(~~
~)~(~
)~(~
~~
)~(~
tAtGtS
tS
td
tAd
A system of three coupled, A system of three coupled, non-linear ordinary non-linear ordinary differential equations:differential equations:
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)~(~
(~)~(
~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/
climate models(diffusion, convection, reaction equations)
parametric equations
www2.kenyon.edu/People/holdenerj/Projects/CalculusProjects.htm
marginal cost
units of pollution
$ v
alu
e
nVnVdt
dn
hVhVdt
dh
mVmVdt
dm
VVngVVhmgVVgdt
dVC
nn
hh
mm
KKNaNaLLm
)1(
)1(
)1(
)()()( 43
Hodgkin-Huxley Equations
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…
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
