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?

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What do the following What do the following have in common?have in common?

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Spartina alterniflora

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www.abclocal.go.com/kabc/weather

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/

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LORD OF THE LORD OF THE RINGS: THE TWO RINGS: THE TWO

TOWERSTOWERS

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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

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~)~(~

)~(~

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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:

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(~)~(

~tAtS

td

tSd

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~tAtS

td

tGd

Where the parameters Where the parameters are given by:are given by:

max

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M

DS

A

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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

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e

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dn

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dm

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nn

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mm

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)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