Post on 24-Jan-2016
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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?
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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
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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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A system of three coupled, A system of three coupled, non-linear ordinary non-linear ordinary differential equations:differential equations:
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Where the parameters Where the parameters are given by:are given by:
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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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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