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Math 110, Fall 2007 Occidental College

Explore the commonalities between various images and concepts related to human health and scientific modeling. Dive into differential calculus, Navier-Stokes equations, reaction-diffusion equations, and more. Prepare for an exciting journey into the world of mathematical modeling.

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Math 110, Fall 2007 Occidental College

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  1. Math 110, Fall 2007Occidental College An introduction to Mathematical Modeling Friday September 14, 2007 (adapted from a presentation by ProfAngela Gallegos)

  2. How Are You Feeling Today? • 1 • 2 • 3 • 4

  3. What do the following have in common?

  4. www.digbysystems.com/emtlist/images/human_heart.jpg

  5. www.lao.ca.gov/2004/budget_overview/04-05_1.gif

  6. Spartina alterniflora two.ucdavis.edu/spartina

  7. www.nlm.nih.gov/medlineplus/ency/images/ency/fullsize/19263.jpgwww.nlm.nih.gov/medlineplus/ency/images/ency/fullsize/19263.jpg

  8. www.abclocal.go.com/kabc/weather

  9. Ascaris suum sperm Image provided courtesy of Alex Mogilner

  10. www.caddigest.com/subjects.mcad/select/alias_wavefront_lance.htm (2003)

  11. Myxococcus xanthus non-motile cells adventurous mutants social mutants wild type cmgm.stanford.edu/devbio/kaiserlab/about_myxo/about_myxococcus.html

  12. www2.kenyon.edu/People/holdenerj/

  13. www.channelopathies.com/health/neuron2.jpg

  14. LORD OF THE RINGS: THE TWO TOWERS prod bud mark bud pub rate crit rate open gr rel date dom gr dom gror 73,668,000 52,620,000 92% 89% 111,343,385 19-May-04 454,725,923 302,660,083 H%grp Dgrp εgrp 0.035 1.1 0.1 %error: 1.24%

  15. Again, what do these all have in common?

  16. 1. Mathematical Modeling!

  17. Mathematical Modeling! 2. Differential Calculus!

  18. Navier-Stokes Equations

  19. predator-prey

  20. elasticity equations

  21. reaction-diffusion equations

  22. Edwards-Buckmire-Shah Model for Cinematic Box-Office Dynamics A system of three coupled, non-linear ordinary differential equations: Where the parameters are given by: http://faculty.oxy.edu/ron/research/

  23. climate models (diffusion, convection, reaction equations)

  24. parametric equations www2.kenyon.edu/People/holdenerj/Projects/CalculusProjects.htm

  25. marginal cost $ value units of pollution

  26. Hodgkin-Huxley Equations

  27. WELCOME!Differential Calculus and Scientific Modeling We’ll begin in the next class by studying Limits…

  28. EXIT SURVEY Math 110 is moving • Too Fast for Me • A Little Fast for Me • A Little Slow for Me • Too Slow for Me

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