CUNY MTH 415 - Study Guide (2 pages)

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Study Guide



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Study Guide

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Lecture Notes


Pages:
2
School:
The City University of New York
Course:
Mth 415 - Mathematical Biology

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THE COLLEGE OF STATEN ISLAND DEPARTMENTS OF MATHEMATICS BIOLOGY COURSE OUTLINE MTH BIO 415 GRAD 761 MATHEMATICAL BIOLOGY SPRING 2006 4CR 4HR Textbook Mathematical Models in Biology Classics in Applied Mathematics by Leah Edelstein Keshet Paperback 586 pages Publisher SIAM Society for Industrial and Applied Mathematics New Ed edition ISBN 10 0898715547 ISBN 13 978 0898715545 Note Each Topic will be covered over the week s indicated In many cases sections in the book will be supplemented by handouts Week Textbook Sections Topics I 1 1 Introduction to building models Scaling example Introduction to MATLAB II III 2 1 2 8 3 1 Theory of difference equations Non linear difference equations recognition steady states stability Graphical methods Applications to population dynamics Cobwebbing using MATLAB III IV 1 3 1 7 Density dependence in single species populations Chaos and its biological relevance Difference equations continued Application to seed banks and insect populations V 3 2 3 5 Age and stage structure Host parasitoid systems The Nicholson Bailey model and extensions Discussion of applications 1 VI VIII 4 1 4 11 Continuous processes and ordinary differential equations Algal growth in a chemostat Building resource saturation into the model Dimensional analysis Scaling Linearization of nonlinear equations Local stability analysis Systems of equations e g albatross foraging behavior use in epidemiological models e g spread of AIDS Use of MATLAB to solve systems of differential equations ODE23 ODE45 MIDTERM EXAM X XI IX XI XII XIII XV XVI 5 1 5 6 Spring Break Phase plane methods oscillatory systems Neurons and neuronal models 8 1 8 9 Limit cycles oscillations and excitable systems 6 1 6 6 Application of continuous models to population dynamics Single and competing species models Predator prey models 7 1 7 4 Models for molecular events Michaelis Menten kinetics Sigmoidal behavior and its implications 9 1 9 7 Role of spatial variation in biological systems Diffusion



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