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source: UCIrvineOCW 上次更新日期：2015年1月26日
UCI Math 113B: Intro to Mathematical Modeling in Biology (Fall 2014)
The book for this class is "Mathematical Models in Biology" by Leah Edelstein-Keshet, SIAM, 2005 and covers materials from chapters 4-8.
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Description: UCI Math 113B is intended for both mathematics and biology undergrads with a basic mathematics background, and it consists of an introduction to modeling biological problems using continuous ODE methods (rather than discrete methods as used in 113A). We describe the basic qualitative behavior of dynamical systems in the context of a simple population model. As time allows, we will then discuss other types of models such as chemical reactions inside the cell, or excitable systems leading to oscillations and neuronal signals. The necessary linear algebra is also discussed to avoid including additional requirements for this course.
UC Irvine OpenCourseWare 0:22
01: Introduction to the Course 32:51
02: Bacterial Growth 46:11
03: Nondimensionalization 49:36
04: Steady States and Linearization 44:14
05: Linear Systems I 51:22
06: Linear Systems II 52:54
07: Stability Analysis 49:53
08: Phase Diagrams 50:34
09: Phase Diagrams II 52:06
10: Phase Diagrams III 47:44
11: Single Species Population Models 46:03
12: Midterm Review 46:37
13: Lotka Volterra Competition 49:26
14: Predator Prey Model 47:07
15: SIR Model 52:25
16: Michaelis Menten Enzyme Model 41:56
17: Timescale Decomposition 52:48
18: Quasi Steady State Analysis 49:23
19: Sigmoidal Functions, Multisite Systems 47:15
20: Chemical Kinetics: Mass Action Law 50:39
21: Hopf Bifurcations 49:41
22: Subcritical Hopf 51:32
23: Poincare-Bendixson 50:12
24: Poincare-Bendixon II 44:56
25: Index Theory 47:58
26: Final Review, Part 1 41:58
27: Final Review, Part 2 53:15