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Math 113B - Mathematical Biology

Math 113B: Mathematical Biology (Winter 2014, UC Irvine). Instructor: Professor German A. Enciso. This course is intended for both mathematics and biology undergraduates 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.

Introduction

Lecture 01 - Introduction to the Course

Lecture 02 - Bacterial Growth

Lecture 03 - Nondimensionalization

Lecture 04 - Steady States and Linearization

Lecture 05 - Linear Systems I

Lecture 06 - Linear Systems II

Lecture 07 - Stability Analysis

Lecture 08 - Phase Diagrams

Lecture 09 - Phase Diagrams II

Lecture 10 - Phase Diagrams III

Lecture 11 - Single Species Population Models

Lecture 12 - Midterm Review

Lecture 13 - Lotka Volterra Competition

Lecture 14 - Predator Prey Model

Lecture 15 - SIR Model

Lecture 16 - Michaelis Menten Enzyme Model

Lecture 17 - Timescale Decomposition

Lecture 18 - Quasi Steady State Analysis

Lecture 19 - Sigmoidal Functions, Multisite Systems

Lecture 20 - Chemical Kinetics: Mass Action Law

Lecture 21 - Hopf Bifurcations

Lecture 22 - Subcritical Hopf

Lecture 23 - Poincare-Bendixson

Lecture 24 - Poincare-Bendixon II

Lecture 25 - Index Theory

Lecture 26 - Final Review, Part 1

Lecture 27 - Final Review, Part 2

References

MATH 113B LEC A: Math Modeling in Bio
Instructor: German Andres Enciso Ruiz. Class Information. Class Links. Class Files. Campus Resources.