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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.