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September 23, 2023

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Description

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.

Course Curriculum

  • Lecture 01 – Introduction to the Course Unlimited
  • Lecture 02 – Bacterial Growth Unlimited
  • Lecture 03 – Nondimensionalization Unlimited
  • Lecture 04 – Steady States and Linearization Unlimited
  • Lecture 05 – Linear Systems I Unlimited
  • Lecture 06 – Linear Systems II Unlimited
  • Lecture 07 – Stability Analysis Unlimited
  • Lecture 08 – Phase Diagrams Unlimited
  • Lecture 09 – Phase Diagrams II Unlimited
  • Lecture 10 – Phase Diagrams III Unlimited
  • Lecture 11 – Single Species Population Models Unlimited
  • Lecture 12 – Midterm Review Unlimited
  • Lecture 13 – Lotka Volterra Competition Unlimited
  • Lecture 14 – Predator Prey Model Unlimited
  • Lecture 15 – SIR Model Unlimited
  • Lecture 16 – Michaelis Menten Enzyme Model Unlimited
  • Lecture 17 – Timescale Decomposition Unlimited
  • Lecture 18 – Quasi Steady State Analysis Unlimited
  • Lecture 19 – Sigmoidal Functions, Multisite Systems Unlimited
  • Lecture 20 – Chemical Kinetics: Mass Action Law Unlimited
  • Lecture 21 – Hopf Bifurcations Unlimited
  • Lecture 22 – Subcritical Hopf Unlimited
  • Lecture 23 – Poincare-Bendixson Unlimited
  • Lecture 24 – Poincare-Bendixon II Unlimited
  • Lecture 25 – Index Theory Unlimited
  • Lecture 26 – Final Review, Part 1 Unlimited
  • Lecture 27 – Final Review, Part 2 Unlimited

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