Math 113B: Intro to Mathematical Modeling in Biology (English)

Course Information

This course is intended for both mathematics and biology undergrads with a basic mathematics background, and 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 and, as time allows, introduce other types of models such as chemical reactions inside the cell or excitable systems leading to oscillations and neuronal signals. Certain topics from linear algebra that are needed for this course are presented as well, so a linear algebra prerequisite is not necessary. 

Mathematics Dept. | Physical Sciences Sch. | University of California, Irvine
Keywords: Mathematics,Biology,oridinary differential equations,qualitative behavior,dynamical systems,chemical reactions inside cells,neuronal signals,linear algebra,oscillation signals
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Author:
German Andres Enciso Ruiz
Title:
Assistant Professor
Department:
Mathematics

Creative Commons License
Math 113B: Intro to Mathematical Modeling in Biology by Germán A. Enciso is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

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Lectures

Week 1

Math 113B. Lec. 01. Intro to Mathematical Modeling in Biology: Introduction to the Course (English)
Math 113B. Lec. 02. Intro to Mathematical Modeling in Biology: Bacterial Growth (English)
Math 113B. Lec. 03. Intro to Mathematical Modeling in Biology: Nondimensionalization (English)

Week 2

Math 113B. Lec. 04. Intro to Mathematical Modeling in Biology: Steady States and Linearization (English)
Math 113B. Lec. 05. Intro to Mathematical Modeling in Biology: Linear Systems 1 (English)
Math 113B. Lec. 06. Intro to Mathematical Modeling in Biology: Linear Systems II (English)

Week 3

Math 113B. Lec. 07. Intro to Mathematical Modeling in Biology: Stability Analysis (English)
Math 113B. Lec. 08. Intro to Mathematical Modeling in Biology: Phase Diagrams (English)

Week 4

Math 113B. Lec. 09. Introduction to Mathematical Modeling in Biology: Phase Diagrams II (English)
Math 113B. Lec. 10. Introduction to Mathematical Modeling in Biology: Phase Diagrams III (English)
Math 113B. Lec. 11. Introduction to Mathematical Modeling in Biology: Single Species Population Models (English)

Week 5

Math 113B. Lec. 12. Introduction to Mathematical Modeling in Biology: Midterm Review (English)
Math 113B. Lec. 13. Introduction to Mathematical Modeling in Biology: Lotka Volterra Competition (English)

Week 6

Math 113B. Lec. 14: Introduction to Mathematical Modeling in Biology: Predator Prey Model (English)
Math 113B. Lec. 15. Introduction to Mathematical Modeling in Biology: SIR Model (English)
Math 113B. Lec. 16. Introduction to Mathematical Modeling in Biology: Michaelis Menten Enzyme Example (English)

Week 7

Math 113B. Lec. 17. Introduction to Mathematical Modeling in Biology: Timescale Decomposition (English)
Math 113B. Lec. 18. Introduction to Mathematical Modeling in Biology: Quasi Steady State Analysis (English)

Week 8

Math 113B. Lec. 19. Introduction to Mathematical Modeling in Biology: Sigmoidal Functions, Multisite Systems (English)
Math 113B. Lec. 20. Introduction to Mathematical Modeling in Biology: Chemical Kinetics: Mass Action Law (English)
Math 113B. Lec. 21. Introduction to Mathematical Modeling in Biology: Hopf Bifurcations (English)

Week 9

Math 113B. Lec. 22. Introduction to Mathematical Modeling in Biology: Subcritical Hopf (English)
Math 113B. Lec. 23. Introduction to Mathematical Modeling in Biology: Poincare-Bendixon (English)
Math 113B. Lec. 24. Introduction to Mathematical Modeling in Biology: Poincare-Bendixon II (English)

Week 10

Math 113B. Lec. 25. Introduction to Mathematical Modeling in Biology: Index Theory (English)
Math 113B. Lec. 26. Introduction to Mathematical Modeling in Biology: Final Review, Part 1 (English)
Math 113B. Lec. 27. Introduction to Mathematical Modeling in Biology: Final Review, Part 2 (English)