Math 170 (Fall 2017)

This website will contain all course material for the Fall 2017 section of “Math 170: Mathematical Modeling for the Life Sciences” as taught by Matthew D. Johnston at San Jose State University.

Green sheet:

Lectures:

  • TuTh 3:00-4:15 p.m., location: MH 234

Instructor Office Hours:

  • M: 12:00 – 1:30 p.m.
  • T: 10:30 a.m. – 12:00 p.m.
  • W: 10:30 a.m. – 12:00 p.m.

Textbook (these resources are provided free of charge and are supported by the TEAM Grant Program):

  • Calculus for the Life Sciences: A Modeling Approach Volume 2, James L. Cornette and Ralph A. Ackerman, available online here. (C&A)
  • Lecture Notes on Systems Biology, Eduard Sontag, available online here. (ES)
  • Note: A lecture-by-lecture guide to the readings (including supplemental reading) will be provided below!

Grade Breakdown:

  • Homework: 20%
  • Term Tests: 15% (x two)
  • Final Project: 20%
  • Final Exam: 30%

Piazza Course Discussion:

Computer Programs:

Python Source Code:

Other computational help:

Homework:

Term Tests:

Final Project

  • Preliminary Report: Thursday, November 16
  • Final Project: Tuesday, December 12
  • Guidelines
  • Topic sign-up spreadsheet
  • Source papers
  • Note: You may work individually or in pairs.
  • Note: The reports must be typeset! (Although I will accept handwritten equations within a typeset body of text.) I would recommend the following programs:
  • Guidelines: 4-5 typeset pages (6-7 pages for groups), including:
    • Description of biological system and derivation of mathematical model
    • Mathematical analysis from class (e.g. fixed points, stability, bifurcations)
    • Original computer-derived figures! (e.g. vector fields, trajectory plots)
    • Interpretation of results
  • Note: You do not need to understand every detail of the paper you have been assigned! A good starting point is to see if you can fill in some details which may be omitted in the paper/textbook chapter (e.g. fixed point and stability/Jacobian computations) and see if you can reproduce the computer plots. If it helps, you may simplify parameters. You may also modify the model and perform your own analysis. The project direction is yours.

Final Exam

  • Thursday, December 14, 2:45-5:00 p.m. in MH 234

Lectures (click link for lecture notes)

  • Aug. 24 – Course Outline, First-Order Difference Equations
  • Aug. 29 – Solutions, Computer simulation
  • Aug. 31 – Fixed points, cobwebbing
  • Sept. 5 – Stability, linearization
  • Sept. 7 – Logistic equation, exotic behavior
  • Sept. 12 – Bifurcations
  • Sept. 14 – Applications: Logistic model with harvesting
  • Sept. 19 – Applications: Ricker model, Beverton-Holt model
  • Sept. 21 – Discrete dynamical systems, SIR model
  • Sept. 26 – Compartmental models, review of matrices
  • Sept. 28 – Stability of linear systems
  • Oct. 3 – Term Test I
  • Oct. 5 – Fixed points, linear and nonlinear systems
  • Oct. 10 – Stability of nonlinear systems
  • Oct. 12 – Applications: Deer harvest, Symbiosis
  • Oct. 17 – Differential equations, solutions and direction fields
  • Oct. 19 – Numerical methods
  • Oct. 24 – First-order linear and separable DEs
  • Oct. 26 – Fixed points, stability
  • Oct. 31 – Systems of first-order DEs
  • Nov. 2 – Linear systems, solutions
  • Nov. 7 – Nonlinear systems, steady states
  • Nov. 9 – Linearization and simulation
  • Nov. 14 – Applications: TBD
  • Nov. 16 – Term Test II
  • Nov. 21 – Applications: TBD
  • Nov. 23 – THANKSGIVING!
  • Nov. 28 – Applications: TBD
  • Nov. 30 – Applications: TBD
  • Dec. 5 – Applications: TBD
  • Dec. 7 – Final exam review!
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