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:**

- Available here

**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:**

- Piazza Sign-up
- Course Home Page
- Auto-enroll with sjsu.edu email account
- Other email accounts, contact instructor

**Computer Programs:**

**Python Source Code:**

**Difference Equations**- Difference Equations (1 variable)
- Difference Equations (2 variables)
- Difference Equations (3 variables)
- Difference Equations (2nd order)
- Cobweb
- Logistic Map – Cobweb, Multiple r, Chaos
- Ricker Model
- Beverton-Holt Model
- SIR Model
- Deer Population Model
- Population Model
- Symbiosis Model

**Differential Equations**- Forward Euler Method (1 variable)
- Runge-Kutta Method (1 variable)
- Runge-Kutta Method (2 variables)
- Runge-Kutta Method (3 variables)
- Competition Model
- Lotka-Volterra Model
- Glycolysis Model

**Other computational help:**

**Homework:**

**Homework 1**(solutions) due**September 5**(in class)**Homework 2**(solutions) due**September 14**(in class)**Homework 3**(solutions) due**September 26**(in class)**Homework 4**(solutions) due**October 12**(in class)**Homework 5**(solutions) due**October 24**(in class)**Homework 6**(solutions) due**November 2**(in class)**Homework 7**(solutions) due**November 14**(in class)**Homework 8**(solutions) due**December 5**(in class)

**Term Tests:**

**October 3**(solutions)- Study sheet (answer key)
**STUDY SESSION:**Monday, October 2, 12:00-1:15 (SH 348)

**November 16**(solutions)- Study sheet (answer key)
- Sample test (solutions) (ignore questions 1. and 3.(a) – we may not cover them)
**STUDY SESSION:**Wednesday, November 15, 12:00-1:15 (SH 348)

**Final Project**

- Preliminary Report:
**Thursday, November 16** - Final Project:
**Thursday, December 14 (at exam)** - 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:**MS Word:**(download here) Use “Insert Equation” icon for mathematics**LaTeX:**(download MikTeX [Windows] here and MacTeX [Mac] here) Template.tex – Template.pdf

**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
- Sample final (answer key) – exclude pages 3 & 4
- Study sheets:

**Lectures (click link for lecture notes)**

- Aug. 24 – Course Outline, First-Order Difference Equations
**C&S**pg. 131-135**Supplemental notes:**Outline, Recursion proof

- Aug. 29 – Solutions, Computer simulation
- Aug. 31 – Fixed points, cobwebbing
- Sept. 5 – Stability, linearization
- Sept. 7 – Logistic equation, exotic behavior
**ES**pg. 17-21**Supplemental note:**Periodicity

- Sept. 12 – Bifurcations
**Supplemental note:**Bifurcations

- Sept. 14 – Applications: Logistic model with harvesting
**C&S**pg. 181-183**Supplemental note:**Harvesting

- Sept. 19 – Applications: Ricker model, Beverton-Holt model
- Sept. 21 – Discrete dynamical systems, SIR model
**C&S**pg. 203-207

- Sept. 26 – Compartmental models, review of matrices
**C&S**pg. 207-211, 214-217, 233-237**Supplemental note:**Review of matrices

- Sept. 28 – Stability of linear systems
**Supplemental note:**Stability**Mathematica screenshot:**Eigenvalues

- Oct. 3 –
**Term Test I** - Oct. 5 – Fixed points, linear and nonlinear systems
**C&S**pg. 257-265**Supplemental note:**Alternative stability result**Mathematica screenshot:**Solving linear systems

- Oct. 10 – Stability of nonlinear systems
**C&S**pg. 270-273

- Oct. 12 – Applications: Deer harvest, Symbiosis
**C&S**pg. 275-281**Mathematica screenshots:**Solving general systems – Jacobian 1 – Jacobian 2

- Oct. 17 – Differential equations, solutions and direction fields
**C&S**pg. 299-303, 309-310, 312-315**Mathematica screenshot:**Direction fields

- Oct. 19 – Numerical methods
**C&S**pg. 328-337**Supplemental note:**Numerical methods**Python scripts:**

- Oct. 24 – First-order linear and separable DEs
- Oct. 26 – Fixed points, stability
**C&S**pg. 317-322

- Oct. 31 – Applications: Logistic plus Harvesting
**Supplemental note:**Linearization and Harvesting

- Nov. 2 – Applications: Biochemical reactions
**Supplemental note:**Biochemical reactions

- Nov. 7 – Systems of first-order DEs
**C&S**pg. 413-422**Supplemental note:**Classifications

- Nov. 9 – Nonlinear systems, linearization
**C&S**pg. 434-437

- Nov. 14 – Applications: Competition
**C&S**pg. 439-443**Python code:**CompetitionModel.py**Mathematica Screenshot:**Competition

- Nov. 16 –
**Term Test II** - Nov. 21 – Applications: Predator-Prey
**C&S**pg. 443-447

- Nov. 23 –
**THANKSGIVING!** - Nov. 28 – Applications: Predator-Prey (continued)
**Supplemental Note:**Lyapunov Functions**Mathematical Screenshot:**Contour Plots**Python code:**LotkaVolterra.py

- Nov. 30 – Applications: Glycolysis
**Supplemental Note:**Limit Cycles**Python code:**Glycolysis.py

- Dec. 5 –
**Final project help!** - Dec. 7 –
**Final exam review!**

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