Math 430    Mathematical Biology



  INSTRUCTOR:   Mark Pernarowski (Schedule)  
  TEXTBOOK:   Mathematical Models in Biology, Leah Edelstein-Keshet  

Grades will be recorded in D2L. The course % will determined as follows:


                         Percent     Date   
Tu 3/28
Thur 5/11: 12pm-1:50pm
      Conversion to letter grade:  
A A- B+ B B- C+ C C- D F
90-100 87-89 84-86 80-83 77-79 74-76 70-73 67-69 60-66  

Homework and due dates will be posted here as class develops. Homework assignments will have varied lengths and difficulty hence will have different raw scores. The HW% for the final grade will be the % from the sum of all the raw HW scores:

                Due Date   
      Homework 1
  Discrete linear population models       
Tues, Feb 7
      Homework 2
  Discrete density Dependent Population Models   Tues, Feb 21
      Homework 3
  Phase Planes and chemostat model   Tues, Mar 7
        Midterm    Take-home   Tues, Mar 28
      Homework 4
   SIR models and Law of Mass Action   Tues, Apr 11
      Homework 5
   Chemical Kinetics   Tues, Apr 18

 Take-home due to me in class Wil 1-130



Thur 5/11




Periodically I will post handwritten and/or typeset lecture notes here.

M430_01   First Order Linear Difference Equation Models
M430_02_new   Second Order Linear Difference Equation Models
M430_03   First Order Nonlinear Difference Equation Models
M430_04   Planar Systems: Mathematical Theory
M430_05   Nutrients and Chemostat population models
M430_06   Chemostat Model Analysis
M430_07   Predator Prey model (with/without density dependence)
M430_08   Competition Models
M430_09    SIR, SIRS epidemic models
M430_10    Buffering, Michaelis Menten kinetics
M430_11    Competetive Inhibition, Cooperativity, Insulin secretion....
M430_12    Conservation Laws, PDEs, models, steady states,...
M430_13    Diffusion, Rx Diffusion, membrane transport, walks,...
M430_14    Transmembrane Ionic currents


  BOOK    Notes (>pg 18) and some HW(at start)      &       HW, Exams and many solutions (zip file)  

Matlab is a program used primarily for solving linear and nonlinear systems. In addition to being able to solve most (large) linear algebra problems it can also be used to solve ordinary and partial differential equations.

          getting matlab

 a link to downloading matlab on MSU campus. You will need

  intro  of campus link with simple introduction to syntax in matlab
  mathworks  company that develops and maintains matlab




To download matlab you'll need your campus email.

Matlab code we will use to approximate solutions of biological models will be posted here as the course develops:

basic_plot  some basic plotting examples - 2D only
harvest.m  matlab for harvest model
cobweb.m  matlab code for cobwebbing (and orbits)
pplane8.m  matlab code for solving planar differential equations
pplane9.m  Same as pplane8 but larger font size!!
   chemostat.pps is a pplane9.m file for the chemostat model
   linear.pps is pplane9.m file for a linear 2 by 2 system

 trajectories as contourplots of phi(x,y)


 pp_density.pps density dependent predator prey

 pp_regular.pps Regular periodic predator prey


  A convenient matlab package for solving a large class of PDE problems  
  is pdepe  
  pdex1.m  code for solving heat equation, Neuman BC  
  pdexbudworm.m  code for diffusive budworm population  
  WAGA   Please inform us of any ADA Web Accessibility issues to the Course Instructor. Specifically, let us know of any  perceived Section 508 and/or WCAG 2.0 AA issues.  
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