Math 1900-001
Calculus in the Sciences
Spring 2008
Course Homepage


Lab Instructor:     Aaron McDonald
Office:                   LCB 333
Office Phone:        585-1637
Email:                    amcdonal@math.utah.edu
Class Meeting:     Wednesdays from 8:35 - 9:25 AM in LCB 115
Office Hours:       TBD
 

Important Course Information:

Math 1170-001 Syllabus
            

Course Objectives:

Experimentation has been and remains to be important in the advancement of science.  In turn, laboratory experimentation and instruction is a fundamental part of science education at the post-secondary education level.  Mathematical "experimention", however, remains largely neglected at the post-secondary education level in spite of the prolific use of mathematical modeling in scientific literature.  This disconnect will begin to be resolved here as we will focus our energies this semester on studying the use of dynamic models in science and what it means to mathematically "experiement" with these models.  The dynamic models we will consider include (1) continuous time dynamical systems taking the form of differential equations and (2) discrete time dynamical systems taking the form of difference (or recursion) equations.  The principal tool we will use for mathematical experimentation is a computational software package called Maple.  No previous experience with Maple is assumed or expected.

We will begin the semester by becoming familar with Maple.  We will study the commands necessary to solve equations, plot functions, differentiate and integrate functions, and solve differential equations in Maple.   This takes some time and finess as Maple is particular about how it takes commands.  Once you have become proficient, you will be able to use Maple to solve (or better, check) your lecture homework problems and, perhaps more importantly, use Maple to study the behavior of dynamical models.

As you may notice on the schedule below, the overarching science theme of this course (at least the first half of it) will be Malaria.   Malaria is a potentially life threatening human disease that is associated with infection by one of four Plasmodium protozoa.  Millions of people are infected with malarial parasites each year and hundreds of thousands of these infecteds perish.  We will study the use of dynamic models in predicting the occurrence and severity of malaria outbreaks, the development of educated control programs, and the physiological ramifications malarial parasites have on their human hosts (sickle cell and blood type).   Along the way we will study the use of differential equations in epidemiology and the use of difference equations in population genetics.   As time allows, we will also study the use of differential equations in studying human red blood cell physiology.

There may be additional time to study modeling outside of epidemiology, genetics, and human physiology.  Additional disciplines of interest may include biochemistry and environmental chemistry.  Requests will be taken and considered carefully!

Tentative Schedule:
Laboratory
In-class Instruction and Implementation
 Report Due Date
Lab 1:
 An Introduction to Maple
January 9


Lab 2: 
  Exponential and Logistic Growth Differential Equations

 January 16
 January 23
Lab 3: 
  SIS and SIR Epidemiology Models

 January 23
 January 30
Lab 4:
 Malaria Epidemiology

 January 30
Lab 5:
  Malaria Modeling

February 6
 February 13
Lab 6: 
   Malaria Control Progams

 February 13
 February 20
Lab 7: 
  Difference Equations

February 20
 February 27
Lab 8: 
   Population Genetics  

February 27
 March 5
Lab 9:
  Sickle Cell Anemia Selfish

March 5
 March 12
Lab 10:
  Selfish Genetic Elements

March 12
 March 26
Lab 11:
  Malaria Control Programs Revisited

 March 26
Lab 12: