MathGroup Archive 1995

[Date Index] [Thread Index] [Author Index]

Search the Archive

Teaching by using Mathematica notebooks

  • To: mathgroup at christensen.Cybernetics.NET
  • Subject: [mg408] Teaching by using Mathematica notebooks
  • From: herrmann at (Joseph M. Herrmann)
  • Date: Sun, 15 Jan 1995 11:36:41 -0600

For those interested in using Mathematica in teaching 

	Mathematical modeling at Texas A&M University has been taught  
by having the students work through Mathematica notebooks which  
assign readings in the textbook "A First Course in Mathematical  
Modeling" by Frank R. Giordano and Maurice D. Weir, contain  
interactive examples and explanations, and assign exercises in which  
students create and analyze a mathematical model.  Students complete  
an individual and group project during the class.

The objective of the course is

1.  Illustrate the broad range of problems which can be modeled  

2.  Synthesize mathematical models from non-mathematical descriptions  
of problems.

3.  Interpret the results of models and evaluate their implications.

4.  Show the necessity of simplification and approximation in models  
and identify their effects.

5.  Work cooperatively in groups.

Currently there are 11 Mathematica notebooks.  Eight Mathematica  
notebooks cover the first 9 topics of the syllabus below.  The  
remaining 3 additional Mathematica notebooks create new Mathematica  
functions and illustrate their use with examples.  

1.  Simplex:  Creates a tableau for a standard linear programming  
maximization problem.  These tableaus are useful for solving linear  
programming problems by the standard maximization method, dual  
method, Big M method, or for achieving a sensitivity analysis.

2.  Natural Spline:  Determines the equations for the natural cubic  
spline functions which fit the data and includes examples of how to  
graph these functions automatically.

3.  Clamped Spline:  Determines the equations for the clamped cubic  
spline functions which fit the data for specified derivatives at the  
endpoints and includes examples of how to graph these functions  

Theory of the Simplex Method
Theory of the Dual Simplex Method
Dimensional Analysis

1.  Nuclear Arms Race
     Develop a simple probabilistic model
     Observe an equilibrium point
     Changing assumptions affects parameter values
     Sensitivity of the equilibrium point to change in parameters

2.  The Modeling Process-identifying a problem
	Vehicular Stopping Distance
	Automobile Gas Mileage
	Elevator Service during the morning rush hour

3.  Using Geometric Similarity in the Modeling Process
	Overall winner in weight lifting across weight classes
	Volume of lumber from the diameter of a tree at waist level
	Predicting Pulse rate from body weight
	Vehicular Stopping distance

4.  Model Fitting--identifying the optimal parameters for a model
	Error criteria--Least square and Chebyshev
	Identifying Kepler's third law from observational data

5.  Models requiring optimization--Linear programming/Critical points
	Linear programming economic models
	Inventory problem--minimize delivery and storage cost 

6.  Experimental Modeling
	Problems with using high order polynomials to interpolate

7.  Project 1:  Find the flow rate and water use of a small town from   
.5in height measurements of the water tank
     Numerical differentiation of data
     Fitting curves to transformed data
     Error analysis

8.  Dimensional Analysis and Similitude
	Range of a cannonball
	Damped pendulum
	Terminal speed of a raindrop
	Turkey cooking times
	Model design for determining the drag force on a submarine

9.  Simulation Modeling
	Monte Carlo simulation of area and volume
	Simulation of gas station delivery and storage cost for a
        stochastic demand
	Simulation of harbor waiting times for stochastic arrival and 

        unloading times

10.  Project 2:  The projects for Spring 93 were
A:	Identifying a near optimal ratio of slurry, greens, and paper
        for composting.
B:	Identifying a near optimal work schedule for a coal tipple.

11.  Differential equation models
	Population models
	Drug dosage
	Managing the fishing industry

The notebooks on the Simplex and the splines are available from  
Mathsource.  From Mosaic you could access it by  Simplex #0207-447 and Natural  
and Clamped Cubic spline coefficients #0207-436.  If you are  
interested in additional information, discussion of the advantages or  
disadvantages of teaching in a format where students work in groups  
or independently at a computer while the teacher acts a coach and  
answers questions and stimulates inquiry, or any of the other  
materials, please contact me.

Joseph Herrmann

Joseph M. Herrmann
Department of Mathematics, Texas A&M University
College Station, Texas  77843-3368
(409) 845-1474
herrmann at

  • Prev by Date: Lottery
  • Next by Date: MathHDF under Windows?
  • Previous by thread: Lottery
  • Next by thread: MathHDF under Windows?