Syntax for the DCF course
Notes for the Macalester College Faculty Meeting discussion of the Online Future, Dec. 11, 2012
From Fall 2012
A demonstration of markdown/knitr
Reading reflection questions for Math 125 Epidemiology
Notes for an orientation-day session for parents of new students at Macalester.
Instructions for logging in to the Macalester RStudio server.
Syllabus for Fall 2012
An orientation to the mosaic package for instructors.
Schedule for Math 125, Epidemiology, at Macalester College
Definitions of modeling at the PREP-2012 conference.
Should a falling ball follow a quadratic? How important is air resistance in a model of ballistics?
Points for a discussion of the differences between modeling and mathematics.
Use fitting to introduce questions of model choice and evaluation, and how the choice of a model depends on the purpose for which it is to be used.
A working draft of calculus concept inventory questions, still in the open-ended questions phase.
Adding some realism to the cross-the-river problem.
Some strategies for introducing functions of multiple variables.
How can a dog do calculus?
Notes about optimization in one variable
Results from a pre-workshop survey given to participants in the PREP 2012 workshop on modeling in calculus.
Instructions for a modeling problem that introduces integration.
Optimization on functions constructed from data.
Turning constrained optimization into unconstrained optimization by elimination of a variable.
A three-variable constrained optimization problem done using concepts from calculus of one variable.
Notes on constraints and objective functions
Some constrained optimization problems done graphically
Some examples of how an algebraic approach to differential equations is problematic.
Two different textbook explanations of Lagrange Multipliers, one algebraic and algorithmic, the other graphical.
An approach to related rates problems based on contour plots.
An example of an optimization problem that conflicts with good modeling ideas.
An example to illustrate the why one should ask, "What's a model for?"
An exercise based on biomechanical data on the energy stored by the arch of the foot when walking.
Revisiting problems from Smith & Minton about Hill functions
A short project introducing splines, monotonicity, continuity and differentiability, and derivatives.
Notes on differentiation in a modeling-based calculus course #PREP2012
Notes on teaching about functions in a modeling-based calculus course. #PREP2012
Some examples of uses of straight line functions to model relationships and the limitations of doing so.
Fitting exponential models to the temperature of cooling coffee. (Data collected by Stan Wagon.)
Finding the monthly payment by integrating a differential equation representing a mortgage payment.
An introduction to the Cobb-Douglas production function illustrating some features of the functional form.
A modeling example involving fitting sine waves to tide data to find the tidal period.