# Modeling in Calculus: Early and Often

## Materials from a 2012 MMA PREP Workshop

This is where we will post materials from our 2012 MAA PREP Workshop. Stay tuned for updates.

### Monday: *Introductions and Overview*

- Campus Map
- Intro Slides
- Concept Inventories Kick-Off
- Calculus-Related Modeling
- Test Anxiety and Course Performance

### Tuesday: *Calculus in One Variable*

#### Mathematics and Modeling

#### Block 1: Functions, Parameters, Limits

**Examples****Notes**

#### Block 2: Derivatives and Integrals

**Examples****Notes****Resources**- Prevalence and incidence of HIV
- Sommer Gentry's (USNA) exercise on derivatives and the economy

#### Block 3: Optimization, Least Squares, Series

#### Block 4: Work Block

- Airline Pricing [html]

#### Additional Examples

#### Other Resources

*Dogs Don't Need Calculus*and a commentary on how the dog might do it.*Rising above the Gathering Storm*

### Wednesday: *Calculus in Multiple Variables*

#### Block 1: From Single to Multi-variable Calculus

Exercises: Walking up and down the hill, eye-balling partial derivatives, the gradient vector

An activity on pressure, volume and temperature in the ideal gas law

Modeling production with the Cobb-Douglas function [html] [Rmd]

Related Resources

- Some contour plots: mountain-shaped, hillside-shaped
- Acid Rain in 1955 and 1980
- Exercise on drawing contours by eye
- The zero-emissions heat engine

#### Block 2: Polynomial Approximation and Modeling

**Examples**- Application in Model Building: Enzyme kinetics Michaelis-Menten dynamics [pdf] [Rnw]
- Notes on polynomials as models. [html] [Rmd]
- Selecting model terms from first principles.

**Additional Resources**- Exercise: Eyeballing interactions
- Celebrity Divorce
- A
`mosaicManip`

applet for visualizing quadratic approximation in two variables. [pdf]

#### Block 3: Optimization

Unconstrained Optimization

- Demo on blind search in two dimensions. (
`mGradSearch`

to be posted to`mosaicManip`

package.)

- Demo on blind search in two dimensions. (
Constrained Optimization

- Constrained optimization analytically vs geometrically [html] [Rmd]
- Solving constrained optimization geometrically [html] [Rmd]
- Some computer exercises on the geometry of constraints [html] [Rmd] and some exercises done by eye.
- Quality-Adjusted Life Years: the match the derivatives approach [html] [Rmd] , optimizing total QALYs with constraints [html] [Rmd] , QALYs from expert opinion and politics [html] [Rmd]

### Thursday: *Dynamics and Differential Equations*

#### Block 1: Differential Equations in an Introductory Course

#### Block 2a: Impact on the Syllabus

- Notes on the discussion Participants can edit.

#### Block 2b: Resources–Finding, Creating, Disseminating

- PRIMUS pdf
- Taylor & Francis Online

#### Block 3: Modeling in the DE Course

**Examples**- Washtenaw County Flu Data [html]

#### Block 4: Work Block

### Friday: *Show and Tell*

- Workshop ends with lunch; the work contintues….

### Additional Resources

A survey of participants about the workshop. If you participated, please do the survey!

The Macalester Applied Calculus course (day-by-day syllabus and notes from Spring 2012)

The Kansas-Indiana distance/time spreadsheet and a quick data collection done during the conference * from Hesston to Goshen [html] [Rmd]

#### Resources Produced by Workshop Participants

Here are some of the topics participants worked on at the workshop.

- Comparing Major League Shortstops
- Oil Spills
- Mass Infertility Coming Soon?
- Cobb-Douglas Production Function
- Modeling an Ascillating Mass on a Spring
- Estimating the Volume of a Lake from a Contour Plot (Topo Map)
- Modeling Travel Time
- How Can We Improve Blood Testing by Pooling Blood Samples?

Workshop participants, as you finish up your projects, send us a link or the sources and we'll post it here.