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Modeling in Calculus: Early and Often

2012 MAA PREP Workshop Materials Project MOSAIC. 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. Test Anxiety and Course Performance. Calculus in One Variable. Our Definitions of Modeling [html]. Introduction to Modeling [html]. Block 1: Functions, Parameters, Limits. Snow Tree Crickets [html]. Tides in Hawaii [html]. StartR in Calculus [pdf]. R/mosaic Pocket Guide [pdf]. Modeling...

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Modeling in Calculus: Early and Often | prep2012.mosaic-web.org Reviews

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2012 MAA PREP Workshop Materials Project MOSAIC. 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. Test Anxiety and Course Performance. Calculus in One Variable. Our Definitions of Modeling [html]. Introduction to Modeling [html]. Block 1: Functions, Parameters, Limits. Snow Tree Crickets [html]. Tides in Hawaii [html]. StartR in Calculus [pdf]. R/mosaic Pocket Guide [pdf]. Modeling...

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1 monday

2 introductions and overview

3 campus map

4 intro slides

5 concept inventories kick off

6 calculus related modeling

7 tuesday

8 mathematics and modeling

9 examples

10 world population html

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monday,introductions and overview,campus map,intro slides,concept inventories kick off,calculus related modeling,tuesday,mathematics and modeling,examples,world population html,hill funcitons html,cooling coffee html,notes,foot arch html,orange juice html

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Modeling in Calculus: Early and Often | prep2012.mosaic-web.org Reviews

https://prep2012.mosaic-web.org

2012 MAA PREP Workshop Materials Project MOSAIC. 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. Test Anxiety and Course Performance. Calculus in One Variable. Our Definitions of Modeling [html]. Introduction to Modeling [html]. Block 1: Functions, Parameters, Limits. Snow Tree Crickets [html]. Tides in Hawaii [html]. StartR in Calculus [pdf]. R/mosaic Pocket Guide [pdf]. Modeling...

INTERNAL PAGES

prep2012.mosaic-web.org

1

Modeling Tides

http://prep2012.mosaic-web.org/Topics/Tides/tides-hawaii.html

Contains hour-by-hour measurements of water level in Pearl Harbor, Hawaii, over approximately 4 days. Library(mosaic, quietly = TRUE) trellis.par.set(theme = col.mosaic() tides = fetchData(hawaii.csv) xyplot(water time, data = tides). How to model these data? They are repetitive, which suggests a sine-wave model. We need to know the period, amplitude, phase, and offset. Looking at the graph suggests a period of about 24 hours, as seems sensible. Is the phase of the sine function. F2 = fitModel(water A B ...

2

Traffic light capacity model

http://prep2012.mosaic-web.org/Topics/Integration/Traffic-Light-Capacity.html

Traffic light capacity model. Your task: Find the capacity of a traffic light. The worst case is a line of cars is standing still at the light when it turns green. Cars accelerate. The last car to get through the light is at braking distance from the light when it turns yellow. What are the parameters of the system? Duty cycle for the light. Speed limit for the road. What estimates do you need to make? Distance between stopped cars, length of cars, etc. How far a car can move during the green-light phase.

3

Fitting Hill Functions

http://prep2012.mosaic-web.org/Topics/Functions/hillFunctions.html

Here is a problem from Smith and Minton,. Calculus: Early Transcendental Functions. What techniques are being used to estimate the parameters of the Hill function? Were going to revisit the problem using least-squares modeling. Library(mosaic, quietly = TRUE) trellis.par.set(theme = col.mosaic(). Hemo = data.frame(air = c(1, 2, 3, 4, 5, 6, 7, 8, 9), hemoglobin = c(2, 13, 32, 52, 67, 77, 84, 88, 91) plotPoints(hemoglobin air, data = hemo). Are the fitted parameter functions reasonable? How about ( n=3 )?

4

Differentiation

http://prep2012.mosaic-web.org/Schedule-Outline/Derivatives.html

Derivatives and integrals are traditionally introduced as very different things — slopes versus areas — with the relationship between them being introduced as if it were a surprise. We advocate a different approach. Is an operation you perform on a function. The result of the operation is another function with the same arguments as the input. Is the inverse operation that swaps the roles of the inputs and outputs. There are two other important operations that you perform on functions. Cumulative/Density&...

5

A Fitting Problem

http://prep2012.mosaic-web.org/Topics/Functions/WorldPopulation.html

A problem from Stewart. Calculus: Concepts and Contexts. 2/e p 38. It appears in Chapter 1. Why use “estimate” rather than “interpolate”? What are the essential properties of the function needed to create a reasonable interpolation? Whats the point of using a cubic? How would you decide whether to use a cubic or some other function? Load the package (you need do this only at the start of a session). Read in the data and display a bit. Pop = fetchData(PREP-Stewart-World-Population.csv). You figure it out!

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2012 MAA PREP Workshop | Project MOSAIC

http://mosaic-web.org/2012-maa-prep-workshop

Modeling, Statistics, Calculus, and Computation. Join our mailing list. Materials & Resources. From Meetings & Workshops. Breakout: Statistics For and With Physical Scientists. 2013 MAA PREP Workshop. 2012 MAA PREP Workshop. Project MOSAIC Kick-Off Workshop. 2012 MAA PREP Workshop. Modeling: Early and Often in Undergraduate Calculus. Daniel Kaplan, Randall Pruim, Eric Marland, and Nicholas Horton. July 9 13, 2012. Grand Rapids, Michigan. 225 ($300 for registrations received after May 28, 2012). Dinner wi...

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Prep 2017 - 2018. April 12, 2018. It was great to see everyone after spring break. It sounds as though many people have fun and adventurous holidays with Easter in the mix. This week we have continued our unit of shelters and in math we are working with shapes and teen numbers using the numicon materials. 8203;Check out the Outdoor Learning tab to see all the excitement with shelter building. Learning from Older Students. We hope everyone has a safe and fun holiday. Where can we find shelter? This unit t...

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Modeling in Calculus: Early and Often

2012 MAA PREP Workshop Materials Project MOSAIC. 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. Test Anxiety and Course Performance. Calculus in One Variable. Our Definitions of Modeling [html]. Introduction to Modeling [html]. Block 1: Functions, Parameters, Limits. Snow Tree Crickets [html]. Tides in Hawaii [html]. StartR in Calculus [pdf]. R/mosaic Pocket Guide [pdf]. Modeling...

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