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### Resources feed

1. 18 Mar 2022 | Potential Scenario Ideas | Contributor(s):: Brian Winkel

2022. Kalman, Dan, Improved Approaches to Discrete and Continuous Logistic Growth. PRIMUS. Preprint at https://maa.tandfonline.com/doi/abs/10.1080/10511970.2022.2040664#.YjUMVurMI_U . Abstract: In the precalculus curriculum, logistic growth generally appears in either a discrete...

2. 05 Mar 2022 | Modeling Scenarios | Contributor(s):: Bill Skerbitz

Students are led step by step through the development of introductory ideas in mathematical modeling with differential equations. They will encounter the fundamental ideas underlying unlimited population growth (exponential models), limited population growth (logistic models), and a coupled...

3. 21 Feb 2022 | Free Online Texts | Contributor(s):: Brian Winkel

Sullivan, Eric. 2015. Numerical Methods - An Inquiry-Based Approach with Python. Available at numericalmethodssullivan.github.io/ .Eric Sullivan of Carroll College, Helena MT USA has authored an exceptional numerical methods textbook. Numerical Methods - An Inquiry-Based...

4. 23 Jan 2022 | Modeling Scenarios | Contributor(s):: Erich McAlister

Pitch velocity is one of the most fascinating statistics in baseball, as documented in the 2015 documentary Fastball. Modern measurements of pitch velocity are taken as the maximum velocity achieved at any point between the pitcher's hand and home plate. However, the velocity of the ball...

5. 22 Jan 2022 | Modeling Scenarios | Contributor(s):: Jakob Kotas

Basic projectile motion without air resistance typically assumes gravity is constant. In reality, the acceleration due to gravity is proportional to the inverse-square of the distance between the centers of mass of the Earth and the projectile. When projectiles are near to Earth's surface,...

6. 21 Jan 2022 | Modeling Scenarios | Contributor(s):: Jacob Paul Duncan

Most projectile motion and free fall models are based on the assumption that gravity is the only force acting on the object. Here we develop, solve, and analyze a second order nonhomogeneous differential equation model for free fall which incorporates air resistance. Students will solve the model...

7. 19 Jan 2022 | Modeling Scenarios | Contributor(s):: Jennie D'Ambroise, Jue Wang

This module is designed for Calculus I class and guides students in the use of differential equation models to predict cancer growth and study treatment outcomes. Several classical models for cancer growth are presented including exponential, power law, Bertalanffy, logistic, and Gompertz....

8. 17 Jan 2022 | Potential Scenario Ideas | Contributor(s):: Andrew M Ross

It occurred to me that students thinking about climate change might want to take a look at electric power generation via nuclear fusion. I know very little about this area, but perhaps someone out there does? I think students would be interested in just about any of the proposed technologies:...

9. 17 Jan 2022 | Potential Scenario Ideas | Contributor(s):: Andrew M Ross

Looking at graphs of atmospheric CO2 and global average temperature, such as this famous one from "An Inconvenient Truth" https://smallpond.ca/jim/ref/inconvenientTruth/full/00_22_49.jpgor the 2nd graph on this...

10. 17 Jan 2022 | Modeling Scenarios | Contributor(s):: Jennie D'Ambroise

We describe a modeling activity for Calculus I students in which modeling with difference and differential equations is appropriate. This model enlightens students as to how derivatives are used in applications as well as a brief introductory encounter with parameter estimation for a linear,...

11. 14 Jan 2022 | Modeling Scenarios | Contributor(s):: Bonnie Moon

In this lab students will collect data on their spring mass systems and compare their empirical models to their theoretical ones—giving them an opportunity to actually test a model against data.  Before this lab, students should have modeled spring-mass systems and solved second-order...

12. 22 Dec 2021 | Modeling Scenarios | Contributor(s):: Jean Marie Linhart, Gary William Epp

Students who have studied models for population are likely to be familiar with the exponential and the logistic population models. The goal here is to explore the role of modeling assumptions in choosing which model to use. We will compare and contrast the United States census data and the...

13. 09 Dec 2021 | General Resources | Contributor(s):: Brian Winkel

We offer Judge assignments of SCUDEM VI 2021 Team videos.

14. 21 Nov 2021 | General Resources | Contributor(s):: Brian Winkel

As a rule the Director of SIMIODE, Brian Winkel, and his wife rent a home (Sunset House) On Lake Superior in Eagle River MI in the Upper Peninsula. It is a temporary move for SIMIODE and a wonderful respite for the Director.This is the view from the deck of Lake Superior rolling in with the...

15. 20 Nov 2021 | General Resources | Contributor(s):: Brian Winkel

Brian Winkel received his PhD in 1971 in the abstract mathematics of ring theory in algebra and during his first teaching position he found the science library at his school, whereupon he discovered applications of mathematics in numerous fields. He began bringing these ideas and models to his...

16. 13 Nov 2021 | General Resources

17. 24 Oct 2021 | Articles and Publications | Contributor(s):: Brian Winkel

We place resources fom the SIMIODE MAA Virtual Programming, 26 and 28 October 2021.   We enclose a number of papers published by Brian Winkel, Director SIMIODE, which  offer support for modeling and application in calculus instruction.

18. 18 Oct 2021 | Modeling Scenarios | Contributor(s):: Maila Hallare, Charles Lamb

This activity analyzes the spread of a technological innovation using the Bass Model from Economics. The equation is a first-order, two-parameter separable equation and the solution has a characteristic S-shaped curve or sigmoid curve. The students derive the solution to the model, use least...

19. 20 Sep 2021 | Modeling Scenarios | Contributor(s):: Arati Nanda Pati

In this modeling scenario, we offer students simulation experience from a given data set which represents the heart death rate during the period 2000 - 2010 using several approaches to include exponential decay, difference equation, differential equation, and parameter estimation using EXCEL. We...

20. 06 Sep 2021 | Articles and Publications | Contributor(s):: T S L Radhika

Radhka, T. S. L. 2021. Notes on Frobenius methodAbstract: This article explains and demonstrates applications of the Frobenius theory as discussed in thebook by Simmons on “Differential Equations with Applications and Historical Notes.” We specificallydiscuss the...