3-051-ProjectileMotions-ModelingScenario

11 Jul 2024 | Contributor(s): Brian Winkel | doi:10.25334/82H3-4F16

We consider several instances of projectile flight without resistance, one on level ground and one from edge of cliff to determine maximum distance and placement.

3-052-OptimalProjectileFiring-ModelingScenario

06 Jul 2024 | Contributor(s): Brian Winkel | doi:10.25334/NBRP-6868

We offer the opportunity to model a projectile's trajectory in several cases, all without resistance.

1-144-HeatCool-ModelingScenario

23 Jun 2024 | Contributor(s): Brian Winkel | doi:10.25334/338H-WJ42

We offer an opportunity to build a mathematical model using Newton's Law of Cooling for a closed plastic baggie of liquid inside a liquid container.

1-078-MonodGrowthModel-ModelingScenario

29 Apr 2024 | Contributor(s): Brian Winkel | doi:10.25334/MDTK-GE30

Students model growth of bacteria E. coli in a limiting nutrient environment using data from a historical study.

5-026-Evictions-MmodelingScenario

27 Feb 2024 | Contributor(s): Mary Vanderschoot | doi:10.25334/NF9K-CB57

In this project, students develop two SIS models to study eviction trends in a population of non-homeowner households using an actual eviction rate. Students can calculate solutions, sketch the phase portrait, and determine long-term trends .

3-033-S-TimeUpTimeDown-ModelingScenario

03 Feb 2024 | Contributor(s): Brian Winkel | doi:10.25334/809Y-8M85

We seek to compare for the time a projectile takes to go vertically up with the time it takes to return to its starting position.

1-027-StochasticProcesses-ModelingScenario

24 Jan 2024 | Contributor(s): Brian Winkel | doi:10.25334/BA33-M747

We build the infinite set of first order differential equations for modeling a stochastic process, the so-called birth and death equations. We will only need to use integrating factor solution strategy or DSolve in Mathematica for success.

1-031-CoolIt-ModelingScenario

08 Dec 2023 | Contributor(s): Brian Winkel | doi:10.25334/37B7-CB11

We offer data on the temperature of water in a beaker in a room of constant temperature and in a room of nonconstant temperature. Students consider both empirical and analytic modeling approaches. We offer additional data sets in Excel spreadsheets.

1-027-StochasticProcesses-ModelingScenario

15 Oct 2023 | Contributor(s): Brian Winkel | doi:10.25334/6FRK-RR71

We build the infinite set of first order differential equations for modeling a stochastic process, the so-called birth and death equations. We will only need to use integrating factor solution strategy or DSolve in Mathematica for success.

5-007-ChemOpt-ModelingScenario

15 Oct 2023 | Contributor(s): Brian Winkel | doi:10.25334/PFV3-6C29

Modeling a chemical reaction and estimating parameters in the model permits optimization of profits from extracting reactants.

3-034-CarSuspension-ModelingScenario

09 Oct 2023 | Contributor(s): Therese Shelton, Brian Winkel | doi:10.25334/JYG7-5953

We examine the spring-mass-dashpot that is part of a car suspension, how the ride is related to parameter values, and the effect of changing the angle of installation. We model a ``quarter car'', meaning a single wheel.

1-026-Evaporation-ModelingScenario

18 Aug 2023 | Contributor(s): Brian Winkel | doi:10.25334/HB2D-9729

We provide data on evaporation of 91% isopropyl alcohol in six different Petri dishes and one conical funnel and on evaporation of water in one Petri dish. We ask students to develop a mathematical model for the rate of change in the respective volumes.

1-015-Torricelli-ModelingScenario

14 May 2023 | Contributor(s): Brian Winkel | doi:10.25334/1VKZ-WY22

We help students develop a model (Torricelli's Law) for the height of a falling column of water with a small hole in the container at the bottom of the column of water through which water exits the column.

1-015-Torricelli-ModelingScenario

14 May 2023 | Contributor(s): Brian Winkel | doi:10.25334/EA7X-P069

We help students develop a model (Torricelli's Law) for the height of a falling column of water with a small hole in the container at the bottom of the column of water through which water exits the column.

1-015-Torricelli-ModelingScenario

14 May 2023 | Contributor(s): Brian Winkel | doi:10.25334/74HW-QE20

We help students develop a model (Torricelli's Law) for the height of a falling column of water with a small hole in the container at the bottom of the column of water through which water exits the column.

6-005-InsectColonySurvivalOpt-ModelingScenario

18 Apr 2023 | Contributor(s): Brian Winkel | doi:10.25334/B4MR-5B69

We present a system of nonlinear differential equations to model the control of energy flow into producing workers or reproducers in an insect colony, using a set of given parameters and a number of different energy functions.

6-005-InsectColonySurvivalOpt-ModelingScenario

18 Apr 2023 | Contributor(s): Brian Winkel | doi:10.25334/YA0F-C978

We present a system of nonlinear differential equations to model the control of energy flow into producing workers or reproducers in an insect colony, using a set of given parameters and a number of different energy functions.

2011-Cruz-Aponte-Herrera-Valdez-Mitigating effects of vaccination on influenza outbreaks given constraints in stockpile size and daily administrati

06 Apr 2023 | Contributor(s): Brian Winkel | doi:10.25334/PRY6-EG24

We present a SIR-like model that explicitly takes into account vaccine supply and the number of vaccines administered per day and places data-informed limits on these parameters.

2011-Brian_Winkel-Parameter Estimates in Differential Equation Models for Population Growth

06 Apr 2023 | Contributor(s): Brian Winkel | doi:10.25334/JXVT-EZ52

We estimate the parameters present in several differential equation models of population growth, specifically logistic growth models and multiple species competition models.

2010-Brian_Winkel-Parameter estimates in differential equation models for chemical kinetics

06 Apr 2023 | Contributor(s): Brian Winkel | doi:10.25334/9RV0-NN69

We discuss the need for devoting time in differential equations courses to modelling and the completion of the modelling process with efforts to estimate the parameters in the models using data.

1-125-DiceyPopulation-ModelingScenario

05 Apr 2023 | Contributor(s): Brian Winkel | doi:10.25334/8AQ2-7K58

We offer students an opportunity to generate data for their team on a death and immigration model using 12 and 20 sided dice and then pass on the data to another student team for analysis with a model they built. The key is to recover the parameters.

1-025-MixingItUp-ModelingScenario

05 Apr 2023 | Contributor(s): Brian Winkel | doi:10.25334/DTJ3-0J43

Students build three different models for levels of salt in a tank of water and at each stage the level of complexity increases with attention to nuances necessary for success.

2012-Brian_Ingalls-Mathematical Modelling in Systems Biology An Introduction

01 Apr 2023 | Contributor(s): Brian Ingalls, Brian Winkel | doi:10.25334/FWBX-WC34

This is a comprehensive text with much biology background to motivate the mathematical modeling, exercises and answers, and many rich examples.

1979-Brian_Winkel-Elementary_My_Dear_Watson_Differential_Equation

13 Mar 2023 | Contributor(s): Brian Winkel | doi:10.25334/MXAQ-8883

Sherlock Homes explains to Doctor Watson how he solves a murdermystery using Newton's Law of Cooling.

2011-Brian_Winkel-Cross_coursing_in_mathematics-physical_modeling_in_differential_equations_crossing_to_discrete_dynamical_systems

13 Mar 2023 | Contributor(s): Brian Winkel | doi:10.25334/B0AG-Q851

We give an example of cross coursing in which a subject or approach in one course in undergraduate mathematics is used in a completely different course.