2013-Brian_Winkel-Browsing_Your_Way_to_Better_Teaching

13 Mar 2023 | Contributor(s): Brian Winkel | doi:10.25334/9JQJ-QB84

We describe the use of browsing and searching (in libraries, on-line, inside sources, at meetings, in abstracts, etc.) as a way to stimulate the teacher of undergraduate mathematics, specifically in differential equations.

2008-Brian_Winkel-Fourier_Series-Optimization_Opportunity

13 Mar 2023 | Contributor(s): Brian Winkel | doi:10.25334/NGJK-V088

We discuss the introduction of Fourier series as an immediate application of optimization of a function of more than one variable.

2011-Brian_Winkel-Sourcing_for_parameter_estimation_and_study_of_logistic_differential_equation

13 Mar 2023 | Contributor(s): Brian Winkel | doi:10.25334/E0GC-R484

We present two simulation activities for students to generate real data and several data sources for the purpose of estimating parameters in the logistic differential equation model.

2011-Brian_Winkel-Parameter_Estimates_in_Differential_Equation_Models_for_Chemical_Kinetics

13 Mar 2023 | Contributor(s): Brian Winkel | doi:10.25334/97MY-CF93

We estimate the parameters present in several differential equation models of chemical kinetics and logistic growth.

2011-Brian_Winkel-Parameter_Estimates_in_Differential_Equation_Models_for_Population_Growth

13 Mar 2023 | Contributor(s): Brian Winkel | doi:10.25334/ZS8R-N570

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

2007-Joseph_Myers-Brian_Winkel-Modeling_a_Mystery_Circuit_in_Mathematics_Class_Using_Differential_Equations_Laplace_Transforms_and_Transfer_Functions

13 Mar 2023 | Contributor(s): Joseph Myers, Brian Winkel | doi:10.25334/J201-8792

We discuss the introduction, student discovery, and teaching of a system of differential equations which model a circuit.

1994-Brian_Winkel-Designated_Student_Grading _as_a_Learning_Device

15 Mar 2023 | Contributor(s): Brian Winkel | doi:10.25334/ZS39-T019

We describe how we engaged students in the course to grade regular homework assignments of that same class and the added learning opportunities in doing so.

2008-Keith_Landry-Brian_Winkel-Peak_Frequency_Responses_and_Tuned_Mass_Dampers

12 Mar 2023 | Contributor(s): Keith Landry, Brian Winkel | doi:10.25334/KXP2-Y972

We present two applications of systems of ordinary differential equations concerning excitation of a structure through resonance and (1) peak frequency responses with stabilization of the structure by means of a (2) Tuned Mass Damper (TMD).

1990-Winkel_Brian-First-year_calculus_students_as_in-class_consultants

12 Mar 2023 | Contributor(s): Brian Winkel | doi:10.25334/T77V-BB87

We demonstrate how we use traditional text book calculus problems to involve first year calculus students as consultants. Students are asked to solve a “real world” problem after interviewing a “guest” client –a printer.

2021-Brian_Winkel-Modelling_sublimation_of_carbon_dioxide

12 Mar 2023 | Contributor(s): Brian Winkel | doi:10.25334/NWVE-5E37

We report results in our efforts to model sublimation of carbon dioxide and the associated kinetics order and parameter estimation issues in our model.

2015-Brian_Winkel-Informed_Conjecturing_of_Solutions_for_Differential_Equations_In_a_Modeling_Contex

12 Mar 2023 | Contributor(s): Brian Winkel | doi:10.25334/30Z1-P874

We examine (1) first order exponential growth or decay and (2) second order, linear, constant coefficient differential equations, and show the advantage of learning differential equations in a modeling context for informed conjectures of their solution.

1994-Brian_Winkel-Ant_Tunnels_and_Calculus

12 Mar 2023 | Contributor(s): Brian Winkel | doi:10.25334/EMWE-YK09

A simple mathematical model describing the time it takes for an ant to construct a linear tunnel of length x is produced from five intuitively acceptable assumptions.

2009-Agnes_Rash-Brian_Winkel-Birth_and_Death_Process_Modeling_Leads_to_the_Poisson_Distribution

12 Mar 2023 | Contributor(s): Agnes Rash, Brian Winkel | doi:10.25334/H32F-ED30

In this paper there are details of development of the general birth and death process from which we can extract the Poisson process as a special case.

2013-Brian_Winkel-An_Optimal_Control_Model_in_Insect_Colonies

12 Mar 2023 | Contributor(s): Brian Winkel | doi:10.25334/7FGX-0N47

we find and develop background material on an application of optimal control theory to model the evolutionary strategy of an insect colony to produce the maximum number of queen or reproducer insects in the colony at the end of a season.

2009-Brian_Winkel-Population_modelling_with_MandMs

11 Mar 2023 | Contributor(s): Brian Winkel | doi:10.25334/3FW5-5650

Several activities in which population dynamics can be modeled by tossing M&M’s® candy are presented.

2009-Brian_Winkel-Modelling_Growth_Of_an_OilSlick

10 Mar 2023 | Contributor(s): Brian Winkel | doi:10.25334/2R3J-CY47

An oil-slick spreads at sea. From time to time, but irregularly, a helicopter is dispatched. On each trip, it arrives over the slick, the pilot takes a picture, waits 10 minutes, takes another, and heads home. Model this.

2013-Brian_Winkel-Reflecting_On_Walls

10 Mar 2023 | Contributor(s): Brian Winkel | doi:10.25334/VJQT-7A47

We reflect on our passion for teaching mathematics, useful mathematics, by considering our understandings of just what a wall is and what a wall means to us.

2017-Brian_Winkel-Let_Us_Do_It_Using_Modeling_in_the_Classroom

10 Mar 2023 | Contributor(s): Brian Winkel | doi:10.25334/YZNK-JM62

In this article the author, Brian Winkel, Director of SIMIODE, attempts to make the case for modeling in the differential equations classroom by giving both rationale and examples.

6-004-VillageEpidemic-ModelingScenario

21 Feb 2023 | Contributor(s): Brian Winkel | doi:10.25334/JQ1A-N963

Students are offered data from a plague epidemic that occurred in the middle of the seventeenth century in Eyam, a small English village. With only two assumptions offered to students they are to build a mathematical model.

1-001-MM-DeathAndImmigration-ModelingScenario

20 Feb 2023 | Contributor(s): Brian Winkel | doi:10.25334/M144-RE41

We conduct a simulation of death and immigration, using a small set of "individuals", m&m candies or any two sided object (coin, chips), in which upon tossing a set of individuals we cause some to die and others then to immigrate. Modeling ensues!

1-128-RocketFlight-ModelingScenario

19 Jul 2022 | Contributor(s): Brian Winkel | doi:10.25334/2EQR-3F80

We offer an opportunity to build a mathematical model using Newton's Second Law of Motion and a Free Body Diagram to analyze the forces acting on the rocket of changing mass in its upward flight under power and then without power followed by its fall to

1-078-MonodGrowthModel-ModelingScenario

16 Jul 2022 | Contributor(s): Brian Winkel | doi:10.25334/2GGV-EF64

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

3-030-SecondOrderIntro-ModelingScenario

05 Jul 2022 | Contributor(s): Brian Winkel | doi:10.25334/X9GK-YP91

We outline the solution strategies involved in solving second-order, linear, constant coefficient ordinary differential equations, both homogeneous and nonhomogeneous and offer many application and modeling activities.

5-001-LSD-ModelingScenario

05 Jul 2022 | Contributor(s): Brian Winkel | doi:10.25334/CNEE-7J76

We describe the use of a two compartment model of a linear system of first order linear differential equations to model lysergic acid diethylamide (LSD) in the body. We provide the data from the literature.

1-031-CoolIt-ModelingScenario

05 Jul 2022 | Contributor(s): Brian Winkel | doi:10.25334/3WG8-EC31

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.