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1-190-S-IntroClass
05 Mar 2022 | | 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...
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4-036-S-AltitudeDependentGravity
22 Jan 2022 | | 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,...
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1-005C-S-OilSlick
17 Jan 2022 | | 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,...
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3-091-S-MassSpringExperiments
14 Jan 2022 | | 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...
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9-030-S-WaterHammer
31 Aug 2021 | | Contributor(s):: Panagiotis D. Scarlatos
The students will develop and apply a numerical algorithm that solves a system of two nonlinear partial differential equations (PDEs). The equations involved are nonlinear and of hyperbolic type. The problem to be solved is an initial-boundary value problem that describes the time evolution of...
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1-098-S-NeuronDetection
25 Aug 2021 | | Contributor(s):: Joshua Goldwyn
In this activity students will study a linear, first order, one-dimensional ordinary differential equation (ODE) and learn how it can be used to understand basics of neural dynamics. The modeling framework is known in the mathematical neuroscience literature as the ``integrate-and-fire''...
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3-073-S-EarthQuake Part II
06 Aug 2021 | | Contributor(s):: Tracy Weyand
This modeling scenario considers a one-story building as a simple structure; the roof is modeled as a single point mass. Movement of the roof can be modeled similar to a mass-spring-damper system. In this activity, students will analyze motion of the roof under different damping and vibration...
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3-072-S-EarthQuake Part I
06 Aug 2021 | | Contributor(s):: Tracy Weyand
This modeling scenario considers a one-story building as a simple structure; the roof is modeled as a single point mass. Movement of the roof can be modeled similar to a mass-spring system. In this activity, students will analyze the motion of the roof caused by ground movement. Here we...
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1-139-S-PlantsVsHerbivores
08 Mar 2021 | | Contributor(s):: Mary Vanderschoot
In a recent study of plants and herbivores on an island in the North Sea, ecologists made a surprising observation: Instead of more vegetation resulting in more grazers, more vegetation resulted in fewer grazers. Consequently, the ecologists hypothesized that, as the vegetation grew more dense,...
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SIMIODE EXPO 2021 - Keynote Speaker - Matt Boelkins - More Linear Algebra
01 Mar 2021 | | Contributor(s):: Matt Boelkins
SIMIODE EXPO 2021 - Keynote Speaker - Matt Boelkins - More Linear AlgebraMore Linear AlgebraMatt Boelkins, Grand Valley State University, Allendale MI USA and Editor PRIMUSThis was a presentation made at the SIMIODE EXPO 2021 - see program.Abstract: In 2001, Gilbert Strang...
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Muhammad Nazam
PhD functional Analysis with successful graduate teaching and 50 + publications
https://www.simiode.org/members/5767
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2020-Shelton, Therese - Remote Teaching Module - Car Suspensions
28 Jul 2020 | | Contributor(s):: Therese Shelton
In this modeling activity, students examine the spring-mass-dashpot that is part of a car suspension. We model a "quarter car'', meaning a single wheel, and compare effects of different masses, spring constants, damping coefficients, and the angle at which the assembly is installed....
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3-105-S-FrequencyResponse
22 Jul 2020 | | Contributor(s):: Brian Winkel
We describe the frequency response to a second order differential equation with a driving function as the maximum steady state solution amplitude and perform some analyses in this regard.
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2020-Malagon, Audrey - Remote Teaching Module - Geometry of Linear Systems
17 Jul 2020 | | Contributor(s):: Audrey Malagon
Geometric Behavior of Linear Systems Module OverviewThis module concentrates on the geometric properties of a system of 2 linear, homogeneous first order differential equations in 2 variables as dictated by the corresponding eigenvalues. Students should be familiar with using eigenvalues to...
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3-034-S-CarSuspensions
14 Jul 2020 | | Contributor(s):: Therese Shelton, Brian Winkel
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.
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3-027-S-BobbingDropping
10 Jul 2020 | | Contributor(s):: Brian Winkel
We present two exercises from a differential equations text in which we ask students to model (1) falling object experiencing terminal velocity and (2) bobbing block of wood in liquid. We model the motion using Newton's Second Law of Motion and Archimedes' Principle.
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2020-Winkel, Brian - Remote Teaching Module - Spring Design to Meet Specs at Minimum Costs
16 Jun 2020 | | Contributor(s):: Brian Winkel
We place here all the materials in support of the SIMIODE Remote Teaching Module - Spring Design to Meet Specs at Minimum Costs. This Module is about second order, linear, ordinary differential equations.The class lesson starts with building a model of a spring-mass using...
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1-088-S-RoomTemperature
15 Jun 2020 | | Contributor(s):: Tracy Weyand
Students will analyze temperature variations in a room using Newton's Cooling Law. In this model, the only influence on the indoor temperature is the (oscillating) outdoor temperature (as we assume the heating/cooling system is broken). The main goal of this project is for students to set up...
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2020-Winkel, Brian - Remote Teaching Module - Modeling the Spread of Oil Slick
10 Jun 2020 | | Contributor(s):: Brian Winkel
We place here and in the Supporting Docs all the materials in support of the SIMIODE Remote Teaching Module - Modeling the Spread of Oil Slick.This module contains1) (Below and separate file in Supporting Docs) A brief Teaching Guide with an overview of the content and...
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3-031-S-SpringCost
28 May 2020 | | Contributor(s):: Brian Winkel
This is a situation where we are charged with analyzing costs for a spring to meet certain specifications.