
1190SIntroClass
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...

4036SAltitudeDependentGravity
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 inversesquare of the distance between the centers of mass of the Earth and the projectile. When projectiles are near to Earth's surface,...

1005CSOilSlick
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,...

3091SMassSpringExperiments
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 springmass systems and solved secondorder...

9030SWaterHammer
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 initialboundary value problem that describes the time evolution of...

1098SNeuronDetection
25 Aug 2021   Contributor(s):: Joshua Goldwyn
In this activity students will study a linear, first order, onedimensional 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 ``integrateandfire''...

3073SEarthQuake Part II
06 Aug 2021   Contributor(s):: Tracy Weyand
This modeling scenario considers a onestory building as a simple structure; the roof is modeled as a single point mass. Movement of the roof can be modeled similar to a massspringdamper system. In this activity, students will analyze motion of the roof under different damping and vibration...

3072SEarthQuake Part I
06 Aug 2021   Contributor(s):: Tracy Weyand
This modeling scenario considers a onestory building as a simple structure; the roof is modeled as a single point mass. Movement of the roof can be modeled similar to a massspring system. In this activity, students will analyze the motion of the roof caused by ground movement. Here we...

1139SPlantsVsHerbivores
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,...

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...

Muhammad Nazam
PhD functional Analysis with successful graduate teaching and 50 + publications
https://www.simiode.org/members/5767

2020Shelton, Therese  Remote Teaching Module  Car Suspensions
28 Jul 2020   Contributor(s):: Therese Shelton
In this modeling activity, students examine the springmassdashpot 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....

3105SFrequencyResponse
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.

2020Malagon, 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...

3034SCarSuspensions
14 Jul 2020   Contributor(s):: Therese Shelton, Brian Winkel
We examine the springmassdashpot 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.

3027SBobbingDropping
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.

2020Winkel, 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 springmass using...

1088SRoomTemperature
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...

2020Winkel, 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...

3031SSpringCost
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.