## Tags: linear

### All Categories (1-20 of 75)

1. 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...

2. 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,...

3. 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,...

4. 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...

5. 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...

6. 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''...

7. 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...

8. 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...

9. 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,...

10. 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...

PhD functional Analysis with successful graduate teaching and 50 + publications

https://www.simiode.org/members/5767

12. 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....

13. 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.

14. 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...

15. 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.

16. 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.

17. 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...

18. 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...

19. 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...

20. 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.