
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,...

4039SFallingDarts
21 Jan 2022   Contributor(s):: Jacob Paul Duncan
Most projectile motion and free fall models are based on the assumption that gravity is the only force acting on the object. Here we develop, solve, and analyze a second order nonhomogeneous differential equation model for free fall which incorporates air resistance. Students will solve the model...

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,...

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.

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.

1128SRocketFlight
04 Jun 2020   Contributor(s):: Brian Winkel
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 earth.

9020SHeatDiffusion
14 Oct 2019   Contributor(s):: Kimberly Spayd, James Puckett
This project guides students through experimental, analytical, and numerical techniques for understanding the heat (diffusion) equation with nonhomogeneous boundary conditions. In particular, students collect data and model a physical scenario in which heat energy diffuses through a long, thin...

1001dSHotelPopulationDecay
03 Jul 2019   Contributor(s):: Dina Yagodich
We offer students an opportunity to create a simulation model a hotel population with clients checking in and checking out according to two different disciplines as well as a number of different starting populations in the hotel.

5030STextLinNonHomoSystemSol
26 Aug 2016   Contributor(s):: Brian Winkel
We offer strategies for solving linear systems of nonhomogeneous differential equations of the form X'(t) = A X(t) + G(t) using a conjectured solution strategy for a system of constant coefficient, linear, nonhomogeneous, differential equations.

1001BSMAndMDeathImmigrationMystery
27 Jun 2016   Contributor(s):: Brian Winkel
We describe a classroom activity in which students use M&M candies to simulate death and immigration. Each student conducts an experiment with an immigration rate unique to that student  of that student's choice. Collected data on generation or iteration and population is then...

1006SFinancingSavingsAndLoans
31 May 2015   Contributor(s):: Brian Winkel
We describe two situations (Pa) one in which we are saving for a purpose and (2) one in which we are borrowing for a purpose. In the first case we ask for discrete and continuous model of the situation and in the second case we ask that the results of the model be used to examine some...

1005BSChemDataCollection
30 May 2015   Contributor(s):: Brian Winkel
We present a situation in which a chemistry graduate student is assigned the task of collecting data on a chemical reaction and does a poor job of collecting the data. Indeed, he only collects the data at the start and end of a number of three minute intervals and does not keep track of...

1005ASChemDataCollection
30 May 2015   Contributor(s):: Brian Winkel
We present a situation in which a chemistry graduate student is assigned the task of collecting data on a chemical reaction and does a poor job of collecting the data. Indeed, she only collects the data at the start and end of a number of ten minute intervals and does not keep track of when...

1005ASOilSlick
30 May 2015   Contributor(s):: Karen Bliss

1005SOilSlick
30 May 2015   Contributor(s):: Brian Winkel
We describe a modeling activity for students in which modeling with difference and differential equations is appropriate. We have used this model in our coursework for years and have found that it enlightens students as to the model building process and parameter estimation for a ...

1004SMicroorganismImmigration
30 May 2015   Contributor(s):: Brian Winkel
We present a modeling opportunity for population death with nonconstant immigration and suggest the use of both discrete and continuous models with a comparison of results.

1001SMandMDeathAndImmigration
30 May 2015   Contributor(s):: Brian Winkel
We describe a classroom activity in which students use M&M candies to simulate death and immigration. Students build a mathematical model, collect data, estimate parameters, and compare their model prediction with their actual data. There is a video of one run of the main simulation in...

1003SCollegeSavings
12 May 2015   Contributor(s):: Brian Winkel
We present a modeling opportunity for students in which they have to plan and model for saving for a child's complete college education.