Tags: non-homogeneous

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  1. 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,...

  2. 4-039-S-FallingDarts

    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...

  3. 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,...

  4. 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.

  5. 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.

  6. 1-128-S-RocketFlight

    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.

  7. 9-020-S-HeatDiffusion

    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...

  8. 1-001d-S-HotelPopulationDecay

    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.

  9. 5-030-S-Text-LinNonHomoSystemSol

    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.

  10. 1-001B-S-MAndM-DeathImmigrationMystery

    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...

  11. 1-006-S-FinancingSavingsAndLoans

    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...

  12. 1-005B-S-ChemDataCollection

    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...

  13. 1-005A-S-ChemDataCollection

    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...

  14. 1-005A-S-OilSlick

    30 May 2015 | | Contributor(s):: Karen Bliss

  15. 1-005-S-OilSlick

    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 ...

  16. 1-004-S-MicroorganismImmigration

    30 May 2015 | | Contributor(s):: Brian Winkel

    We present a modeling opportunity for population death with non-constant immigration and suggest the use of both discrete and continuous models with a comparison of results.

  17. 1-001-S-MandMDeathAndImmigration

    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...

  18. 1-003-S-CollegeSavings

    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.