27 Aug 2021 | | Contributor(s):: Brody Dylan Johnson
This modeling scenario examines the deflection of a cantilever beam under two different distributed loads. Students will have the opportunity to conduct experiments with their own cantilever beam or use data provided in the student version. A mathematical model for the beam deflection will be...
14 Aug 2021 | | Contributor(s):: Vladimir Riabov
Students will use computer programs (or create their own programming code) based on exponential box-scheme approximations for solving systems of nonlinear differential equations that contain small parameters for the highest derivative terms or singularities in boundary conditions. The uniform...
12 Aug 2021 | | Contributor(s):: Yuxin Zhang
The temperature distribution along a uniform slender bar due to conduction and convection is investigated through experimental, analytical, and numerical approaches. A series of experiments are designed to study the effects of materials, ambient fluid flows, geometric characteristics, and...
Engineering Design Optimization using Calculus Level Methods: A Casebook Approach (Manual)
20 Mar 2021 |
Posted by Phil B Brubaker
31 Aug 2020 | | Contributor(s):: Jeremy Christman, Kenneth Luther, Michael Karls
The goals of this project are to compare a conceptual one-dimensional groundwater flow model to observations made in a laboratory setting, and to discuss the differences. We derive the initial groundwater flow equation, and guide students through a solution. We describe the laboratory set up and...
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...
18 Aug 2018 | | Contributor(s):: Suruchi Singh
The heat equation is an important partial differential equation (PDE) which describes the distribution of heat in a given region over time. Here we learn to solve a heat equation numerically. It is difficult to study the behavior of temperature in problems with interfaces analytically so...
2017-Roux, Jean -Mathematical Models in Air Quality Problems - Notes
11 Sep 2017 | | Contributor(s):: Brian Winkel
Roux, Jean. Mathematical Models in Air Quality Problems. Notes. 26 pages.Presents many models with analysis in air quality control. Starts with chemical kinetics models and builds complexity to PDE models.Keywords: differential equation, model, finite difference, chemical kinetics,...
22 Nov 2016 | | Contributor(s):: Gregg Waterman, Tiernan R Fogarty
This scenario is designed to lead students to discover a differential equation that models the vertical deflection of a horizontal beam under different boundary conditions. Vertical deflection occurs as a result of the weight of the beam alone, with no compressive force at the ends or distributed...
1992-Bulte, C. H. F. - The differential equation of the deflection curve.
26 Jun 2015 | | Contributor(s):: C. H. F. Bulte
Bulte, C. H. F. 1992. The differential equation of the deflection curve. International Journal of Mathematical Education in Science and Technology. 23(1): 5-63.See https://www.tandfonline.com/doi/abs/10.1080/0020739920230106 .Article Abstract: This paper presents the derivation...
04 Jun 2015 | | Contributor(s):: Brian Winkel
We present a derivation of a partial differential equation which models the motion of a string held at both ends, a case of the one-dimensional wave equation. We immediately offer numerical solutions in a computer algebra system (we use Mathematica, but any...