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Modeling Scenarios 22 Apr 2016 Contributor(s): Brian Winkel
SPANISH LANGUAGE VERSION We have placed in Supporting Docs both Student and Teacher Version (LaTeX and PDF Versions) with a Spanish LaTeX Class file, SIMIODE-SPANISH.… Names will be x-y-S-Title-StudentVersion-Spanish and x-y--T-Title-TeacherVersion-Spanish.
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Modeling Scenarios 2 Jun 2015 Contributor(s): Brian Winkel
We offer a mathematical modeling experience using differential equations to model the volume of an intraocular gas bubble used by ophthalmologists to aid the healing of a surgically repaired region of the retina. We ask students to compare the traditional ``empirical'' model used by the ophthalmological profession with more…
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Modeling Scenarios 28 Nov 2019 Contributor(s): Eric Stachura
Chemical and biomedical applications of differential equations SPANISH LANGUAGE VERSION We have placed in Supporting Docs a Spanish version of this Student Modeling Scenario.
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Modeling Scenarios 31 May 2015 Contributor(s): Brian Winkel
We pose the prospect of modeling just how long an ant takes to build a tunnel. With a bit of guidance students produce a model for the time it takes to build a tunnel of length x into the side of a damp sandy hill. SPANISH LANGUAGE VERSION We have placed in Supporting Docs both Student and Teacher Version (LaTeX and PDF Versions) with a…
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Modeling Scenarios 31 May 2015 Contributor(s): Brian Winkel
We pose the prospect of modeling just how long an ant takes to build a tunnel. With a bit of guidance students produce a model for the time it takes to build a tunnel of length x into the side of a damp sandy hill. SPANISH LANGUAGE VERSION We have placed in Supporting Docs both Student and Teacher Version (LaTeX and PDF Versions) with a…
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Modeling Scenarios 31 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 linear, first-order, non-homogeneous, ordinary…
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Modeling Scenarios 2 Jun 2015 Contributor(s): Brian Winkel
We offer data on the temperature of water in a beaker which resides in a room of constant temperature and also in an environment of nonconstant temperature. Students are encouraged to consider both empirical and analytic modeling approaches. We offer additional data sets in Excel spreadsheets for further work. SPANISH LANGUAGE…
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Modeling Scenarios 31 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 linear, first-order, non-homogeneous, ordinary…
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Modeling Scenarios 2 Jun 2015 Contributor(s): Brian Winkel
We describe the use of a two compartment model of a linear system of first order linear differential equations to model lysergic acid diethylamide (LSD) in the body. We provide the data from the literature. We offer students the opportunity to build a two compartment model to fully analyze the administration and absorption of LSD in 8…
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Modeling Scenarios 2 Jun 2015 Contributor(s): Brian Winkel
We offer a mathematical modeling experience using differential equations to model the volume of an intraocular gas bubble used by ophthalmologists to aid the healing of a surgically repaired region of the retina. We ask students to compare the traditional ``empirical'' model used by the ophthalmological profession with more…
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Modeling Scenarios 2 Jun 2015 Contributor(s): Brian Winkel
We ask students to build differential equations to model lysergic acid diethylamide (LSD) in the body. We provide the data from the literature. We offer students the opportunity to build a model to fully analyze the administration and absorption of LSD in 8 student volunteers. We also compare the model predictions with data from the…
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Modeling Scenarios 28 Nov 2019 Contributor(s): Eric Stachura
Students will be lead through a classical chemical engineering problem: to calculate the concentration profile of cyclohexane within a catalyst pellet by solving a second order linear differential equation. Then students will analyze the concentration as the radius of the catalyst shrinks to zero. Finally, they will explore a Mathematica Module…
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Modeling Scenarios 22 Apr 2016 Contributor(s): Brian Winkel
Abstract: We outline the solution strategies involved in solving second order, linear, constant coefficient ordinary differential equations, both homogeneous and nonhomogeneous and offer many application and modeling activities. COMMENTS (to teacher): We have assembled all the techniques, theory, and machinery for solving second order,…
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Modeling Scenarios 2 Jun 2015 Contributor(s): Brian Winkel
We offer data on the temperature of water in a beaker which resides in a room of constant temperature and also in an environment of nonconstant temperature. Students are encouraged to consider both empirical and analytic modeling approaches. We offer additional data sets in Excel spreadsheets for further work. SPANISH LANGUAGE…
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Modeling Scenarios 3 Jun 2015 Contributor(s): Brian Winkel
We help students develop a model (Torricelli's Law) for the height of a falling column of water with a small hole in the container at the bottom of the column of water. We offer several sources of simulations on YouTube and at this site from which we collect data and ask students to verify their model through parameter estimation. SPANISH…
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1-001-S-MandMDeathAndImmigration
Modeling Scenarios 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, usually a linear first order, difference or differential equation, collect data, estimate parameters, and compare their model prediction with their actual data. We describe a number of different faculty…
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Modeling Scenarios 3 Jun 2015 Contributor(s): Brian Winkel
We help students develop a model (Torricelli's Law) for the height of a falling column of water with a small hole in the container at the bottom of the column of water. We offer several sources of simulations on YouTube and at this site from which we collect data and ask students to verify their model through parameter estimation. SPANISH…
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1-001-T-MandMDeathAndImmigration
Modeling Scenarios 30 May 2015 Contributor(s): Brian Winkel, Norma Louise Miller, Gabriel Nagy
We describe a classroom activity in which students use M&M candies to simulate death and immigration. Students build a mathematical model, usually a linear first order, difference or differential equation, collect data, estimate parameters, and compare their model prediction with their actual data. We describe a number of different faculty…
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Modeling Scenarios 31 May 2015
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Modeling Scenarios 31 May 2015
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