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Instructor Solutions Second Edition SIMIODE Textbook HTML Version
This is material we make available for instructors teaching a modeling-first approach to differential equations when using the Second Edition of SIMIODE Textbook, Differential Equations: A Toolbox for Modeling the Real World in HTML Version.
Modeling Scenario
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3-051-ProjectileMotions-ModelingScenario
We consider several instances of projectile flight without resistance, one on level ground and one from edge of cliff to determine maximum distance and placement.
Modeling Scenario
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3-052-OptimalProjectileFiring-ModelingScenario
We offer the opportunity to model a projectile's trajectory in several cases, all without resistance.
Modeling Scenario
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1-144-HeatCool-ModelingScenario
We offer an opportunity to build a mathematical model using Newton's Law of Cooling for a closed plastic baggie of liquid inside a liquid container.
Modeling Scenario
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1-131-CaffeineElimination-ModelingScenario
We model the concentration of caffeine eliminated from the human body at a rate proportional to the concentration. This is a ``first-order reaction'' in the language of pharmacokinetics -- the study of how drugs move in the body.
Article or Presentation
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SIMIODE Spring 2024 Webinars - Insightmaker
We discuss the use of the FREE system dynamics software Insightmaker (https://insightmaker.com/) in a first course in Ordinary Differential Equations (with a modeling emphasis).
Article or Presentation
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SIMIODE Spring 2024 Webinars - WikiModel
WikiModel is cloud-based application and requires no installation and is run via a web-browser to facilitate rapid implementation. Equations are typed in as they appear in a textbook. ODEs are automatically integrated via Runge-Kutta methods.
Article or Presentation
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SIMIODE Spring 2024 Webinars - Ethics Modeling
A Practical Guide for Incorporating Ethical Reasoning into Mathematics Courses through Modeling Problems
Modeling Scenario
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1-078-MonodGrowthModel-ModelingScenario
Students model growth of bacteria E. coli in a limiting nutrient environment using data from a historical study.
Modeling Scenario
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5-026-Evictions-ModelingScenario
In this project, students develop two SIS models to study eviction trends in a population of non-homeowner households using an actual eviction rate. Students can calculate solutions, sketch the phase portrait, and determine long-term trends .
Article or Presentation
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2018-Vajravelu-Teaching Large DE Classes
Practical problem solving in science and engineering programs require proficiency in mathematics. Improving student performance and retention in mathematics classes requires inventive approaches.
Modeling Scenario
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3-033-S-TimeUpTimeDown-ModelingScenario
We seek to compare for the time a projectile takes to go vertically up with the time it takes to return to its starting position.
Modeling Scenario
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1-027-StochasticProcesses-ModelingScenario
We build the infinite set of first order differential equations for modeling a stochastic process, the so-called birth and death equations. We will only need to use integrating factor solution strategy or DSolve in Mathematica for success.
Modeling Scenario
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5-024-PhGreatLakes
In this teaching modeling scenario, we demonstrate how lessons on salt-tank compartmental modeling can be used to predict phosphorus levels in the Great Lakes.
Modeling Scenario
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1-031-CoolIt-ModelingScenario
We offer data on the temperature of water in a beaker in a room of constant temperature and in a room of nonconstant temperature. Students consider both empirical and analytic modeling approaches. We offer additional data sets in Excel...
Modeling Scenario
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6-022-CannibalismPredatorPrey-ModelingScenario
The Lotka-Volterra model tells us that the prey and predator exhibit a shifted cyclic behavior over time. In this module, we look at modifying this prey-predator model to consider the case when there is cannibalism in the predator species.
Modeling Scenario
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5-007-ChemOpt-ModelingScenario
Modeling a chemical reaction and estimating parameters in the model permits optimization of profits from extracting reactants.
Modeling Scenario
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3-034-CarSuspension-ModelingScenario
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.
Article or Presentation
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2020-TeachingModule-CarSuspension
The modeling activity on car suspensions assumes that students have grappled with second order linear homogeneous differential equations with constant coefficients.
Modeling Scenario
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