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Downloads
Views
Date
Relevance
Technique Narrative
346
views
146
downloads
0
comments
2-001-NumericalMethodsComparisons-TechniqueNarrative
This material teaches the basics of numerical methods for first order differential equations by following graphical and numerical approaches. We discuss the order of accuracy of the methods and compare their CPU times.
Euler's method
improved Euler's method
RK3 methods
RK4 methods
order of accuracy
absolute error
CPU time
Modeling Scenario
219
views
394
downloads
0
comments
1-091-InvestigatingSlopeFields-ModelingScenario
Students will gain experience writing differential equations to model various population scenarios, they will create slope fields to view the solution curves using software, and they will discuss the behavior of the solution curves.
slope fields
population
Potential Scenario
142
views
46
downloads
0
comments
2017-Sim-EtAl-Optimal control of a coupled tanks system with model-reality differences
In this paper, an efficient computational approach is proposed to optimize and control a coupled tanks system.
optimal control
flow
tanks
coupled tanks
Modeling Scenario
266
views
125
downloads
0
comments
1-001c-PopulationDecayThenSome-ModelingScenario
You will be modeling the following situation: 100 people are in a hotel. Each day, each person has a random chance of 50% of leaving the hotel. No new people enter the hotel.
simulation
occupancy
population
hotel
Technique Narrative
375
views
166
downloads
0
comments
5-030-LinNonHomoSystemSol-TechniqueNarrative
We offer strategies for solving linear systems of nonhomogeneous differential equations using a conjectured solution strategy for a system of constant coefficient, linear, n
strategies
discovery learning
eigenvectors
eigenvalue
Potential Scenario
99
views
30
downloads
0
comments
1992-CHF_Bulte-The differential equation of the deflection curve
This paper presents the derivation and physical meaning of the general fourth-order linear differential equation (with sectionally continuous derivatives) of the deflection curve and its general formulation and solution as a multipoint BVP.
beam
deflection
shear force
bending moment
critical load
natural frequency
Potential Scenario
140
views
36
downloads
0
comments
2019-Hu-Treinen-One-step_method_for_modelling_longitudinal_data_with_differential_equations
This study proposes a new approach to estimate the parameters in differential equation models used to describe non-linear trajectories of longitudinal data.
simulation
parameter estimation
shopping
fitting
behaviour
Modeling Scenario
429
views
377
downloads
0
comments
1-042-KoolAid-ModelingScenario
Students run experiments involving concentrated solution of drink powder flowing from upper to lower tank, initially filled with plain water. They make qualitative observations about the intensity of the color in the tanks, record data, and build...
concentration
compartment
tanks
KoolAid
Modeling Scenario
313
views
126
downloads
0
comments
1-001d-HotelPopulationDecay-ModelingScenario
You will be modeling the following situation: 100 people are in a hotel. Each day, each person has a random chance of 50% of leaving the hotel. No new people enter the hotel. Before you run the simulation in MATLAB, answer some questions.
simulation
logistic
exponential decay
fitting
Modeling Scenario
270
views
246
downloads
0
comments
6-002-EulerCromerPendulum-ModelingScenario
This activity introduces students to the concept of numerical stability. While modeling a simple pendulum, students compare performance of the semi-implicit Euler-Cromer method with Euler's method and the higher-order Improved Euleror algorithm.
pendulum
semi-implicit methods
Euler-Cromer
numerical solvers
Modeling Scenario
296
views
407
downloads
0
comments
6-007-FunctionsAndDerivativesInSIRModels-ModelingScenario
Given a system of differential equations, how do the solution graphs compare with the graphs of the differential equations? Students tackle this question using SIR models for well-known infectious diseases.
epidemiology
species interactions
derivatives
visualization
infection
SIR models
Law of Mass Action
Modeling Scenario
242
views
512
downloads
0
comments
6-024-DronePackageDelivery-ModelingScenario
Students will derive a system of first order differential equations which describe the flight path of a drone delivering a package.
Vectors
Trigonometry
Flight
drones
parametric curve
Improved Euler Method
Runge-Kutta
Modeling Scenario
185
views
105
downloads
0
comments
3-020-ChordPathTime-ModelingScenario
Using Newton's Second Law of motion we can determine the time it takes for a mass to slide along a chord of a vertical circle from high point to any point along the circle. Initially, the result is nonintuitive and challenging to understand.
Unit Circle
path
falling
gravity
chord
Netwon's Second Law of Motion
Modeling Scenario
201
views
149
downloads
0
comments
3-071-WirelessTelegraphy-ModelingScenario
This project has three parts, (1) done at home, (2) and (3) in class. In (1) we recall how to solve second order differential equations with constant coefficients and simple source functions. In class understand resonance and beats.
b
RLC circuit
resonance
beats
current
wireless telegraphy
LC circuit
Potential Scenario
206
views
62
downloads
0
comments
2017-Justin_Krueger-Parameter Estimation Methods for Ordinary Differential Equation Models with Applications to Microbiology
We demonstrate the feasibility of principal differential analysis using simulation studies and then apply the method to intestinal and vaginal microbiota data.
microbiology
Lotka Volterrra
microbiota
Modeling Scenario
265
views
302
downloads
0
comments
3-103-PullBackCars-ModelingScenario
This activity offers analysis of a toy pull-back car: solution of a differential equation from model; data collection and parameter estimation; and adapting the model to predict maximum speed and distance traveled for a new pull-back distance.
modeling
dynamics
hands-on
toy
pull-back car
pullback
Modeling Scenario
247
views
145
downloads
0
comments
1-136-MarriageAge-ModelingScenario
Students will build and analyze a model of the fraction of people who are married (for the first time) by a certain age. Students are asked to set up and solve these differential equations. They are then expected to analyze the behavior of these...
messages
marriage
using social sciences in forecasting
directed
Potential Scenario
218
views
73
downloads
0
comments
2018-Joseph-EtAl-A Nonlinear differential equation model of Asthma effect of environmental pollution using LHAM
In this paper, we investigated a nonlinear differential equation mathematical model to study the spread of asthma in the environmental pollutants from industry and mainly from tobacco smoke from smokers in different type of population.
asthma
tobacco smoke
Liao’s Homotopy analysis Method (
environmental pollutants
Potential Scenario
93
views
70
downloads
0
comments
2015-G_Knott-Chemical Kinetics - Simple Binding F + G to and from B
The study of this reaction, F + G goes to and from B, is common in chemistry and biochemistry. For example, F could be a hormone or drug and G the associated receptor sites.
binding
reaction
chemical kinetics
deterministic
Biochem Labs
probabilistic
kinetic reaction
Potential Scenario
117
views
70
downloads
0
comments
2015-Doust-Saraj-The logistic modeling population having harvesting factor
The present paper deals with the logistic equation having harvesting factor, which is studied in two cases constant and non-constant.
logistic
harvest
harvesting factor
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