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Article or Presentation
184
views
56
downloads
0
comments
2007-Joseph_Myers-Brian_Winkel-Modeling_a_Mystery_Circuit_in_Mathematics_Class_Using_Differential_Equations_Laplace_Transforms_and_Transfer_Functions
We discuss the introduction, student discovery, and teaching of a system of differential equations which model a circuit.
circuit
Laplace transform
transfer function
mystery circuit
voltage frequency
two loop circuit
Modeling Scenario
442
views
263
downloads
0
comments
7-011-CoupledSystemLaplace-ModelingScenario
Differential equations and Laplace transforms are an integral part of control problems in engineering systems. We consider a baby warming device.
transfer function
polycarbonate
baby heater
coupled system
heating
Modeling Scenario
254
views
246
downloads
0
comments
7-020-ThermometerInVaryingTempStream-ModelingScenario
We present a first order differential equation model for the temperature of a mercury thermometer which is sitting in a stream of water whose temperature oscillates. We suggest a solving strategy which uses Laplace Transforms.
temperature
steady state
thermometer
heat exchange
transfer function
phase lag
Invers Laplace Transform
Potential Scenario
203
views
72
downloads
0
comments
2017-GR_Gustafson-Differential Equations Course Materials
There are many applications from compartment and cascade analysis, recycling brine tank, home heating with multiple rooms, chemostat, microbes, heartbeats, lidocaine, nutrient flow in an aquarium, biomass transfer, pesticides, forecasting prices,...
chemostat
microbes
biomass
forecasting
transfer
compartment
pesticides
earthquake
tank
heating
lidocaine
brine
heartbeats
nutrient flow
aquarium
electric networks
circuits
logging
building
cascade
Potential Scenario
112
views
37
downloads
0
comments
2004-Hill-Lozowski-Sampson-Experiments on ice spikes and a simple growth model
We observed ice-spike growth using time-lapse digital photography, using two water types in two different containers.
ice
ice spike
bulk heat transfer
mass conservation
Potential Scenario
214
views
51
downloads
0
comments
2004-Mitchell-von Meien-Krieger-Dalsenter-A review of recent developments in modeling of microbial growth kinetics
Mathematical models are important tools for optimizing the design and operation of solid-state fermentation (SSF) bioreactors. Such models must describe the kinetics of microbial growth.
Filamentous Fungi
solid-state fermentation
growth kinetics
diffusion-reaction
oxygen transfer
Potential Scenario
182
views
55
downloads
0
comments
2000-Idels-Wang-Harvesting Fisheries Management Strategies With Modified Effort Function
This study concludes that a control parameter beta (the magnitude of the effect of the fish population size on the fishing effort function E), changes not only the rate at which the population goes to equilibrium, but also the equilibrium values.
sustainability
fish
Fishing
management
harvest
fisher
strategy
overfishing
Modeling Scenario
430
views
263
downloads
0
comments
3-092-WirelessPower-ModelingScenario
We present an engineering application (wireless power transmission) modelled by a coupled system of two linear second-order differential equations with constant coefficients. One equation is homogeneous while the other one is non-homogeneous.
DESMOS
wireless power transmission
electric circuits
Kirchhoff's Voltage Law
Potential Scenario
151
views
83
downloads
0
comments
2016-Mehmet_Pakdemirli-Mathematical design of a highway exit curve
Using fundamental principles of physics and calculus, the differential equation determining the curve function is derived.
kinematics
curve design
highway exit
tangential acceleration
Modeling Scenario
400
views
176
downloads
0
comments
7-008-MachineReplacement-ModelingScenario
Students build an integro-differential equation model using a convolution for machine replacement strategies for two different machine failure models.
Probability
replacement number
Laplace transform
industrial engineering
machine
convolution
distributioj
step function
derivative definition
Potential Scenario
134
views
52
downloads
0
comments
2015-Carl_Lutzer-Using Expected Value to Introduce the Laplace Transform
We propose an introduction to the Laplace transform in which Riemann sums are used to approximate the expected net change in a function, assuming that it quantifies a process that can terminate at random.
Expected Value
Riemann sum
net change
Potential Scenario
151
views
33
downloads
0
comments
2011-W_Wood-Squigonometry
The differential equations used to define a unit circle, namely x’(t) = - y(t), y’(t) = x(t), x(0) = 1, y(0) = 0 are generalized to produce interesting functions which satisfy trig like identities.
Trigonometry
Trigonometric Functions
parametric equations
circle
sine
cosine
squigonometry
inverse function
Modeling Scenario
293
views
133
downloads
0
comments
1-089-SpreadOfDisease-ModelingScenario
In this project I want to use the algebra based concept “difference quotient” to solve differential equations models with the help of Excel. That means even students with only a College Algebra background, can still enjoy differential equation...
SIR model
Proportion
derivative
difference quotient
Sleeping Beauty
contagious disease
Potential Scenario
258
views
88
downloads
0
comments
2023-Roberto_Camassaa-Richard_McLaughlina-Tauberian identities and the connection to Wile E Coyote physics
The application of the motion of a vertically suspended mass-spring system released under tension is studied focusing upon the delay timescale for the bottom mass as a function of the spring constants and masses.
Hangtime
Tauberian Identities
Road Runner
Wile E. Coyote
Potential Scenario
132
views
40
downloads
0
comments
2005-P_Howard-Modeling with ODE
In these notes we consider three critical aspects in the theory of ordinary differential equations: developing models of physical phenomena, mathematically well-posed, solving ODE numerically .
Fluid Mechanics
compartment
populations
variational methods
Hamiltonian mechanics
Potential Scenario
148
views
56
downloads
0
comments
2018-Adeniji-EtAl-InverseProblemHolling-TannerModel
We consider the inverse problem of parameter identification of nonlinear system of ODEs for a specific case of complete information about solution of the Holling-Tanner model for finite number of points for the finite time interval.
goal function
absolute error curves
invers method
holling-Tanner model
Potential Scenario
136
views
80
downloads
0
comments
2014-Wang-EtAl-Estimating Mixed-Effects Differential Equation Models
When multiple replicates of measurements are available for the dynamic process, it is of great interest to estimate mixed-effects in the ODE model for the process. We propose a semiparametric method to estimate mixed-effects ODE models.
pharmacokinetics
dynamic models
smoothing
spline
mixed-effects models
HiV combination therapy
Potential Scenario
157
views
61
downloads
0
comments
1989-R_Blickhan-Spring Mass Model For Running-Hopping
A simple spring—mass model consisting of a massless spring attached to a point mass describes the interdependency of mechanical parameters characterizing running and hopping of humans as a function of speed.
spring mass
jump
jumping
Potential Scenario
172
views
40
downloads
0
comments
1967-Israelsson- Johnsson-Circumnutations In Helianthus Annuus
A theory is given for circumnutations in plants, especially hypocotyls of Helianthus annuus, which were used as experimental material.
plant
oscillation
delay
circumnutation
turning
Potential Scenario
171
views
56
downloads
0
comments
2016-Wilkie-EtAl-Using ODEs to Explore Cancer-Immune Dynamics and Tumor Dormancy
Here we present a general method using ordinary differential equations (ODEs) to model and analyze cancer-immune interactions, and in particular, immune-induced tumor dormancy.
cancer
tumor-inhibiting cytotoxic action
tumor-promoting inflammation
immune-induced tumor dormancy
tumor growth dynamics
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