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Views
Date
Relevance
Potential Scenario
136
views
66
downloads
0
comments
2017-Adolfo_Rumbos-Differential Equations and modeling
The study of any phenomenon in the physical or biological sciences, in which continuity and differentiability assumptions about the quantities in question can be made, invariably leads to a differential equation, or a system of differential...
pendulum
Lotka Volterra equations
existence
uniqueness
Potential Scenario
275
views
58
downloads
0
comments
2012-Hassan_Moore-Using projects to stimulate learning in mathematics and engineering mathematics courses
Given that time is a premium in the academy and project creation is a time consumer, three original projects, which may be injected into any Calculus III, Differential Equations, or Engineering Mathematics course, have been created.
solutions
class projects
physical phenomenon
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
Modeling Scenario
245
views
157
downloads
0
comments
1-068-WaterBottleCooling-ModelingScenario
Students create of a differential equation describing how fluid in a water bottle will change its temperature to approach the ambient temperature in a room.
b
Newton's Law of Cooling
water bottle
autonomous
bottle
Potential Scenario
174
views
45
downloads
0
comments
2017-Helen-Byrne-Further Mathematics Biology
These studies will be in the context of ecological, biological and biochemical applications.
epidemics
chemotaxis
enzyme-substrate
ion channels
nerve pulses
gene proagation
tumour
Technique Narrative
527
views
599
downloads
0
comments
5-005-StiffDifferentialEquations-TechniqueNarrative
This material introduces the topic of ``stiffness'' for a system of ordinary differential equations (ODE's), through a series of examples. Stiffness is a property that a system of ODE's may posses that make it difficult to solve numerically.
Euler's method
explicit methods
implicit methods
stiff
sitffness
stiff differential equation
instability
Potential Scenario
170
views
41
downloads
0
comments
1999-Kowalczyk-Hausknecht-Using DEs To Model Real World Data
With the increasing availability of easy to use interactive differential equation software, we convinced ourselves to completely redesign the way we teach differential equations.
circuit
Torricelli's Law
Hooke's Law
RC circuit
harmonic oscillator
glucose
glucose tolerance test
Modeling Scenario
199
views
147
downloads
0
comments
9-030-WaterHammer-ModelingScenario
We develop and apply a numerical algorithm that solves a system of two nonlinear partial differential equations (PDEs) that describes the time evolution of the water hammer phenomenon.
Stock and Flow model
hyperbolic equations
finite differences
water hammer
hydrodynamics
compressibility
wave celerity
Potential Scenario
211
views
82
downloads
0
comments
2018-W_Hohenauer-Physical modelling based on first order ODEs
An introduction in techniques to solve first order ODE´s is given. Barometric formula, charging and discharging of a capacitor including its application for AMV, magnetic induction and growth effects are discussed.
discharge
capacitor
magnetic field
induction
magnetic induction
Potential Scenario
132
views
56
downloads
0
comments
1994-M_Yamaguti-Discrete Models in Social Sciences
Also, a finite difference model in sociology is given as a chaotic phenomenon.
economics
chaos
sociology
discrete
discretization
Potential Scenario
133
views
38
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
Modeling Scenario
170
views
90
downloads
0
comments
1-036-NeutralBuoyancy-ModelingScenario
An object may hang suspended at, say, ten foot depth in a column of water if at ten feet underwater the density of the object equals the density of water. We study this phenomenon
Density
buoyancy
Archimedes’ Principle
float
neutral buoyance
Technique Narrative
185
views
298
downloads
0
comments
1-061-SingularPerturbation-TechniqueNarrative
This paper introduces the basics of singular perturbation methods for solving ordinary differential equations. Interactive examples will show how the smallness of physical parameters can drastically change the nature of the solutions.
perturbation
singular perturbation
Free Online Textbook
151
views
100
downloads
0
comments
2013-Marcel_Finan-A_Second_Course_in_Differential_Equations
Location: http://faculty.atu.edu/mfinan/nnotes.html . Accessed 9 March 2023. Here you will find a whole collection of differential equations texts:
differential equations
textbook
Free Online Textbook
158
views
60
downloads
0
comments
2016-Langtangen-Pedersen - Scaling of Differential Equations
Nowadays, the greatest practical benefit of scaling is related to running numerical simulations, since scaling greatly simplifies the choice of values for the input data and makes the simulations results more widely applicable.
scaling
dimensionless
continuum mechanics
Free Online Textbook
239
views
75
downloads
0
comments
2011-Richard_Fitzpatrick-Newtonian_Dynamics
This 300 page text is packed with motivational physics. Indeed, Professor Fitzpatrick brings us to the origins of why differential equations are the dominant tools of mathematics in the study of motion.
modeling
textbook
physics
bifurcation
Potential Scenario
279
views
98
downloads
0
comments
2006-Wilensky-Reisman-Thinking Like a Wolf a Sheep or a Firefly
We describe a computation-based approach that enables students to investigate the connections between different biological levels using agent-based, embodied modeling tools.
simulation
NetLogo
predator-prey
agent-based
wolf
fox
Modeling Scenario
383
views
653
downloads
0
comments
1-155-CruiseControl-ModelingScenario
In this project we illustrate the design of a proportional-integral-derivative (PID) cruise control algorithm for an automobile. PID control is one of the most common techniques in control engineering.
PID controller
feedback control
Control theory
cruise control
automobile
closed-loop control
input-ouput
block diagram
Potential Scenario
137
views
65
downloads
0
comments
2013-Michael-Evans-Growth and Decay
Sometimes, we can describe processes of growth and decay—whether physical, chemical, biological or sociological—by mathematical models.
exponential growth
exponential decay
isotopes
populations
resource depletion
Potential Scenario
158
views
49
downloads
0
comments
2009-Reid-King-Pendulum Motion and Differential Equations
This article presents a relatively simple, real-world example that instructors can use in the classroom to let students explore the effect of simplifying assumptions on a model’s ability to reflect real-world behavior.
pendulum
physical pendulum
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