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Views
Date
Relevance
Technique Narrative
322
views
181
downloads
0
comments
1-030-RandomPerturbation-TechniqueNarrative
After a brief historical view of this problem, we will demonstrate the derivation of first order linear differential equations with random perturbations.
random perturbation
Brownian motion
Langevin equation
Riemann-Steiltjes integral
Wiener process
Ito's calculus
Technique Narrative
801
views
213
downloads
0
comments
5-010-MatrixExponential-TechniqueNarrative
The matrix exponential is a powerful computational and conceptual tool for analyzing systems of linear, constant coefficient, ordinary differential equations (ODE's). This narrative offers a quick introduction to the technique, with examples and...
matrix esponential
Putzer's Algorithm
diagonalization
eigenvalues
eigenvectors
Technique Narrative
408
views
199
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
Technique Narrative
433
views
101
downloads
0
comments
7-005-OverViewLaplaceTransforms-TechniqueNarrative
This is a specialized overview of Laplace Transform application to solving differential equations in Mathematica.
integration
Laplace transform
Inverse Laplace transofrm
integration by parts
Technique Narrative
542
views
215
downloads
0
comments
1-001-SepartionOfVariables-TechniqueNarrative
We discuss strategies to solve first order, ordinary differential equations with mathematical models when the variables may be separated.
solutions
strategy
method
applications
Modeling Scenario
1050
views
158
downloads
0
comments
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.
trajectory
launching radiant
projectile motion
projectile
no resistance
angle of launch
Technique Narrative
220
views
242
downloads
0
comments
1-015-DimensionlessVariables-TechniqueNarrative
This material introduces the idea of ``rescaling'' for ordinary differential equations (ODE's) by the use of dimensionless variables. In practice this is an extremely common and useful prelude to the analysis and solution of ODE's.
linearization
dimensional analysis
time scale
scaling
dimensionless variables
spatial scale
Technique Narrative
727
views
200
downloads
0
comments
7-006-LaplaceTransformBirth-TechniqueNarrative
We present a way of introducing the Laplace Transform as the continuous analogue of a power series expression of a function.
Transformations
power series
Technique Narrative
415
views
155
downloads
0
comments
5-012-LinearSystemConjecture-TechniqueNarrative
Students go from the solution for y'(t) = k*y(t) to a natural extension to the solution conjecture of a system of two constant coefficient, homogeneous, linear differential equations introducing eigenvalues and eigenvectors through student...
discovery learning
conjecture
solution
substitution
Technique Narrative
857
views
113
downloads
0
comments
3-090-ChebyshevPolynomialSolution-TechniqueNarrative
The Chebyshev equation is presented as a vehicle to view series solutions techniques for linear, second order homogeneous differential equations with non-constant coefficients.
series soluotion
polynomial solutions
Chebyshev polynomials
Chebyshev differential equations
Technique Narrative
391
views
193
downloads
0
comments
2-005-LinearizeItAll-TechniqueNarrative
Linear approximations are often used to simplify nonlinear ordinary differential equations (ODEs) for ease in analysis. The resulting linear approximation produces an ODE where closed form solutions may be obtained.
computation
error
Torricelli's Law
data fitting
linear approximation
Technique Narrative
494
views
308
downloads
0
comments
1-010-AtmosphericCO2Bifurcation-TechniqueNarrative
Students are introduced to the concept of a bifurcation in a first-order ordinary differential equation (ODE) through a modeling scenario involving atmospheric carbon dioxide whish is taken as a parameter and temperature is a function of time.
carbon dioxide
Surface Atmosphere Exchange
bifurcation
fold bifurcation
saddle node
Modeling Scenario
378
views
445
downloads
0
comments
6-068-VisualizingPredator-PreyCycles
In this modeling scenario, we propose a gentle introduction to limit cycles using nullcline analysis and a spreadsheet graphical approach via the fourth-order Runge-Kutta method. We will be offering three predator-prey models, each more complex...
nullclines
predator-prey
Geometry
predator
Runge-Kutta
prey
limit cycle
Technique Narrative
474
views
576
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
Technique Narrative
393
views
799
downloads
0
comments
8-002-TrigSumRepresentation-TechniqueNarrative
Students discover how to represent functions as sums of trigonometric functions and the value of such representations in many fields. This is an introduction to the study of Fourier Series.
estimation
Trigonometry
Trigonometric Functions
sum of square errors
finite sum
Fourier series
Fouriere sum
spectrum
approximatiopn
Modeling Scenario
187
views
350
downloads
0
comments
4-055-ShatterWineGlass-ModelingScenario
This module takes students through real life scenarios to examine resonance and its destructive power using differential equation models. What is resonance? How does it happen? Why is it important?
frequency
damping
amplitude
resonance
oscillation
shattering
wine glass
bridges
aircraft
external force
Article or Presentation
909
views
73
downloads
0
comments
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).
modeling
simulation
Software
python
systems
InsightMaker
flow
Category Theory
stock
stock-flow
Modeling Scenario
261
views
201
downloads
0
comments
1-035-DotseroVolcanoEruption-ModelingScenario
In this scenario, we use Carbon-14 dating of the Dotsero volcano in Colorado as a way of emphasizing this multistage process of modeling.
exponential decay
half-life
decay
Euler's method
carbon dating
decay rate
Carbon-14
Dotsero volcano
volcano
Technique Narrative
452
views
471
downloads
0
comments
1-005-NavigatingNumericalMethods-TechniqueNarrative
This technique narrative is a discovery-based approach to learning the basics of numerical methods for first order differential equations, by following the graphical and analytical perspectives of the forward Euler method and second order Taylor...
Euler's method
Taylor's Method
search and rescue
Coaast Guard
lost at sea
longitude
latitude
limit definition
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