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Downloads
Views
Date
Relevance
Technique Narrative
876
views
116
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
495
views
229
downloads
0
comments
1-002-IntegratingFactor-TechniqueNarrative
We develop a strategy to solve first order differential equations by transforming one side of the equation to the derivative of a product of two functions, thereby making it easy to antidifferentiate that side.
Integrating Factor
Technique Narrative
572
views
236
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
Technique Narrative
433
views
202
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
455
views
109
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
383
views
194
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
Technique Narrative
341
views
186
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
350
views
185
downloads
0
comments
1-003-IntroNumericalMethods-TechniqueNarrative
We develop elementary approaches to numerically solving first order differential equations with Euler's Method, Improved Euler's Method and develop these geometrically to compute numeric solutions and compare them to analytic solutions.
analytic solution
Euler's method
improved Euler's method
Technique Narrative
447
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
351
views
207
downloads
0
comments
1-009-Bifurcation-TechniqueNarrative
We lead students to investigate first-order differential equations that contain unknown parameters. Students discover what happens to the qualitative behavior of solutions to these equations as these parameters vary.
bifurcation
qualitative behavior
bifurcation diagram
Technique Narrative
165
views
284
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
Technique Narrative
234
views
244
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
742
views
214
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
830
views
214
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
200
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
498
views
580
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
512
views
312
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
Technique Narrative
370
views
197
downloads
0
comments
9-001-SkinBurnModelNumericalMethods-TechniqueNarrative
The heat equation is an important partial differential equation (PDE) which describes the distribution of heat in a given region over time. Numerical methods play an important role in solving these.
Maternal-Fetal interface
heat equation
Conservation of Energyt
heat flux
Euler's forward method
central difference
skin burn
hyperthermia
thermal conductivity
layers
Technique Narrative
202
views
341
downloads
0
comments
1-060-RegularPerturbation-TechniqueNarrative
This paper presents an introduction to a set of analytical approximations referred to as regular perturbation. This is a particular mathematical tool within the broader set of perturbation methods.
perturbation
regular perturbation
asymptotic expansions
analytical approximation
Bernoulli equation
Technique Narrative
463
views
492
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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