SIMIODE resources are here. Use the Browse menu to find Modeling Scenarios and Resources migrated from the old website.

Close

## Resources

##### Includes clear efforts on Issues
Technique Narrative
142

views

38

0

##### 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
150

views

25

0

##### 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
441

views

71

0

##### 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
140

views

108

0

##### 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
630

views

44

0

##### 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
165

views

37

0

##### 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
150

views

43

0

##### 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
123

views

35

0

##### 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
110

views

68

0

##### 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
126

views

28

0

##### 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
136

views

135

0

##### 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
Technique Narrative
149

views

94

0

##### 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
Technique Narrative
105

views

43

0

##### 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
118

views

54

0

##### 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
153

views

43