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Physical Sciences and Mathematics Commons™
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Articles 1 - 4 of 4
Full-Text Articles in Physical Sciences and Mathematics
Linear Ode Systems Having A Fundamental Matrix Of The Form F(Mt), Kevin L. Shirley, Vicky W. Klima
Linear Ode Systems Having A Fundamental Matrix Of The Form F(Mt), Kevin L. Shirley, Vicky W. Klima
CODEE Journal
We interweave scaffolded problem statements with exposition and examples to support the reader as they explore specific linear systems of differential equations with variable coefficients, $\vec{x}'(t)=A(t)\vec{x}(t)$ and initial value $\vec{x}(0)$. We begin with a constant $n\times n$ matrix $M$ and a real or complex-valued function $f$, analytic at the eigenvalues of $M$ with $f(0) = 1$, and construct a linear system of differential equations with solutions $x(t)=f(Mt)\vec{x}(0)$, where $t$ is a parameter in some interval including zero. In general, the solutions to the resulting non-autonomous system are more difficult to analyze than solutions to the constant coefficient case. However, some …
Fibonacci Differential Equation And Associated Spiral Curves, Mehmet Pakdemirli
Fibonacci Differential Equation And Associated Spiral Curves, Mehmet Pakdemirli
CODEE Journal
The Fibonacci differential equation is defined with analogy from the Fibonacci difference equation. The linear second order differential equation is solved for suitable initial conditions. The solutions constitute spirals in the polar coordinates. The properties of the spirals with respect to the Fibonacci numbers and the differences between the new spirals and classical spirals are discussed.
Modeling Immune System Dynamics During Hiv Infection And Treatment With Differential Equations, Nicole Rychagov
Modeling Immune System Dynamics During Hiv Infection And Treatment With Differential Equations, Nicole Rychagov
CODEE Journal
An inquiry-based project that discusses immune system dynamics during HIV infection using differential equations is presented. The complex interactions between healthy T-cells, latently infected T-cells, actively infected T-cells, and the HIV virus are modeled using four nonlinear differential equations. The model is adapted to simulate long term HIV dynamics, including the AIDS state, and is used to simulate the long term effects of the traditional antiretroviral therapy (ART). The model is also used to test viral rebound over time of combined application of ART and a new drug that blocks the reactivation of the viral genome in the infected cells …
Introducing Systems Via Laplace Transforms, Ollie Nanyes
Introducing Systems Via Laplace Transforms, Ollie Nanyes
CODEE Journal
The purpose of this note is to show how to move from Laplace Transforms to a brief introduction to two dimensional systems of linear differential equations with only basic matrix algebra.