Differential Equations: New Applications
https://www.maplesoft.com/applications/category.aspx?cid=2883
en-us2019 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemSun, 17 Nov 2019 08:49:57 GMTSun, 17 Nov 2019 08:49:57 GMTNew applications in the Differential Equations categoryhttps://www.maplesoft.com/images/Application_center_hp.jpgDifferential Equations: New Applications
https://www.maplesoft.com/applications/category.aspx?cid=2883
Center manifolds for two-dimensional systems of differential equations
https://www.maplesoft.com/applications/view.aspx?SID=154568&ref=Feed
This worksheet implements a reduction principle. It allows us to compute a polynomial approximation of center manifold with a specified maximal degree of the polynomial.<img src="https://www.maplesoft.com/view.aspx?si=154568/center.png" alt="Center manifolds for two-dimensional systems of differential equations" style="max-width: 25%;" align="left"/>This worksheet implements a reduction principle. It allows us to compute a polynomial approximation of center manifold with a specified maximal degree of the polynomial.https://www.maplesoft.com/applications/view.aspx?SID=154568&ref=FeedSun, 29 Sep 2019 04:00:00 ZVeronika HajnováVeronika HajnováCenter manifolds for three-dimensional systems of differential equations
https://www.maplesoft.com/applications/view.aspx?SID=154575&ref=Feed
This worksheet implements a reduction principle. It allows us to compute a polynomial approximation of center manifold with a specified maximal degree of the polynomial.<img src="https://www.maplesoft.com/view.aspx?si=154575/center2.png" alt="Center manifolds for three-dimensional systems of differential equations" style="max-width: 25%;" align="left"/>This worksheet implements a reduction principle. It allows us to compute a polynomial approximation of center manifold with a specified maximal degree of the polynomial.https://www.maplesoft.com/applications/view.aspx?SID=154575&ref=FeedSun, 29 Sep 2019 04:00:00 ZVeronika HajnováVeronika HajnováBialternate matrix products and its application in bifurcation theory
https://www.maplesoft.com/applications/view.aspx?SID=154567&ref=Feed
The central theorems in bifurcation theory are normal form theorems. The structure of all the theorems is the same. It claims, under certain assumptions, an arbitrary system of differential, resp, difference, equations is locally topologically equivalent to the normal form. One type of assumption can be formulated as equalities. For generic one-parameter bifurcations, there is always only one equality assumption. It stands as a condition for eigenvalues of the Jacobi matrix of the system. Those assumptions, so-called test functions, are formulated in section Bifurcation of this sheet. Bialternate product is a matrix product, which allows expressing test functions for Hopf and Neimark-Sacker bifurcations detection and continuation.<img src="https://www.maplesoft.com/view.aspx?si=154567/bif.PNG" alt="Bialternate matrix products and its application in bifurcation theory" style="max-width: 25%;" align="left"/>The central theorems in bifurcation theory are normal form theorems. The structure of all the theorems is the same. It claims, under certain assumptions, an arbitrary system of differential, resp, difference, equations is locally topologically equivalent to the normal form. One type of assumption can be formulated as equalities. For generic one-parameter bifurcations, there is always only one equality assumption. It stands as a condition for eigenvalues of the Jacobi matrix of the system. Those assumptions, so-called test functions, are formulated in section Bifurcation of this sheet. Bialternate product is a matrix product, which allows expressing test functions for Hopf and Neimark-Sacker bifurcations detection and continuation.https://www.maplesoft.com/applications/view.aspx?SID=154567&ref=FeedSat, 28 Sep 2019 04:00:00 ZVeronika HajnováVeronika HajnováFree movement damped and not damped
https://www.maplesoft.com/applications/view.aspx?SID=154485&ref=Feed
With this app we solve problems of muffled and undamped movement. In the following steps:
- We select mass, rigidity and damping coefficient.
- We solve without initial conditions.
- We set the initial conditions with the buttons and sliders.
- We show the solution with its respective graph.
- We chose the time "t" to calculate: displacement, verlocity and acceleration.
- Click on the button evaluating and graphing. To show the respective graphs.
Creating for engineering students.
In Spanish.<img src="https://www.maplesoft.com/view.aspx?si=154485/masrest.png" alt="Free movement damped and not damped" style="max-width: 25%;" align="left"/>With this app we solve problems of muffled and undamped movement. In the following steps:
- We select mass, rigidity and damping coefficient.
- We solve without initial conditions.
- We set the initial conditions with the buttons and sliders.
- We show the solution with its respective graph.
- We chose the time "t" to calculate: displacement, verlocity and acceleration.
- Click on the button evaluating and graphing. To show the respective graphs.
Creating for engineering students.
In Spanish.https://www.maplesoft.com/applications/view.aspx?SID=154485&ref=FeedSat, 01 Sep 2018 04:00:00 ZLenin Araujo CastilloLenin Araujo CastilloSolving 2nd Order Differential Equations
https://www.maplesoft.com/applications/view.aspx?SID=154426&ref=Feed
This worksheet illustrates how to use Maple to solve examples of homogeneous and non-homogeneous second order differential equations, including several different methods for visualizing solutions.<img src="https://www.maplesoft.com/view.aspx?si=154426/2nd_order_des.PNG" alt="Solving 2nd Order Differential Equations" style="max-width: 25%;" align="left"/>This worksheet illustrates how to use Maple to solve examples of homogeneous and non-homogeneous second order differential equations, including several different methods for visualizing solutions.https://www.maplesoft.com/applications/view.aspx?SID=154426&ref=FeedMon, 26 Mar 2018 04:00:00 ZEmilee CarsonEmilee CarsonDE Phase Portraits - Animated Trajectories
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This worksheet shows an animation of a phase portrait with three different trajectories, as well as animating distance plots.<img src="https://www.maplesoft.com/view.aspx?si=154427/phase_portrait.PNG" alt="DE Phase Portraits - Animated Trajectories" style="max-width: 25%;" align="left"/>This worksheet shows an animation of a phase portrait with three different trajectories, as well as animating distance plots.https://www.maplesoft.com/applications/view.aspx?SID=154427&ref=FeedMon, 26 Mar 2018 04:00:00 ZEmilee CarsonEmilee CarsonSlow Manifold Analysis
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This worksheet goes through the slow manifold analysis following Hek's discussion of the predator prey system.<img src="https://www.maplesoft.com/view.aspx?si=154425/slow_manifold_analysis.PNG" alt="Slow Manifold Analysis" style="max-width: 25%;" align="left"/>This worksheet goes through the slow manifold analysis following Hek's discussion of the predator prey system.https://www.maplesoft.com/applications/view.aspx?SID=154425&ref=FeedFri, 23 Mar 2018 04:00:00 ZEmilee CarsonEmilee CarsonSolving ODEs using Maple: An Introduction
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In Maple it is easy to solve a differential equation. In this worksheet, we show the basic syntax. With this you should be able to use the same basic commands to solve many second-order DEs.<img src="https://www.maplesoft.com/view.aspx?si=154422/ode.PNG" alt="Solving ODEs using Maple: An Introduction" style="max-width: 25%;" align="left"/>In Maple it is easy to solve a differential equation. In this worksheet, we show the basic syntax. With this you should be able to use the same basic commands to solve many second-order DEs.https://www.maplesoft.com/applications/view.aspx?SID=154422&ref=FeedFri, 23 Mar 2018 04:00:00 ZDr. Francis PoulinDr. Francis PoulinImplementation of Maple apps for the creation of mathematical exercises in engineering
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In this research work has allowed to show the implementation of applications developed in the Maple software for the creation of mathematical exercises given the different levels of education whether basic or higher.
For the majority of teachers in this area, it seems very difficult to implement apps in Maple; that is why we show the creation of exercises easily and permanently. The purpose is to get teachers from our institutions to use applications ready to be evaluated in the classroom. The results of these apps (applications with components made in Maple) are supported on mobile devices such as tablets and / or laptops and taken to the cloud to be executed online from any computer. The generation of patterns is a very important alternative leaving aside random numbers, which would allow us to lose results
onscreen. With this; Our teachers in schools or universities would evaluate their students in parallel on the blackboard without losing the results of any student and thus achieve the competencies proposed in the learning sessions. In Spanish.<img src="https://www.maplesoft.com/view.aspx?si=154388/genexr.png" alt="Implementation of Maple apps for the creation of mathematical exercises in engineering" style="max-width: 25%;" align="left"/>In this research work has allowed to show the implementation of applications developed in the Maple software for the creation of mathematical exercises given the different levels of education whether basic or higher.
For the majority of teachers in this area, it seems very difficult to implement apps in Maple; that is why we show the creation of exercises easily and permanently. The purpose is to get teachers from our institutions to use applications ready to be evaluated in the classroom. The results of these apps (applications with components made in Maple) are supported on mobile devices such as tablets and / or laptops and taken to the cloud to be executed online from any computer. The generation of patterns is a very important alternative leaving aside random numbers, which would allow us to lose results
onscreen. With this; Our teachers in schools or universities would evaluate their students in parallel on the blackboard without losing the results of any student and thus achieve the competencies proposed in the learning sessions. In Spanish.https://www.maplesoft.com/applications/view.aspx?SID=154388&ref=FeedFri, 26 Jan 2018 05:00:00 ZProf. Lenin Araujo CastilloProf. Lenin Araujo CastilloMathematics for Chemistry
https://www.maplesoft.com/applications/view.aspx?SID=154267&ref=Feed
This interactive electronic textbook in the form of Maple worksheets comprises two parts.
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Part I, mathematics for chemistry, is supposed to cover all mathematics that an instructor of chemistry might hope and expect that his students would learn, understand and be able to apply as a result of sufficient courses typically, but not exclusively, presented in departments of mathematics. Its nine chapters include (0) a summary and illustration of useful Maple commands, (1) arithmetic, algebra and elementary functions, (2) plotting, descriptive geometry, trigonometry, series, complex functions, (3) differential calculus of one variable, (4) integral calculus of one variable, (5) multivariate calculus, (6) linear algebra including matrix, vector, eigenvector, vector calculus, tensor, spreadsheet, (7) differential and integral equations, and (8) probability, distribution, treatment of laboratory data, linear and non-linear regression and optimization.
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Part II presents mathematical topics typically taught within chemistry courses, including (9) chemical equilibrium, (10) group theory, (11) graph theory, (12a) introduction to quantum mechanics and quantum chemistry, (14) applications of Fourier transforms in chemistry including electron diffraction, x-ray diffraction, microwave spectra, infrared and Raman spectra and nuclear-magnetic-resonance spectra, and (18) dielectric and magnetic properties of chemical matter.
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Other chapters are in preparation and will be released in due course.
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Last updated on March 19, 2019<img src="https://www.maplesoft.com/view.aspx?si=154267/molecule.PNG" alt="Mathematics for Chemistry" style="max-width: 25%;" align="left"/>This interactive electronic textbook in the form of Maple worksheets comprises two parts.
<BR><BR>
Part I, mathematics for chemistry, is supposed to cover all mathematics that an instructor of chemistry might hope and expect that his students would learn, understand and be able to apply as a result of sufficient courses typically, but not exclusively, presented in departments of mathematics. Its nine chapters include (0) a summary and illustration of useful Maple commands, (1) arithmetic, algebra and elementary functions, (2) plotting, descriptive geometry, trigonometry, series, complex functions, (3) differential calculus of one variable, (4) integral calculus of one variable, (5) multivariate calculus, (6) linear algebra including matrix, vector, eigenvector, vector calculus, tensor, spreadsheet, (7) differential and integral equations, and (8) probability, distribution, treatment of laboratory data, linear and non-linear regression and optimization.
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Part II presents mathematical topics typically taught within chemistry courses, including (9) chemical equilibrium, (10) group theory, (11) graph theory, (12a) introduction to quantum mechanics and quantum chemistry, (14) applications of Fourier transforms in chemistry including electron diffraction, x-ray diffraction, microwave spectra, infrared and Raman spectra and nuclear-magnetic-resonance spectra, and (18) dielectric and magnetic properties of chemical matter.
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Other chapters are in preparation and will be released in due course.
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Last updated on March 19, 2019https://www.maplesoft.com/applications/view.aspx?SID=154267&ref=FeedTue, 30 May 2017 04:00:00 ZProf. John OgilvieProf. John OgilviePhysics of Silicon Based P-N Junction
https://www.maplesoft.com/applications/view.aspx?SID=154248&ref=Feed
In this worksheet, the physics of Silicon based P-N junction in thermal equilibrium is investigated. Special attention is devoted to the case where no bias voltage is applied to the junction. Poisson equation governing the electrostatic potential throughout the P-N junction is solved using two different approaches. According the first approach, the thin layer which extends on both sides of the junction is considered as depleted and Poisson equation is simplified and solved analytically. According to the second approach, a rigorous numerical resolution of Poisson equation is performed without resorting to any simplifying hypothesis. The worksheet presents a demonstration of Maple's capabilities in tackling the resolution of Poisson equation as a second order nonlinear nonhomogeneous ordinary differential equation and also in extracting, in addition to electrostatic potential, important physical quantities such as electrostatic field, negative and positive charge carriers densities, total charge as well as electric currents densities.<img src="https://www.maplesoft.com/view.aspx?si=154248/PN_Junction.png" alt="Physics of Silicon Based P-N Junction" style="max-width: 25%;" align="left"/>In this worksheet, the physics of Silicon based P-N junction in thermal equilibrium is investigated. Special attention is devoted to the case where no bias voltage is applied to the junction. Poisson equation governing the electrostatic potential throughout the P-N junction is solved using two different approaches. According the first approach, the thin layer which extends on both sides of the junction is considered as depleted and Poisson equation is simplified and solved analytically. According to the second approach, a rigorous numerical resolution of Poisson equation is performed without resorting to any simplifying hypothesis. The worksheet presents a demonstration of Maple's capabilities in tackling the resolution of Poisson equation as a second order nonlinear nonhomogeneous ordinary differential equation and also in extracting, in addition to electrostatic potential, important physical quantities such as electrostatic field, negative and positive charge carriers densities, total charge as well as electric currents densities.https://www.maplesoft.com/applications/view.aspx?SID=154248&ref=FeedThu, 25 May 2017 04:00:00 ZH. EL ACHOUBY, M. ZAIMI, A. IBRALH. EL ACHOUBY, M. ZAIMI, A. IBRALDifferential Equation Solver
https://www.maplesoft.com/applications/view.aspx?SID=154102&ref=Feed
The application allows you to solve Ordinary Differential Equations. Enter an ODE, provide initial conditions and then click solve.
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An online version of this <A HREF="http://maplecloud.maplesoft.com/application.jsp?appId=5691363796451328">Differential Equation Solver</A> is also available in the MapleCloud.<img src="https://www.maplesoft.com/view.aspx?si=154102/solver.PNG" alt="Differential Equation Solver" style="max-width: 25%;" align="left"/>The application allows you to solve Ordinary Differential Equations. Enter an ODE, provide initial conditions and then click solve.
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An online version of this <A HREF="http://maplecloud.maplesoft.com/application.jsp?appId=5691363796451328">Differential Equation Solver</A> is also available in the MapleCloud.https://www.maplesoft.com/applications/view.aspx?SID=154102&ref=FeedTue, 17 May 2016 04:00:00 ZMaplesoftMaplesoftOrdinary differential equation with Laplace Transform
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Here the development of an ordinary differential equation using Laplace transforms, using interactive components. This worksheet is shown for teaching purposes. You can download the file to be used in a class for engineering students. <br/><br/> In Spanish.<img src="https://www.maplesoft.com/view.aspx?si=154063/tl.png" alt="Ordinary differential equation with Laplace Transform" style="max-width: 25%;" align="left"/>Here the development of an ordinary differential equation using Laplace transforms, using interactive components. This worksheet is shown for teaching purposes. You can download the file to be used in a class for engineering students. <br/><br/> In Spanish.https://www.maplesoft.com/applications/view.aspx?SID=154063&ref=FeedSat, 19 Mar 2016 04:00:00 ZProf. Lenin Araujo CastilloProf. Lenin Araujo CastilloDemo Worksheet for Numerical Delay Differential Equation Solution
https://www.maplesoft.com/applications/view.aspx?SID=153939&ref=Feed
<P>This application shows several examples of modeling using delay differential equations in Maple. These examples are from the webinar <A HREF="http://www.maplesoft.com/products/maple/demo/player/2015/solvingdelaydiffeq.aspx">Solving Delay Differential Equations</A>.</P>
<P>Note: Requires Maple 2015.2 or later.</P><img src="https://www.maplesoft.com/view.aspx?si=153939/dde.PNG" alt="Demo Worksheet for Numerical Delay Differential Equation Solution" style="max-width: 25%;" align="left"/><P>This application shows several examples of modeling using delay differential equations in Maple. These examples are from the webinar <A HREF="http://www.maplesoft.com/products/maple/demo/player/2015/solvingdelaydiffeq.aspx">Solving Delay Differential Equations</A>.</P>
<P>Note: Requires Maple 2015.2 or later.</P>https://www.maplesoft.com/applications/view.aspx?SID=153939&ref=FeedWed, 16 Dec 2015 05:00:00 ZAllan WittkopfAllan WittkopfThe SIR model with births and deaths
https://www.maplesoft.com/applications/view.aspx?SID=153878&ref=Feed
<P>This interactive application explores a variation of the classic SIR model for the spread of disease. The classical SIR model assumes that a population can be divided into three distinct compartments: S is the proportion of susceptibles, I is the proportion of infected persons and R is the proportion of persons that have recovered from infection and are now immune against the disease. One extension to the classic SIR model is to add births and deaths to the model. Thus there is an inflow of new susceptibles and an outflow from all three compartments.</P>
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<B>Also:</B> <A HREF="http://maplecloud.maplesoft.com/application.jsp?appId=6584880737550336">View and interact with this app in the MapleCloud!</A></P><img src="https://www.maplesoft.com/view.aspx?si=153878/sir_births_deaths.png" alt="The SIR model with births and deaths" style="max-width: 25%;" align="left"/><P>This interactive application explores a variation of the classic SIR model for the spread of disease. The classical SIR model assumes that a population can be divided into three distinct compartments: S is the proportion of susceptibles, I is the proportion of infected persons and R is the proportion of persons that have recovered from infection and are now immune against the disease. One extension to the classic SIR model is to add births and deaths to the model. Thus there is an inflow of new susceptibles and an outflow from all three compartments.</P>
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<B>Also:</B> <A HREF="http://maplecloud.maplesoft.com/application.jsp?appId=6584880737550336">View and interact with this app in the MapleCloud!</A></P>https://www.maplesoft.com/applications/view.aspx?SID=153878&ref=FeedWed, 16 Sep 2015 04:00:00 ZGünter EdenharterGünter EdenharterThe SEIR model with births and deaths
https://www.maplesoft.com/applications/view.aspx?SID=153879&ref=Feed
<P>This interactive application explores the SEIR model for the spread of disease. The SEIR model is an extension of the classical SIR (Susceptibles, Infected, Recovered) model, where a fourth compartment is added that contains exposed persons which are infected but are not yet infectious. The SEIR (Susceptibles, Exposed, Infectious, Recovered) model as presented here covers also births and deaths.</P>
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<B>Also:</B> <A HREF="http://maplecloud.maplesoft.com/application.jsp?appId=6407056173039616">View and interact with this app in the MapleCloud!</A></P><img src="https://www.maplesoft.com/view.aspx?si=153879/seirThumb.jpg" alt="The SEIR model with births and deaths" style="max-width: 25%;" align="left"/><P>This interactive application explores the SEIR model for the spread of disease. The SEIR model is an extension of the classical SIR (Susceptibles, Infected, Recovered) model, where a fourth compartment is added that contains exposed persons which are infected but are not yet infectious. The SEIR (Susceptibles, Exposed, Infectious, Recovered) model as presented here covers also births and deaths.</P>
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<B>Also:</B> <A HREF="http://maplecloud.maplesoft.com/application.jsp?appId=6407056173039616">View and interact with this app in the MapleCloud!</A></P>https://www.maplesoft.com/applications/view.aspx?SID=153879&ref=FeedWed, 16 Sep 2015 04:00:00 ZGünter EdenharterGünter EdenharterThe Classic SIR Model
https://www.maplesoft.com/applications/view.aspx?SID=153877&ref=Feed
<P>This interactive application explores the classical SIR model for the spread of disease, which assumes that a population can be divided into three distinct compartments - S is the proportion of susceptibles, I is the proportion of infected persons and R is the proportion of persons that have recovered from infection and are now immune against the disease.</P>
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<B>Also:</B> <A HREF="http://maplecloud.maplesoft.com/application.jsp?appId=4837052487041024">View and interact with this app in the MapleCloud!</A></P><img src="https://www.maplesoft.com/view.aspx?si=153877/sir_classic.png" alt="The Classic SIR Model" style="max-width: 25%;" align="left"/><P>This interactive application explores the classical SIR model for the spread of disease, which assumes that a population can be divided into three distinct compartments - S is the proportion of susceptibles, I is the proportion of infected persons and R is the proportion of persons that have recovered from infection and are now immune against the disease.</P>
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<B>Also:</B> <A HREF="http://maplecloud.maplesoft.com/application.jsp?appId=4837052487041024">View and interact with this app in the MapleCloud!</A></P>https://www.maplesoft.com/applications/view.aspx?SID=153877&ref=FeedWed, 16 Sep 2015 04:00:00 ZGünter EdenharterGünter EdenharterThe Mortgage Payment Problem: Approximating a Discrete Process with a Differential Equation
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In this guest article in the Tips and Techniques series, Dr. Michael Monagan uses mortgage interest to test how well a differential equation models what is essentially a discrete process.<img src="https://www.maplesoft.com/view.aspx?si=153511/thumb.jpg" alt="The Mortgage Payment Problem: Approximating a Discrete Process with a Differential Equation" style="max-width: 25%;" align="left"/>In this guest article in the Tips and Techniques series, Dr. Michael Monagan uses mortgage interest to test how well a differential equation models what is essentially a discrete process.https://www.maplesoft.com/applications/view.aspx?SID=153511&ref=FeedThu, 20 Feb 2014 05:00:00 ZProf. Michael MonaganProf. Michael Monagan