Differential Equations: New Applications
https://www.maplesoft.com/applications/category.aspx?cid=136
en-us2019 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemThu, 14 Nov 2019 18:01:49 GMTThu, 14 Nov 2019 18:01:49 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=136
Bialternate matrix products and its application in bifurcation theory
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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 CastilloInterpretación geométrica del proceso de solución de una ecuación trigonométrica
https://www.maplesoft.com/applications/view.aspx?SID=154110&ref=Feed
Esta aplicación tiene como objetivo ayudar al estudiante a comprender el significado geométrico de resolver la ecuación trigonométrica sen(theta) = c en un intervalo de longitud 2Pi.
La barra deslizante de la aplicación permite variar el valor de c, mientras que los gráficos ayudan al estudiante a visualizar y comprender el proceso de búsqueda de soluciones de la ecuación trigonométrica de interés.<img src="https://www.maplesoft.com/view.aspx?si=154110/app.png" alt="Interpretación geométrica del proceso de solución de una ecuación trigonométrica" style="max-width: 25%;" align="left"/>Esta aplicación tiene como objetivo ayudar al estudiante a comprender el significado geométrico de resolver la ecuación trigonométrica sen(theta) = c en un intervalo de longitud 2Pi.
La barra deslizante de la aplicación permite variar el valor de c, mientras que los gráficos ayudan al estudiante a visualizar y comprender el proceso de búsqueda de soluciones de la ecuación trigonométrica de interés.https://www.maplesoft.com/applications/view.aspx?SID=154110&ref=FeedWed, 06 Jun 2018 04:00:00 ZRanferi GutierrezRanferi GutierrezRomeo y Julieta: Un clasico de las historias de amor... y de las ecuaciones diferenciales.
https://www.maplesoft.com/applications/view.aspx?SID=154451&ref=Feed
En esta hoja Maple se introduce a los estudiantes en el tema de los sistemas de ecuaciones diferenciales lineales, mediante un problema que es de mucho interés para ellos: el amor.
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Utilizando las capacidades de Maple para construir con facilidad los diagramas de espacio fase y mediante las adecuadas preguntas, es posible ayudar a los estudiantes para que comprendan la forma en como pueden interpretar la información gráfica que proporcionan los diagramas de espacio fase acerca de las soluciones de un sistema de ecuaciones diferenciales.
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En la hoja se proporcionan algunos ejemplos de preguntas que pueden plantearse a los estudiantes. La hoja puede ser modificada fácilmete para que pueda adaptarse a las necesidades de cada profesor.<img src="https://www.maplesoft.com/view.aspx?si=154451/5025e068f21b86e51bf86a5ad50e4e6b.gif" alt="Romeo y Julieta: Un clasico de las historias de amor... y de las ecuaciones diferenciales." style="max-width: 25%;" align="left"/>En esta hoja Maple se introduce a los estudiantes en el tema de los sistemas de ecuaciones diferenciales lineales, mediante un problema que es de mucho interés para ellos: el amor.
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Utilizando las capacidades de Maple para construir con facilidad los diagramas de espacio fase y mediante las adecuadas preguntas, es posible ayudar a los estudiantes para que comprendan la forma en como pueden interpretar la información gráfica que proporcionan los diagramas de espacio fase acerca de las soluciones de un sistema de ecuaciones diferenciales.
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En la hoja se proporcionan algunos ejemplos de preguntas que pueden plantearse a los estudiantes. La hoja puede ser modificada fácilmete para que pueda adaptarse a las necesidades de cada profesor.https://www.maplesoft.com/applications/view.aspx?SID=154451&ref=FeedWed, 23 May 2018 04:00:00 ZRanferi GutierrezRanferi GutierrezSolving 2nd Order Differential Equations
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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 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 PoulinSlow 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 CarsonImplementation 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 CastilloPolarization of Dielectric Sphere .....
https://www.maplesoft.com/applications/view.aspx?SID=154296&ref=Feed
In this worksheet, we investigate the polarization of a dielectric sphere (dot) with a relative permittivitty "epsilon[Dot]" embedded in a dielectric matrix with a relative permittivitty "epsilon[Matrix]" and submitted to an uniform electrostatic field F oriented in z-axis direction. It's a fondamental and popular problem present in most of electromagnetism textbooks. First of all, we express Poisson equation in appropriate coordinates system:
"Delta V(r,theta,phi) = 0". We proceed to a full separation of variables and derive general expression of scalar electrostatic potential V(r,theta,phi). Then we particularize to a dielectric sphere surrounded by a dielectric matrix and give expressions of electrostatic potential V(r,theta) in the meridian plane (x0z) inside and outside the sphere by taking into account:
i) invariance property of the system under rotation around z-axis,
ii) choice of the plane z=0 as a reference of scalar electrostatic potential,
iii) regularity of V(r,theta) at the origine and very far from the sphere,
iv) continuity condition of scalar electrostatic potential V(r,theta) at the sphere surface,
v) continuity condition of normal components of electric displacement field D at the sphere surface.
The obtained expressions of V(r,theta) inside and outside the sphere allows as to derive expressions of electrostatic field F, electric displacement field D and polarization field P inside and outside dielectric dot in spherical coordinates as well as in cartesian rectangular coordinates. The paper is a proof of Maple algebraic and graphical capabilities in tackling the resolution of Poisson equation as a second order partial differential equation and also in displaying scalar electrostatic potential contourplot, electrostatic field lines as well as fieldplots of F, D and P inside and outside dielectric sphere.<img src="https://www.maplesoft.com/view.aspx?si=154296/fieldplot.PNG" alt="Polarization of Dielectric Sphere ....." style="max-width: 25%;" align="left"/>In this worksheet, we investigate the polarization of a dielectric sphere (dot) with a relative permittivitty "epsilon[Dot]" embedded in a dielectric matrix with a relative permittivitty "epsilon[Matrix]" and submitted to an uniform electrostatic field F oriented in z-axis direction. It's a fondamental and popular problem present in most of electromagnetism textbooks. First of all, we express Poisson equation in appropriate coordinates system:
"Delta V(r,theta,phi) = 0". We proceed to a full separation of variables and derive general expression of scalar electrostatic potential V(r,theta,phi). Then we particularize to a dielectric sphere surrounded by a dielectric matrix and give expressions of electrostatic potential V(r,theta) in the meridian plane (x0z) inside and outside the sphere by taking into account:
i) invariance property of the system under rotation around z-axis,
ii) choice of the plane z=0 as a reference of scalar electrostatic potential,
iii) regularity of V(r,theta) at the origine and very far from the sphere,
iv) continuity condition of scalar electrostatic potential V(r,theta) at the sphere surface,
v) continuity condition of normal components of electric displacement field D at the sphere surface.
The obtained expressions of V(r,theta) inside and outside the sphere allows as to derive expressions of electrostatic field F, electric displacement field D and polarization field P inside and outside dielectric dot in spherical coordinates as well as in cartesian rectangular coordinates. The paper is a proof of Maple algebraic and graphical capabilities in tackling the resolution of Poisson equation as a second order partial differential equation and also in displaying scalar electrostatic potential contourplot, electrostatic field lines as well as fieldplots of F, D and P inside and outside dielectric sphere.https://www.maplesoft.com/applications/view.aspx?SID=154296&ref=FeedMon, 18 Sep 2017 04:00:00 ZE. H. EL HAROUNY, A. IBRAL, S. NAKRA MOHAJER and J. EL KHAMKHAMIE. H. EL HAROUNY, A. IBRAL, S. NAKRA MOHAJER and J. EL KHAMKHAMIClassroom Tips and Techniques: Eigenvalue Problems for ODEs
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Some boundary value problems for partial differential equations are amenable to analytic techniques. For example, the constant-coefficient, second-order linear equations called the heat, wave, and potential equations are solved with some type of Fourier series representation obtained from the Sturm-Liouville eigenvalue problem that arises upon separating variables. The role of Maple in the solution of such boundary value problems is examined. Efficient techniques for separating variables, and a way to guide Maple through the solution of the resulting Sturm-Liouville eigenvalue problems are shown.<img src="https://www.maplesoft.com/view.aspx?si=4971/R-23EigenvalueProblemsforODEs.jpg" alt="Classroom Tips and Techniques: Eigenvalue Problems for ODEs" style="max-width: 25%;" align="left"/>Some boundary value problems for partial differential equations are amenable to analytic techniques. For example, the constant-coefficient, second-order linear equations called the heat, wave, and potential equations are solved with some type of Fourier series representation obtained from the Sturm-Liouville eigenvalue problem that arises upon separating variables. The role of Maple in the solution of such boundary value problems is examined. Efficient techniques for separating variables, and a way to guide Maple through the solution of the resulting Sturm-Liouville eigenvalue problems are shown.https://www.maplesoft.com/applications/view.aspx?SID=4971&ref=FeedMon, 14 Aug 2017 04:00:00 ZDr. Robert LopezDr. Robert LopezMathematics 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
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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. IBRALODEs, PDEs and Special Functions
https://www.maplesoft.com/applications/view.aspx?SID=154164&ref=Feed
This presentation illustrates the Maple capabilities for studying and solving ODEs and PDEs, implemented within the <A HREF="/support/help/Maple/view.aspx?path=DEtools">DEtools</A> and <A HREF="/support/help/Maple/view.aspx?path=PDEtools">PDEtools</A> packages, as well as getting information about and working with Special functions of the mathematical language, implemented within the <A HREF="/support/help/Maple/view.aspx?path=FunctionAdvisor">FunctionAdvisor</A>, the conversion network for mathematical functions and the <A HREF="/support/help/Maple/view.aspx?path=MathematicalFunctions">MathematicalFunctions</A> package.<BR><BR>
This application is also the subject of a <A HREF="http://www.mapleprimes.com/posts/149877-ODEs-PDEs-And-Special-Functions">blog post on MaplePrimes</A>.<img src="https://www.maplesoft.com/applications/images/app_image_blank_lg.jpg" alt="ODEs, PDEs and Special Functions" style="max-width: 25%;" align="left"/>This presentation illustrates the Maple capabilities for studying and solving ODEs and PDEs, implemented within the <A HREF="/support/help/Maple/view.aspx?path=DEtools">DEtools</A> and <A HREF="/support/help/Maple/view.aspx?path=PDEtools">PDEtools</A> packages, as well as getting information about and working with Special functions of the mathematical language, implemented within the <A HREF="/support/help/Maple/view.aspx?path=FunctionAdvisor">FunctionAdvisor</A>, the conversion network for mathematical functions and the <A HREF="/support/help/Maple/view.aspx?path=MathematicalFunctions">MathematicalFunctions</A> package.<BR><BR>
This application is also the subject of a <A HREF="http://www.mapleprimes.com/posts/149877-ODEs-PDEs-And-Special-Functions">blog post on MaplePrimes</A>.https://www.maplesoft.com/applications/view.aspx?SID=154164&ref=FeedFri, 30 Sep 2016 04:00:00 ZDr. Edgardo Cheb-TerrabDr. Edgardo Cheb-TerrabNew developments on exact solutions for PDEs with Boundary Conditions
https://www.maplesoft.com/applications/view.aspx?SID=154169&ref=Feed
A collection of two presentations that discuss and illustrate newly implemented methods for computing exact solutions to Partial Differential Equations subject to Boundary conditions.<BR><BR>
These applications are also discussed in two MaplePrimes blog posts:
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<LI><A HREF="http://www.mapleprimes.com/posts/204436-New-Developments-On-Exact-Solutions">New developments on exact solutions for PDEs with Boundary Conditions</A>
<LI><A HREF="http://www.mapleprimes.com/posts/201226-PDEs-And-Boundary-Conditions--New-Developments">PDEs and Boundary Conditions - new developments</A>
</UL><img src="https://www.maplesoft.com/applications/images/app_image_blank_lg.jpg" alt="New developments on exact solutions for PDEs with Boundary Conditions" style="max-width: 25%;" align="left"/>A collection of two presentations that discuss and illustrate newly implemented methods for computing exact solutions to Partial Differential Equations subject to Boundary conditions.<BR><BR>
These applications are also discussed in two MaplePrimes blog posts:
<UL>
<LI><A HREF="http://www.mapleprimes.com/posts/204436-New-Developments-On-Exact-Solutions">New developments on exact solutions for PDEs with Boundary Conditions</A>
<LI><A HREF="http://www.mapleprimes.com/posts/201226-PDEs-And-Boundary-Conditions--New-Developments">PDEs and Boundary Conditions - new developments</A>
</UL>https://www.maplesoft.com/applications/view.aspx?SID=154169&ref=FeedFri, 30 Sep 2016 04:00:00 ZDr. Edgardo Cheb-TerrabDr. Edgardo Cheb-TerrabODEs, PDE solutions: when are they "general"?
https://www.maplesoft.com/applications/view.aspx?SID=154165&ref=Feed
This presentation discusses the concept of “general solution” of a Partial Differential Equation, or a system of them, possibly including ODEs and/or algebraic equations, and shows how to tell whether a solution returned by Maple’s <A HREF="/support/help/Maple/view.aspx?path=pdsolve">pdsolve</A> is or not a general (as opposed to particular) solution.<BR><BR>
This application is also the subject of a <A HREF="http://www.mapleprimes.com/posts/204437-PDE-Solutions-When-Are-They-general">blog post on MaplePrimes</A>.<img src="https://www.maplesoft.com/applications/images/app_image_blank_lg.jpg" alt="ODEs, PDE solutions: when are they "general"?" style="max-width: 25%;" align="left"/>This presentation discusses the concept of “general solution” of a Partial Differential Equation, or a system of them, possibly including ODEs and/or algebraic equations, and shows how to tell whether a solution returned by Maple’s <A HREF="/support/help/Maple/view.aspx?path=pdsolve">pdsolve</A> is or not a general (as opposed to particular) solution.<BR><BR>
This application is also the subject of a <A HREF="http://www.mapleprimes.com/posts/204437-PDE-Solutions-When-Are-They-general">blog post on MaplePrimes</A>.https://www.maplesoft.com/applications/view.aspx?SID=154165&ref=FeedFri, 30 Sep 2016 04:00:00 ZDr. Edgardo Cheb-TerrabDr. Edgardo Cheb-TerrabFactorizing with non-commutative variables
https://www.maplesoft.com/applications/view.aspx?SID=154166&ref=Feed
New capabilities for factorizing expressions involving noncommutative variables are presented and illustrated with a set of examples.<BR><BR>
This application is also the subject of a <A HREF="http://www.mapleprimes.com/posts/201368-New-Factorizing-With-Noncommutative-Variables">blog post on MaplePrimes</A>.<img src="https://www.maplesoft.com/applications/images/app_image_blank_lg.jpg" alt="Factorizing with non-commutative variables" style="max-width: 25%;" align="left"/>New capabilities for factorizing expressions involving noncommutative variables are presented and illustrated with a set of examples.<BR><BR>
This application is also the subject of a <A HREF="http://www.mapleprimes.com/posts/201368-New-Factorizing-With-Noncommutative-Variables">blog post on MaplePrimes</A>.https://www.maplesoft.com/applications/view.aspx?SID=154166&ref=FeedFri, 30 Sep 2016 04:00:00 ZDr. Edgardo Cheb-TerrabDr. Edgardo Cheb-TerrabEl Niño Temperature Anomalies Modeled by a Delay Differential Equation
https://www.maplesoft.com/applications/view.aspx?SID=154142&ref=Feed
Delay differential equations are differential equations in which the derivative of the unknown function at a certain time depends on past values of the function and/or its derivatives. Max J. Suarez and Paul S. Schopf used such an equation to model the El Niño phenomenon. This worksheet demonstrate how Maple's dsolve command can be used to solve a delay differential equation numerically.<img src="https://www.maplesoft.com/view.aspx?si=154142/waves.png" alt="El Niño Temperature Anomalies Modeled by a Delay Differential Equation" style="max-width: 25%;" align="left"/>Delay differential equations are differential equations in which the derivative of the unknown function at a certain time depends on past values of the function and/or its derivatives. Max J. Suarez and Paul S. Schopf used such an equation to model the El Niño phenomenon. This worksheet demonstrate how Maple's dsolve command can be used to solve a delay differential equation numerically.https://www.maplesoft.com/applications/view.aspx?SID=154142&ref=FeedMon, 29 Aug 2016 04:00:00 ZDr. Frank WangDr. Frank WangDifferential 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 ZMaplesoftMaplesoftCampo de direcciones: Un caso de estudio.
https://www.maplesoft.com/applications/view.aspx?SID=153954&ref=Feed
En esta hoja se aplica el campo de direcciones al estudio cualitativo de las soluciones de una ecuación diferencial que describe, utilizando un modelo sencillo, el fenómeno de la pesca.
En el modelo se asume que puede exitir sobrepoblación y/o captura, lo que da oportunidad al estudiante de lograr una mayor comprensión del fenómeno, así como de aprender cómo extraer información cualitativa de los campos de direcciones.<img src="https://www.maplesoft.com/view.aspx?si=153954/Captura.PNG" alt="Campo de direcciones: Un caso de estudio." style="max-width: 25%;" align="left"/>En esta hoja se aplica el campo de direcciones al estudio cualitativo de las soluciones de una ecuación diferencial que describe, utilizando un modelo sencillo, el fenómeno de la pesca.
En el modelo se asume que puede exitir sobrepoblación y/o captura, lo que da oportunidad al estudiante de lograr una mayor comprensión del fenómeno, así como de aprender cómo extraer información cualitativa de los campos de direcciones.https://www.maplesoft.com/applications/view.aspx?SID=153954&ref=FeedSat, 23 Jan 2016 05:00:00 ZDr. Ranferi GutierrezDr. Ranferi Gutierrez