Differential Equations: New Applications
http://www.maplesoft.com/applications/category.aspx?cid=136
en-us2017 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemSun, 19 Nov 2017 05:01:05 GMTSun, 19 Nov 2017 05:01:05 GMTNew applications in the Differential Equations categoryhttp://www.mapleprimes.com/images/mapleapps.gifDifferential Equations: New Applications
http://www.maplesoft.com/applications/category.aspx?cid=136
Polarization 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="/view.aspx?si=154296/fieldplot.PNG" alt="Polarization of Dielectric Sphere ....." 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.154296Mon, 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
https://www.maplesoft.com/applications/view.aspx?SID=4971&ref=Feed
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="/view.aspx?si=4971/R-23EigenvalueProblemsforODEs.jpg" alt="Classroom Tips and Techniques: Eigenvalue Problems for ODEs" 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.4971Mon, 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.
<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.
<BR><BR>
Other chapters are in preparation and will be released in due course.<img src="/view.aspx?si=154267/molecule.PNG" alt="Mathematics for Chemistry" 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.
<BR><BR>
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.
<BR><BR>
Other chapters are in preparation and will be released in due course.154267Tue, 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="/view.aspx?si=154248/PN_Junction.png" alt="Physics of Silicon Based P-N Junction" 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.154248Thu, 25 May 2017 04:00:00 ZH. EL ACHOUBY, M. ZAIMI, A. IBRALH. EL ACHOUBY, M. ZAIMI, A. IBRALNew 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:
<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><img src="/applications/images/app_image_blank_lg.jpg" alt="New developments on exact solutions for PDEs with Boundary Conditions" 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>154169Fri, 30 Sep 2016 04:00:00 ZDr. Edgardo Cheb-TerrabDr. Edgardo Cheb-TerrabODEs, 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="/applications/images/app_image_blank_lg.jpg" alt="ODEs, PDEs and Special Functions" 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>.154164Fri, 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="/applications/images/app_image_blank_lg.jpg" alt="Factorizing with non-commutative variables" 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>.154166Fri, 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="/applications/images/app_image_blank_lg.jpg" alt="ODEs, PDE solutions: when are they "general"?" 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>.154165Fri, 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="/view.aspx?si=154142/waves.png" alt="El Niño Temperature Anomalies Modeled by a Delay Differential Equation" 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.154142Mon, 29 Aug 2016 04:00:00 ZDr. Frank WangDr. Frank WangInterpretación 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="/view.aspx?si=154110/232a3a3435a381a76ee84170be3fcee2.gif" alt="Interpretación geométrica del proceso de solución de una ecuación trigonométrica" 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.154110Tue, 24 May 2016 04:00:00 ZRanferi GutierrezRanferi GutierrezDifferential 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.
<BR><BR>
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="/view.aspx?si=154102/solver.PNG" alt="Differential Equation Solver" align="left"/>The application allows you to solve Ordinary Differential Equations. Enter an ODE, provide initial conditions and then click solve.
<BR><BR>
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.154102Tue, 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="/view.aspx?si=153954/Captura.PNG" alt="Campo de direcciones: Un caso de estudio." 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.153954Sat, 23 Jan 2016 05:00:00 ZDr. Ranferi GutierrezDr. Ranferi GutierrezDemo 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="/view.aspx?si=153939/dde.PNG" alt="Demo Worksheet for Numerical Delay Differential Equation Solution" 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>153939Wed, 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>
<P>
<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="/view.aspx?si=153878/sir_births_deaths.png" alt="The SIR model with births and deaths" 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>
<P>
<B>Also:</B> <A HREF="http://maplecloud.maplesoft.com/application.jsp?appId=6584880737550336">View and interact with this app in the MapleCloud!</A></P>153878Wed, 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>
<P>
<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="/view.aspx?si=153879/seirThumb.jpg" alt="The SEIR model with births and deaths" 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>
<P>
<B>Also:</B> <A HREF="http://maplecloud.maplesoft.com/application.jsp?appId=6407056173039616">View and interact with this app in the MapleCloud!</A></P>153879Wed, 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>
<P>
<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="/view.aspx?si=153877/sir_classic.png" alt="The Classic SIR Model" 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>
<P>
<B>Also:</B> <A HREF="http://maplecloud.maplesoft.com/application.jsp?appId=4837052487041024">View and interact with this app in the MapleCloud!</A></P>153877Wed, 16 Sep 2015 04:00:00 ZGünter EdenharterGünter EdenharterThe Comet 67P/Churyumov-Gerasimenko, Rosetta & Philae
https://www.maplesoft.com/applications/view.aspx?SID=153706&ref=Feed
<p> Abstract<br /><br />The Rosetta space probe launched 10 years ago by the European Space Agency (ESA) arrived recently (November 12, 2014) at the site of the comet known as 67P/Churyumov-Gerasimenco after a trip of 4 billions miles from Earth. After circling the comet, Rosetta released its precious load : the lander Philae packed with 21 different scientific instruments for the study of the comet with the main purpose : the origin of our solar system and possibly the origin of life on our planet.<br /><br />Our plan is rather a modest one since all we want is to get , by calculations, specific data concerning the comet and its lander.<br />We shall take a simplified model and consider the comet as a perfect solid sphere to which we can apply Newton's laws.<br /><br />We want to find:<br /><br />I- the acceleration on the comet surface ,<br />II- its radius,<br />III- its density,<br />IV- the velocity of Philae just after the 1st bounce off the comet (it has bounced twice),<br />V- the time for Philae to reach altitude of 1000 m above the comet .<br /><br />We shall compare our findings with the already known data to see how close our simplified mathematical model findings are to the duck-shaped comet already known results.<br />It turned out that our calculations for a sphere shaped comet are very close to the already known data.<br /><br />Conclusion<br /><br />Even with a shape that defies the application of any mechanical laws we can always get very close to reality by adopting a simplified mathematical model in any preliminary study of a complicated problem.<br /><br /></p><img src="/applications/images/app_image_blank_lg.jpg" alt="The Comet 67P/Churyumov-Gerasimenko, Rosetta & Philae" align="left"/><p> Abstract<br /><br />The Rosetta space probe launched 10 years ago by the European Space Agency (ESA) arrived recently (November 12, 2014) at the site of the comet known as 67P/Churyumov-Gerasimenco after a trip of 4 billions miles from Earth. After circling the comet, Rosetta released its precious load : the lander Philae packed with 21 different scientific instruments for the study of the comet with the main purpose : the origin of our solar system and possibly the origin of life on our planet.<br /><br />Our plan is rather a modest one since all we want is to get , by calculations, specific data concerning the comet and its lander.<br />We shall take a simplified model and consider the comet as a perfect solid sphere to which we can apply Newton's laws.<br /><br />We want to find:<br /><br />I- the acceleration on the comet surface ,<br />II- its radius,<br />III- its density,<br />IV- the velocity of Philae just after the 1st bounce off the comet (it has bounced twice),<br />V- the time for Philae to reach altitude of 1000 m above the comet .<br /><br />We shall compare our findings with the already known data to see how close our simplified mathematical model findings are to the duck-shaped comet already known results.<br />It turned out that our calculations for a sphere shaped comet are very close to the already known data.<br /><br />Conclusion<br /><br />Even with a shape that defies the application of any mechanical laws we can always get very close to reality by adopting a simplified mathematical model in any preliminary study of a complicated problem.<br /><br /></p>153706Mon, 17 Nov 2014 05:00:00 ZDr. Ahmed BaroudyDr. Ahmed BaroudyThe Mortgage Payment Problem: Approximating a Discrete Process with a Differential Equation
https://www.maplesoft.com/applications/view.aspx?SID=153511&ref=Feed
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="/view.aspx?si=153511/thumb.jpg" alt="The Mortgage Payment Problem: Approximating a Discrete Process with a Differential Equation" 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.153511Thu, 20 Feb 2014 05:00:00 ZProf. Michael MonaganProf. Michael MonaganThe House Warming Model
https://www.maplesoft.com/applications/view.aspx?SID=153491&ref=Feed
In this guest article in the Tips and Techniques series, Dr. Michael Monagan discusses a model of heat-flow in a house, and shows how he uses this model in his class.<img src="/view.aspx?si=153491/thumb.jpg" alt="The House Warming Model" align="left"/>In this guest article in the Tips and Techniques series, Dr. Michael Monagan discusses a model of heat-flow in a house, and shows how he uses this model in his class.153491Wed, 22 Jan 2014 05:00:00 ZProf. Michael MonaganProf. Michael MonaganClassroom Tips and Techniques: Slider-Control of Parameters in an ODE
https://www.maplesoft.com/applications/view.aspx?SID=152112&ref=Feed
Several ways to provide slider-control of parameters in a differential equation are considered. In particular, the cases of one and two parameters are illustrated, and for the case of two parameters, a 2-dimensional slider is constructed.<img src="/view.aspx?si=152112/thumb.jpg" alt="Classroom Tips and Techniques: Slider-Control of Parameters in an ODE" align="left"/>Several ways to provide slider-control of parameters in a differential equation are considered. In particular, the cases of one and two parameters are illustrated, and for the case of two parameters, a 2-dimensional slider is constructed.152112Mon, 23 Sep 2013 04:00:00 ZDr. Robert LopezDr. Robert Lopez