Calculus III: New Applications
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en-us2021 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemTue, 19 Oct 2021 23:52:05 GMTTue, 19 Oct 2021 23:52:05 GMTNew applications in the Calculus III categoryhttps://www.maplesoft.com/images/Application_center_hp.jpgCalculus III: New Applications
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Mathematics for Chemistry
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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,b,c) introduction to quantum mechanics and quantum chemistry, (13) optical molecular spectrometry, (14) applications of Fourier transforms in chemistry including electron diffraction, x-ray diffraction, microwave spectra, infrared and Raman spectra and nuclear-magnetic-resonance spectra, (15) advanced chemical kinetics, and (16) dielectric and magnetic properties of chemical matter.
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Also included in this collection are an essay on Teaching Mathematics to Chemistry Students with Symbolic Computation and a periodic chart of the chemical elements incorporating various
data on elemental properties.
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Edition 6.
Last updated Aug. 15, 2021.<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,b,c) introduction to quantum mechanics and quantum chemistry, (13) optical molecular spectrometry, (14) applications of Fourier transforms in chemistry including electron diffraction, x-ray diffraction, microwave spectra, infrared and Raman spectra and nuclear-magnetic-resonance spectra, (15) advanced chemical kinetics, and (16) dielectric and magnetic properties of chemical matter.
<br><br>
Also included in this collection are an essay on Teaching Mathematics to Chemistry Students with Symbolic Computation and a periodic chart of the chemical elements incorporating various
data on elemental properties.
<br><br>
Edition 6.
Last updated Aug. 15, 2021.https://www.maplesoft.com/applications/view.aspx?SID=154267&ref=FeedThu, 19 Aug 2021 14:22:04 ZJohn OgilvieJohn OgilvieFirst equilibrium condition
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With this application our students of science and engineering in the areas of physics will check the first condition of balance using Maple technology. Only with entering mass and angles we obtain graphs and data for a better interpretation.<img src="https://www.maplesoft.com/view.aspx?si=154624/first_eq.png" alt="First equilibrium condition" style="max-width: 25%;" align="left"/>With this application our students of science and engineering in the areas of physics will check the first condition of balance using Maple technology. Only with entering mass and angles we obtain graphs and data for a better interpretation.https://www.maplesoft.com/applications/view.aspx?SID=154624&ref=FeedWed, 01 Apr 2020 04:00:00 ZLenin Araujo CastilloLenin Araujo CastilloPole simulation with tensions
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Application developed using Maple and MapleSim. You can observe the vector analysis using Maple and the simulation using MapleSim. Also included a video of the result. It is a simple structure. A pole fastened by two cables and a force applied to the top. The results are to calculate tensions one and two. Consider the mass of each rope. In Spanish.<img src="https://www.maplesoft.com/view.aspx?si=154577/structure.png" alt="Pole simulation with tensions" style="max-width: 25%;" align="left"/>Application developed using Maple and MapleSim. You can observe the vector analysis using Maple and the simulation using MapleSim. Also included a video of the result. It is a simple structure. A pole fastened by two cables and a force applied to the top. The results are to calculate tensions one and two. Consider the mass of each rope. In Spanish.https://www.maplesoft.com/applications/view.aspx?SID=154577&ref=FeedMon, 14 Oct 2019 04:00:00 ZProf. Lenin Araujo CastilloProf. Lenin Araujo CastilloPlot of curvature and radius of curvature
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This app is basically made for engineering students. Calculate the curvature and radius of curvature of two trajectories given its vector position for times greater than zero seconds. You will observe the graphs Curvature vs time and also radius of curvature vs time and finally the graphs of the two trajectories. A student of civil engineering can use this app without problem to compare if the two highways are parallel and optimal for its construction. Each graph with its corresponding data table and its respective equation. In spanish.<img src="https://www.maplesoft.com/view.aspx?si=154486/radcurv.png" alt="Plot of curvature and radius of curvature" style="max-width: 25%;" align="left"/>This app is basically made for engineering students. Calculate the curvature and radius of curvature of two trajectories given its vector position for times greater than zero seconds. You will observe the graphs Curvature vs time and also radius of curvature vs time and finally the graphs of the two trajectories. A student of civil engineering can use this app without problem to compare if the two highways are parallel and optimal for its construction. Each graph with its corresponding data table and its respective equation. In spanish.https://www.maplesoft.com/applications/view.aspx?SID=154486&ref=FeedMon, 03 Sep 2018 04:00:00 ZLenin Araujo CastilloLenin Araujo CastilloSolving 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 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 PoulinGenerator of exercises with vectors
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Application created for teachers. This works to evaluate the students on the blackboard simultaneously on the topics of vector sum, direction, unit vector and projections. Perform the generation of exercises through patterns so that teachers can rescue their answers. Created professors of universities and engineering students. In Spanish.<img src="https://www.maplesoft.com/view.aspx?si=154371/appteach.png" alt="Generator of exercises with vectors" style="max-width: 25%;" align="left"/>Application created for teachers. This works to evaluate the students on the blackboard simultaneously on the topics of vector sum, direction, unit vector and projections. Perform the generation of exercises through patterns so that teachers can rescue their answers. Created professors of universities and engineering students. In Spanish.https://www.maplesoft.com/applications/view.aspx?SID=154371&ref=FeedSun, 03 Dec 2017 05:00:00 ZProf. Lenin Araujo CastilloProf. Lenin Araujo CastilloKinematics Curvilinear
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With this application you can calculate the components of the acceleration. The scalar and vector components of the tangent and the normal. In addition to curvilinear kinetics in polar coordinates. It can be used in different engineers, especially mechanical, civil and more.
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In Spanish.<img src="https://www.maplesoft.com/view.aspx?si=154269/kc.png" alt="Kinematics Curvilinear" style="max-width: 25%;" align="left"/>With this application you can calculate the components of the acceleration. The scalar and vector components of the tangent and the normal. In addition to curvilinear kinetics in polar coordinates. It can be used in different engineers, especially mechanical, civil and more.
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In Spanish.https://www.maplesoft.com/applications/view.aspx?SID=154269&ref=FeedTue, 14 Nov 2017 05:00:00 ZProf. Lenin Araujo CastilloProf. Lenin Araujo CastilloPlot of equation impulse-momentum
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In this application you can visualize the impulse generated by a constant and variable force for the interaction of a particle with an object in a state of rest or movement. It is also the calculation of the momentum-momentum equation by entering the mass of the particle to solve initial and final velocities respectively according to the case study. Engineering students can quickly display the calculations and then their interpretation.<img src="https://www.maplesoft.com/view.aspx?si=154347/mivis.png" alt="Plot of equation impulse-momentum" style="max-width: 25%;" align="left"/>In this application you can visualize the impulse generated by a constant and variable force for the interaction of a particle with an object in a state of rest or movement. It is also the calculation of the momentum-momentum equation by entering the mass of the particle to solve initial and final velocities respectively according to the case study. Engineering students can quickly display the calculations and then their interpretation.https://www.maplesoft.com/applications/view.aspx?SID=154347&ref=FeedTue, 17 Oct 2017 04:00:00 ZProf. Lenin Araujo CastilloProf. Lenin Araujo CastilloMoment of a force using vectors
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The development of the calculation of moments using force vectors is clearly observed by taking a point and also a line. Different exercises are solved with the help of Maple syntax. We can also visualize the vector behavior in the different configurations of the position vector. Applications designed exclusively for engineering students. In Spanish.<img src="https://www.maplesoft.com/view.aspx?si=154345/moment of force.PNG" alt="Moment of a force using vectors" style="max-width: 25%;" align="left"/>The development of the calculation of moments using force vectors is clearly observed by taking a point and also a line. Different exercises are solved with the help of Maple syntax. We can also visualize the vector behavior in the different configurations of the position vector. Applications designed exclusively for engineering students. In Spanish.https://www.maplesoft.com/applications/view.aspx?SID=154345&ref=FeedTue, 26 Sep 2017 04:00:00 ZProf. Lenin Araujo CastilloProf. Lenin Araujo CastilloVector space with projections and forces
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With this application you will learn the beginning of the study of the vectors. Graphing it in a vector space from the plane to the space. You can calculate its fundamental characteristics as triangle laws, projections and strength. App made entirely in Maple for engineering students so they can develop their exercises and save time. It is recommended to first use the native syntax then the embedded components. In Spanish.<img src="https://www.maplesoft.com/view.aspx?si=154294/vectors.PNG" alt="Vector space with projections and forces" style="max-width: 25%;" align="left"/>With this application you will learn the beginning of the study of the vectors. Graphing it in a vector space from the plane to the space. You can calculate its fundamental characteristics as triangle laws, projections and strength. App made entirely in Maple for engineering students so they can develop their exercises and save time. It is recommended to first use the native syntax then the embedded components. In Spanish.https://www.maplesoft.com/applications/view.aspx?SID=154294&ref=FeedMon, 11 Sep 2017 04:00:00 ZProf. Lenin Araujo CastilloProf. Lenin Araujo CastilloDisplacement and distance traveled with vectors
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In this app you can use from the creation of curve, birth of the position vector and finally applied to the displacement and the distance traveled. All this application revolves around the creation of a path and the path of a particle over this generated by vectors. You will only have to insert the vector components and the times to evaluate. Designed for engineering students guided through Maple. In Spanish.<img src="https://www.maplesoft.com/view.aspx?si=154293/desplvp.png" alt="Displacement and distance traveled with vectors" style="max-width: 25%;" align="left"/>In this app you can use from the creation of curve, birth of the position vector and finally applied to the displacement and the distance traveled. All this application revolves around the creation of a path and the path of a particle over this generated by vectors. You will only have to insert the vector components and the times to evaluate. Designed for engineering students guided through Maple. In Spanish.https://www.maplesoft.com/applications/view.aspx?SID=154293&ref=FeedMon, 28 Aug 2017 04:00:00 ZProf. Lenin Araujo CastilloProf. Lenin Araujo CastilloPlot of Position Vector
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This app performs the trace of a given path r(t), then locates the position vector in a specific time. It also graphs the velocity vector, acceleration, tangential and normal unit vectors, along with the binormal. The numerical value of velocity, acceleration and curvature are also observed for a better analysis of the movement of particles in a curvilinear trajectory. Developed for our engineering students. In Spanish.<img src="https://www.maplesoft.com/view.aspx?si=154290/bnrvp.png" alt="Plot of Position Vector" style="max-width: 25%;" align="left"/>This app performs the trace of a given path r(t), then locates the position vector in a specific time. It also graphs the velocity vector, acceleration, tangential and normal unit vectors, along with the binormal. The numerical value of velocity, acceleration and curvature are also observed for a better analysis of the movement of particles in a curvilinear trajectory. Developed for our engineering students. In Spanish.https://www.maplesoft.com/applications/view.aspx?SID=154290&ref=FeedThu, 10 Aug 2017 04:00:00 ZProf. Lenin Araujo CastilloProf. Lenin Araujo CastilloKinematics using syntax
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In this file you will be able to observe and analyze how the exercises and problems of Kinematics and Dynamics are solved using the commands and operators through a very well-structured syntax. Allowing me to save time and use it in interpretation. I hope you can share and spread to break the traditional and unnecessary myths. Only for Engineering and Science. Share if you like.
In Spanish.<img src="https://www.maplesoft.com/view.aspx?si=154271/kinematicssint.png" alt="Kinematics using syntax" style="max-width: 25%;" align="left"/>In this file you will be able to observe and analyze how the exercises and problems of Kinematics and Dynamics are solved using the commands and operators through a very well-structured syntax. Allowing me to save time and use it in interpretation. I hope you can share and spread to break the traditional and unnecessary myths. Only for Engineering and Science. Share if you like.
In Spanish.https://www.maplesoft.com/applications/view.aspx?SID=154271&ref=FeedWed, 14 Jun 2017 04:00:00 ZProf. Lenin Araujo CastilloProf. Lenin Araujo CastilloClassroom Tips and Techniques: Roles for the Laplace Transform's Shifting Laws
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The shifting laws for the Laplace transform are examined, and the argument is made that the transform of f(t) Heaviside(t - a) should be done with the third shifting law, reserving the second shifting law strictly for inverting functions of the form e^(-a s) F(s). It is needlessly complicated to apply the second shifting law to functions of the form f(t) Heaviside(t - a)<img src="https://www.maplesoft.com/view.aspx?si=1723/laplace.PNG" alt="Classroom Tips and Techniques: Roles for the Laplace Transform's Shifting Laws" style="max-width: 25%;" align="left"/>The shifting laws for the Laplace transform are examined, and the argument is made that the transform of f(t) Heaviside(t - a) should be done with the third shifting law, reserving the second shifting law strictly for inverting functions of the form e^(-a s) F(s). It is needlessly complicated to apply the second shifting law to functions of the form f(t) Heaviside(t - a)https://www.maplesoft.com/applications/view.aspx?SID=1723&ref=FeedTue, 25 Apr 2017 04:00:00 ZDr. Robert LopezDr. Robert LopezClassroom Tips and Techniques: Drawing a Normal and Tangent Plane on a Surface
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Four different techniques are given for obtaining a graph showing a surface with a normal and tangent plane attached. The work is a response to <a href="http://www.mapleprimes.com/questions/147681-A-Problem-About-Plot-The-Part-Of-The-Surface">a MaplePrimes question asked on May 25, 2013</a>.<img src="https://www.maplesoft.com/view.aspx?si=150722/thumb.jpg" alt="Classroom Tips and Techniques: Drawing a Normal and Tangent Plane on a Surface" style="max-width: 25%;" align="left"/>Four different techniques are given for obtaining a graph showing a surface with a normal and tangent plane attached. The work is a response to <a href="http://www.mapleprimes.com/questions/147681-A-Problem-About-Plot-The-Part-Of-The-Surface">a MaplePrimes question asked on May 25, 2013</a>.https://www.maplesoft.com/applications/view.aspx?SID=150722&ref=FeedTue, 20 Aug 2013 04:00:00 ZDr. Robert LopezDr. Robert LopezClassroom Tips and Techniques: An Inequality-Constrained Optimization Problem
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<p>This article shows how to work both analytically and numerically to find the global maximum of</p>
<p><em>w</em> = ƒ(<em>x, y, z</em>) ≡ <em>x</em><sup>2</sup>(1 + <em>x</em>) + <em>y</em><sup>2</sup>(1 + <em>y</em>) + z<sup>2</sup>(1 + <em>z</em>)</p>
<p>in that part of the first octant on, or below, the plane <em>x</em> + <em>y</em> + <em>z</em> = 6.</p><img src="https://www.maplesoft.com/view.aspx?si=135904/thumb.jpg" alt="Classroom Tips and Techniques: An Inequality-Constrained Optimization Problem" style="max-width: 25%;" align="left"/><p>This article shows how to work both analytically and numerically to find the global maximum of</p>
<p><em>w</em> = ƒ(<em>x, y, z</em>) ≡ <em>x</em><sup>2</sup>(1 + <em>x</em>) + <em>y</em><sup>2</sup>(1 + <em>y</em>) + z<sup>2</sup>(1 + <em>z</em>)</p>
<p>in that part of the first octant on, or below, the plane <em>x</em> + <em>y</em> + <em>z</em> = 6.</p>https://www.maplesoft.com/applications/view.aspx?SID=135904&ref=FeedMon, 16 Jul 2012 04:00:00 ZDr. Robert LopezDr. Robert LopezClassroom Tips and Techniques: Directional Derivatives in Maple
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Several identities in vector calculus involve the operator A . (VectorCalculus[Nabla]) acting on a vector B. The resulting expression (A . (VectorCalculus[Nabla]))B is interpreted as the directional derivative of the vector B in the direction of the vector A. This is not easy to implement in Maple's VectorCalculus packages. However, this functionality exists in the Physics:-Vectors package, and in the DifferentialGeometry package where it is properly called the DirectionalCovariantDerivative.
This article examines how to obtain (A . (VectorCalculus[Nabla]))B in Maple.<img src="https://www.maplesoft.com/view.aspx?si=126623/thumb.jpg" alt="Classroom Tips and Techniques: Directional Derivatives in Maple" style="max-width: 25%;" align="left"/>Several identities in vector calculus involve the operator A . (VectorCalculus[Nabla]) acting on a vector B. The resulting expression (A . (VectorCalculus[Nabla]))B is interpreted as the directional derivative of the vector B in the direction of the vector A. This is not easy to implement in Maple's VectorCalculus packages. However, this functionality exists in the Physics:-Vectors package, and in the DifferentialGeometry package where it is properly called the DirectionalCovariantDerivative.
This article examines how to obtain (A . (VectorCalculus[Nabla]))B in Maple.https://www.maplesoft.com/applications/view.aspx?SID=126623&ref=FeedFri, 14 Oct 2011 04:00:00 ZDr. Robert LopezDr. Robert LopezClassroom Tips and Techniques: Gems 16-20 from the Red Book of Maple Magic
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From the Red Book of Maple Magic, Gems 16-20: Vectors with assumptions in VectorCalculus, aliasing commands to symbols, setting iterated integrals from the Expression palette, writing a slider value to a label, and writing text to a math container.<img src="https://www.maplesoft.com/view.aspx?si=125886/thumb.jpg" alt="Classroom Tips and Techniques: Gems 16-20 from the Red Book of Maple Magic" style="max-width: 25%;" align="left"/>From the Red Book of Maple Magic, Gems 16-20: Vectors with assumptions in VectorCalculus, aliasing commands to symbols, setting iterated integrals from the Expression palette, writing a slider value to a label, and writing text to a math container.https://www.maplesoft.com/applications/view.aspx?SID=125886&ref=FeedFri, 23 Sep 2011 04:00:00 ZDr. Robert LopezDr. Robert LopezPhénomène de Runge - subdivision de Chebychev
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<p>On observe d'abord la divergence du polynôme de Lagrange interpolant la fonction densité de probabilité de la loi de Cauchy lorsque la <strong>subdivision est équirépartie</strong> sur [-1;1]. C'est le <u>phénomène de Runge</u>.<br />
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On observe ensuite qu'en choisissant une <strong>subdivision de Chebychev</strong> le phénomène de divergence au voisinage des bornes disparait.<br />
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Cette activité a été réalisé dans le cadre de la préparation à l'agrégation interne de mathématiques de Rennes le 10 Mars 2010.<br />
Les nouveaux programmes du concours incitent à proposer des exercices utilisant les TICE. Il semble difficile de proposer une preuve convaincante du phénomène de Runge pour une épreuve orale. Ceci justifie de ne s'en tenir qu'à la seule observation.</p><img src="https://www.maplesoft.com/view.aspx?si=35301/thumb.jpg" alt="Phénomène de Runge - subdivision de Chebychev" style="max-width: 25%;" align="left"/><p>On observe d'abord la divergence du polynôme de Lagrange interpolant la fonction densité de probabilité de la loi de Cauchy lorsque la <strong>subdivision est équirépartie</strong> sur [-1;1]. C'est le <u>phénomène de Runge</u>.<br />
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On observe ensuite qu'en choisissant une <strong>subdivision de Chebychev</strong> le phénomène de divergence au voisinage des bornes disparait.<br />
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Cette activité a été réalisé dans le cadre de la préparation à l'agrégation interne de mathématiques de Rennes le 10 Mars 2010.<br />
Les nouveaux programmes du concours incitent à proposer des exercices utilisant les TICE. Il semble difficile de proposer une preuve convaincante du phénomène de Runge pour une épreuve orale. Ceci justifie de ne s'en tenir qu'à la seule observation.</p>https://www.maplesoft.com/applications/view.aspx?SID=35301&ref=FeedFri, 26 Mar 2010 04:00:00 ZKERNIVINEN SebastienKERNIVINEN Sebastien