Numerical Analysis: New Applications
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en-us2015 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemMon, 26 Jan 2015 12:27:59 GMTMon, 26 Jan 2015 12:27:59 GMTNew applications in the Numerical Analysis categoryhttp://www.mapleprimes.com/images/mapleapps.gifNumerical Analysis: New Applications
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Measuring Water Flow of Rivers
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In this guest article in the Tips & Techniques series, Dr. Michael Monagan discusses the art and science of measuring the amount of water flowing in a river, and relates his personal experiences with this task to its morph into a project for his calculus classes.<img src="/view.aspx?si=153480/thumb.jpg" alt="Measuring Water Flow of Rivers" align="left"/>In this guest article in the Tips & Techniques series, Dr. Michael Monagan discusses the art and science of measuring the amount of water flowing in a river, and relates his personal experiences with this task to its morph into a project for his calculus classes.153480Fri, 13 Dec 2013 05:00:00 ZProf. Michael MonaganProf. Michael MonaganWaves propagation in chain of atoms
http://www.maplesoft.com/applications/view.aspx?SID=102086&ref=Feed
<p><img title="vizu3D" src="http://pc1kleber.free.fr/download/Image2.jpg" alt="40 atomes" width="595" height="370" /><img title="model" src="http://pc1kleber.free.fr/download/Image6.jpg" alt="model" width="681" height="649" /></p>
<h1><strong>Compute and show the propagation of waves along a chain of N (N tunable) "atoms"</strong></h1>
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<p> </p><img src="/view.aspx?si=102086/320527\53f7d592028d5bb6cfec3b35e445ee9d.gif" alt="Waves propagation in chain of atoms" align="left"/><p><img title="vizu3D" src="http://pc1kleber.free.fr/download/Image2.jpg" alt="40 atomes" width="595" height="370" /><img title="model" src="http://pc1kleber.free.fr/download/Image6.jpg" alt="model" width="681" height="649" /></p>
<h1><strong>Compute and show the propagation of waves along a chain of N (N tunable) "atoms"</strong></h1>
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<p> </p>102086Mon, 28 Feb 2011 05:00:00 ZSerge GAZAIXSerge GAZAIXVarInt
http://www.maplesoft.com/applications/view.aspx?SID=88830&ref=Feed
<p><strong>VarInt</strong> - <em>Computer Algebra Aided Design of Variational Integrators</em>.</p>
<p>Create, design and analyse (new) variational integrators for autonomous dynamical systems (with non-conservative forces) up to arbitary order with VarInt, a package for Maple.</p><img src="/view.aspx?si=88830/VarIntSmall.jpg" alt="VarInt" align="left"/><p><strong>VarInt</strong> - <em>Computer Algebra Aided Design of Variational Integrators</em>.</p>
<p>Create, design and analyse (new) variational integrators for autonomous dynamical systems (with non-conservative forces) up to arbitary order with VarInt, a package for Maple.</p>88830Tue, 25 Jan 2011 05:00:00 ZChristian HellströmChristian HellströmPhénomène 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="/view.aspx?si=35301/thumb.jpg" alt="Phénomène de Runge - subdivision de Chebychev" 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 />
<br />
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>35301Fri, 26 Mar 2010 04:00:00 ZKERNIVINEN SebastienKERNIVINEN SebastienComparison of Multivariate Optimization Methods
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<p>The worksheet demonstrates the use of Maple to compare methods of unconstrained nonlinear minimization of multivariable function. Seven methods of nonlinear minimization of the n-variables objective function f(x1,x2,.,xn) are analyzed:</p>
<p>1) minimum search by coordinate and conjugate directions descent; 2) Powell's method; 3) the modified Hooke-Jeeves method; 4) simplex Nelder-Meed method; 5) quasi-gradient method; 6) random directions search; 7) simulated annealing. All methods are direct searching methods, i.e. they do not require the objective function f(x1,x2,.,xn) to be differentiable and continuous. Maple's Optimization package efficiency is compared with these programs. Optimization methods have been compared on the set of 21 test functions.</p><img src="/view.aspx?si=1718/SearchPaths2.PNG" alt="Comparison of Multivariate Optimization Methods" align="left"/><p>The worksheet demonstrates the use of Maple to compare methods of unconstrained nonlinear minimization of multivariable function. Seven methods of nonlinear minimization of the n-variables objective function f(x1,x2,.,xn) are analyzed:</p>
<p>1) minimum search by coordinate and conjugate directions descent; 2) Powell's method; 3) the modified Hooke-Jeeves method; 4) simplex Nelder-Meed method; 5) quasi-gradient method; 6) random directions search; 7) simulated annealing. All methods are direct searching methods, i.e. they do not require the objective function f(x1,x2,.,xn) to be differentiable and continuous. Maple's Optimization package efficiency is compared with these programs. Optimization methods have been compared on the set of 21 test functions.</p>1718Tue, 15 Sep 2009 04:00:00 ZOrthogonal Functions, Orthogonal Polynomials, and Orthogonal Wavelets series expansions of function
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The worksheet includes all the best known continuous orthogonal series expansions in the closed form. It demonstrates the use of Maple to evaluate expansion of a function by Fourier, Hartley, Fourier-Bessel, Orthogonal Rational Tangent, Rectangular, Haar Wavelet, Walsh, Slant, Piece-Linear-Quadratic, Associated Legandre, Orthogonal Rational, Generalized sinc, Sinc, Sinc Wavelet, Jacobi, Chebyshev first kind, Chebyshev second kind, Gegenbauer, Generalized Laguerre, Laguerre, Hermite, and classical polynomials orthogonal series. Also the worksheet demonstrates how to create new orthonormal basis of functions by using the Gram-Schmidt orthogonalization process by the example of Slant, and Piece-Linear-Quadratic orthonormal functions creating.<img src="/view.aspx?si=7256/thumb.gif" alt="Orthogonal Functions, Orthogonal Polynomials, and Orthogonal Wavelets series expansions of function" align="left"/>The worksheet includes all the best known continuous orthogonal series expansions in the closed form. It demonstrates the use of Maple to evaluate expansion of a function by Fourier, Hartley, Fourier-Bessel, Orthogonal Rational Tangent, Rectangular, Haar Wavelet, Walsh, Slant, Piece-Linear-Quadratic, Associated Legandre, Orthogonal Rational, Generalized sinc, Sinc, Sinc Wavelet, Jacobi, Chebyshev first kind, Chebyshev second kind, Gegenbauer, Generalized Laguerre, Laguerre, Hermite, and classical polynomials orthogonal series. Also the worksheet demonstrates how to create new orthonormal basis of functions by using the Gram-Schmidt orthogonalization process by the example of Slant, and Piece-Linear-Quadratic orthonormal functions creating.7256Wed, 18 Feb 2009 00:00:00 ZDr. Sergey MoiseevDr. Sergey Moiseev1-D Finite Element N-element P-order Bar
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This sheet can solve a simple 1-D bar problem with N-element P-order finite element formulation.<img src="/view.aspx?si=6404/1.jpg" alt="1-D Finite Element N-element P-order Bar" align="left"/>This sheet can solve a simple 1-D bar problem with N-element P-order finite element formulation.6404Thu, 03 Jul 2008 00:00:00 ZMike ArunMike ArunClassroom Tips and Techniques: Numeric Solution of a Two-Point BVP
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Maple's dsolve command will solve nonlinear two-point boundary value problems numerically. We investigate one such problem that has multiple solutions, and show how a shooting method can be used to reproduce the solutions.<img src="/view.aspx?si=5634/R-30NumericSolutionofaTwo-PointBVP_34.jpg" alt="Classroom Tips and Techniques: Numeric Solution of a Two-Point BVP" align="left"/>Maple's dsolve command will solve nonlinear two-point boundary value problems numerically. We investigate one such problem that has multiple solutions, and show how a shooting method can be used to reproduce the solutions.5634Thu, 31 Jan 2008 00:00:00 ZDr. Robert LopezDr. Robert LopezCurve Fitting with Maple
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Maple includes a number of assistants that allows a user to experiment and easily perform key tasks. This Tips and Technique will focus on the Curve Fitting Assistant. This assistant provides a quick and easy method to fit a curve to a set of data points and to experiment to find the best curve for your data set. The assistant provides a graph showing both the points in your data as well as the curve returned by the choosen curve fitting algorithm.<img src="/view.aspx?si=5473/CurveFitting_12.jpg" alt="Curve Fitting with Maple" align="left"/>Maple includes a number of assistants that allows a user to experiment and easily perform key tasks. This Tips and Technique will focus on the Curve Fitting Assistant. This assistant provides a quick and easy method to fit a curve to a set of data points and to experiment to find the best curve for your data set. The assistant provides a graph showing both the points in your data as well as the curve returned by the choosen curve fitting algorithm.5473Thu, 01 Nov 2007 04:00:00 ZMaplesoftMaplesoftBack-Solving Assistant
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In Maple 11, one of the new additions to the Assistants list is the Back-Solving Assistant. This Tips and Techniques will show you how to get the most out of this new tool.
The Back-Solving Assistant automatically generates a back-solver for your equation, allowing you to instantly solve for any variable in your formula, given the values of the other parameters. You can also plot the behavior of your formula as parameters vary.<img src="/view.aspx?si=5066/BackSolver3.jpg" alt="Back-Solving Assistant" align="left"/>In Maple 11, one of the new additions to the Assistants list is the Back-Solving Assistant. This Tips and Techniques will show you how to get the most out of this new tool.
The Back-Solving Assistant automatically generates a back-solver for your equation, allowing you to instantly solve for any variable in your formula, given the values of the other parameters. You can also plot the behavior of your formula as parameters vary.5066Tue, 03 Jul 2007 04:00:00 ZMaplesoftMaplesoftClassroom Tips and Techniques: Teaching Fourier Series with Maple - Part 4
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<p>We describe the Fourier package announced by Karel Srot in a post to MaplePrimes on August 21, 2006. Although a significant portion of the functionality in this package is available elsewhere, the nuances of the commands make for a different feel to the package. In addition, there is a Fourier series Maplet that is worth considering. Instructions for downloading and installing the package are available at www.math.muni.cz/~xsrot/frady. Although the author notes that this site is primarily in Czech, installation instructions within the download are in English.</p><img src="/view.aspx?si=4898/R-22TeachingFourierSerieswithMaple-Part4_46.jpg" alt="Classroom Tips and Techniques: Teaching Fourier Series with Maple - Part 4" align="left"/><p>We describe the Fourier package announced by Karel Srot in a post to MaplePrimes on August 21, 2006. Although a significant portion of the functionality in this package is available elsewhere, the nuances of the commands make for a different feel to the package. In addition, there is a Fourier series Maplet that is worth considering. Instructions for downloading and installing the package are available at www.math.muni.cz/~xsrot/frady. Although the author notes that this site is primarily in Czech, installation instructions within the download are in English.</p>4898Tue, 24 Apr 2007 04:00:00 ZDr. Robert LopezDr. Robert LopezClassroom Tips and Techniques:Teaching Fourier Series with Maple - Part 3
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<p>The FourierSeries package by Professor Wilhalm Werner is described. It was the first such package available on the Maple Application Center, and it has recently been updated to run in the latest versions of Maple. This article continues earlier discussions that showed how to implement, in Maple itself, the calculations related to Fourier series, then described the Fourier Series package submitted to the Maple Application Center by Professor Amir Khanshan.</p><img src="/view.aspx?si=4885/TeachingFourierSerieswithMaple-Part3_img.jpg" alt="Classroom Tips and Techniques:Teaching Fourier Series with Maple - Part 3" align="left"/><p>The FourierSeries package by Professor Wilhalm Werner is described. It was the first such package available on the Maple Application Center, and it has recently been updated to run in the latest versions of Maple. This article continues earlier discussions that showed how to implement, in Maple itself, the calculations related to Fourier series, then described the Fourier Series package submitted to the Maple Application Center by Professor Amir Khanshan.</p>4885Mon, 26 Mar 2007 04:00:00 ZDr. Robert LopezDr. Robert LopezClassroom Tips and Techniques: Teaching Fourier Series with Maple - Part 2
http://www.maplesoft.com/applications/view.aspx?SID=4876&ref=Feed
<p>The Fourier Series package by Professor Amir Khanshan is described. This package was first documented in the Proceedings of the Maple Conference 2006, and was recently added to the Maple Application Center. This article continues an earlier discussion that showed how to implement, in Maple itself, the calculations related to Fourier series.</p><img src="/view.aspx?si=4876/R-20 Teaching Fourier Series with Maple - Part 2_62.jpg" alt="Classroom Tips and Techniques: Teaching Fourier Series with Maple - Part 2" align="left"/><p>The Fourier Series package by Professor Amir Khanshan is described. This package was first documented in the Proceedings of the Maple Conference 2006, and was recently added to the Maple Application Center. This article continues an earlier discussion that showed how to implement, in Maple itself, the calculations related to Fourier series.</p>4876Mon, 26 Feb 2007 04:00:00 ZDr. Robert LopezDr. Robert LopezPolynomial Regression through Least Square Method
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The goals of this document are to show the approximation of a Point Dispersion through Quadratic Regression Polynomials using the Least Square Method and Maple 10 tools.<img src="/view.aspx?si=4845/PolyReg.htm_67.gif" alt="Polynomial Regression through Least Square Method" align="left"/>The goals of this document are to show the approximation of a Point Dispersion through Quadratic Regression Polynomials using the Least Square Method and Maple 10 tools.4845Tue, 21 Nov 2006 00:00:00 ZProf. David Macias FerrerProf. David Macias FerrerMéthode de bissection et méthode de Newton
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Application sur deux méthodes d'estimation des zéros d'une fonction: la méthode de bissection et la méthode de Newton.<img src="/view.aspx?si=4831/image.jpg" alt="Méthode de bissection et méthode de Newton" align="left"/>Application sur deux méthodes d'estimation des zéros d'une fonction: la méthode de bissection et la méthode de Newton.4831Tue, 24 Oct 2006 00:00:00 ZAndre LevesqueAndre LevesquePrimes in Irrational Numbers
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Google set up an imaginative recruiting teaser in the form {first 10-digit prime found in consecutive digits of e}.com. The present general application permits the discovery of sequences of n-digit primes existing in any irrational number.<img src="/view.aspx?si=1715//applications/images/app_image_blank_lg.jpg" alt="Primes in Irrational Numbers" align="left"/>Google set up an imaginative recruiting teaser in the form {first 10-digit prime found in consecutive digits of e}.com. The present general application permits the discovery of sequences of n-digit primes existing in any irrational number.1715Mon, 27 Feb 2006 00:00:00 ZProf. Leslie GlasserProf. Leslie GlasserDirect Method of Polynomial Interpolation
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This worksheet demonstrates the use of Maple to illustrate the direct method of interpolation. We limit this worksheet to using first, second, and third order polynomials. <img src="/view.aspx?si=4399//applications/images/app_image_blank_lg.jpg" alt="Direct Method of Polynomial Interpolation " align="left"/>This worksheet demonstrates the use of Maple to illustrate the direct method of interpolation. We limit this worksheet to using first, second, and third order polynomials. 123873Fri, 13 Jun 2003 14:25:27 ZDr. Autar KawDr. Autar KawLagrangian Method of Interpolation
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This worksheet demonstrates the use of Maple to illustrate the Lagrangian method of interpolation. We limit this worksheet to using first, second, and third order polynomials. <img src="/view.aspx?si=4398//applications/images/app_image_blank_lg.jpg" alt="Lagrangian Method of Interpolation " align="left"/>This worksheet demonstrates the use of Maple to illustrate the Lagrangian method of interpolation. We limit this worksheet to using first, second, and third order polynomials. 123872Fri, 13 Jun 2003 14:22:38 ZDr. Autar KawDr. Autar KawSpline Method of Interpolation
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This worksheet demonstrates the use of Maple to illustrate the spline method of interpolation. We limit this worksheet to linear and quadratic spline interpolation.<img src="/view.aspx?si=4397//applications/images/app_image_blank_lg.jpg" alt="Spline Method of Interpolation " align="left"/>This worksheet demonstrates the use of Maple to illustrate the spline method of interpolation. We limit this worksheet to linear and quadratic spline interpolation.123871Fri, 13 Jun 2003 14:03:38 ZDr. Autar KawDr. Autar KawNewton Divided Difference Method of Interpolation
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This worksheet demonstrates the use of Maple to illustrate the Newton's Divided Difference Method of interpolation. We limit this worksheet to using first, second, and third order polynomials.<img src="/view.aspx?si=4396//applications/images/app_image_blank_lg.jpg" alt="Newton Divided Difference Method of Interpolation " align="left"/>This worksheet demonstrates the use of Maple to illustrate the Newton's Divided Difference Method of interpolation. We limit this worksheet to using first, second, and third order polynomials.123870Fri, 13 Jun 2003 14:00:45 ZDr. Autar KawDr. Autar Kaw