Engineering Mathematics: New Applications
http://www.maplesoft.com/applications/category.aspx?cid=190
en-us2014 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemFri, 18 Apr 2014 10:49:06 GMTFri, 18 Apr 2014 10:49:06 GMTNew applications in the Engineering Mathematics categoryhttp://www.mapleprimes.com/images/mapleapps.gifEngineering Mathematics: New Applications
http://www.maplesoft.com/applications/category.aspx?cid=190
Wavelet analysis of the blood pressure and pulse frequency measurements with Maple
http://www.maplesoft.com/applications/view.aspx?SID=149420&ref=Feed
<p>A significant part of medical signals, or observations, is non-stationary, discrete time sequences. Thus, the computer methods analysis, as well as refinement and compression, are very helpful as for the problems of recognition and detection of their key diagnostic features. We are going to illustrate here this statement with examples of very common, and even routine medical measurements of blood pressure as well as pulse rate and with possibilities of Maple.<br />The package of Discrete Wavelet transforms (DWT) within Maple 16 [1] was recently added as new research software just for such tasks. The practical testing of this package was additional goal of present study.</p><img src="/view.aspx?si=149420/4b9024ee653d2c7be8febb717b1df52a.gif" alt="Wavelet analysis of the blood pressure and pulse frequency measurements with Maple" align="left"/><p>A significant part of medical signals, or observations, is non-stationary, discrete time sequences. Thus, the computer methods analysis, as well as refinement and compression, are very helpful as for the problems of recognition and detection of their key diagnostic features. We are going to illustrate here this statement with examples of very common, and even routine medical measurements of blood pressure as well as pulse rate and with possibilities of Maple.<br />The package of Discrete Wavelet transforms (DWT) within Maple 16 [1] was recently added as new research software just for such tasks. The practical testing of this package was additional goal of present study.</p>149420Sun, 14 Jul 2013 04:00:00 ZIrina A. DanishewskaIrina A. DanishewskaHardening of Aluminium Alloy AA 7075 T 7351
http://www.maplesoft.com/applications/view.aspx?SID=140361&ref=Feed
<p><span id="ctl00_mainContent__documentViewer"><span><span class="body summary">This worksheet is concerned with the hardening of aluminium alloy, the behaviour of which can be expressed by a simple power law with two hardening parameters. Based upon experimental data these parameters have been determined by both a linear regrssion and the nonlinear <em>MARQUARDT-LEVENBERG algorithm.</em></span></span></span></p><img src="/applications/images/app_image_blank_lg.jpg" alt="Hardening of Aluminium Alloy AA 7075 T 7351" align="left"/><p><span id="ctl00_mainContent__documentViewer"><span><span class="body summary">This worksheet is concerned with the hardening of aluminium alloy, the behaviour of which can be expressed by a simple power law with two hardening parameters. Based upon experimental data these parameters have been determined by both a linear regrssion and the nonlinear <em>MARQUARDT-LEVENBERG algorithm.</em></span></span></span></p>140361Wed, 14 Nov 2012 05:00:00 ZJosef BettenJosef BettenClassroom Tips and Techniques: Fourier Series and an Orthogonal Expansions Package
http://www.maplesoft.com/applications/view.aspx?SID=134198&ref=Feed
The OrthogonalExpansions package contributed to the Maple Application Center by Dr. Sergey Moiseev is considered as a tool for generating a Fourier series and its partial sums. This package provides commands for expansions in 17 other bases of orthogonal functions. In addition to looking at the Fourier series option, this article also considers the Bessel series expansion.<img src="/view.aspx?si=134198/thumb.jpg" alt="Classroom Tips and Techniques: Fourier Series and an Orthogonal Expansions Package" align="left"/>The OrthogonalExpansions package contributed to the Maple Application Center by Dr. Sergey Moiseev is considered as a tool for generating a Fourier series and its partial sums. This package provides commands for expansions in 17 other bases of orthogonal functions. In addition to looking at the Fourier series option, this article also considers the Bessel series expansion.134198Mon, 14 May 2012 04:00:00 ZDr. Robert LopezDr. Robert LopezSolving Equations with Maple
http://www.maplesoft.com/applications/view.aspx?SID=130644&ref=Feed
<p>This worksheet is concerned with methods implemented in Maple to solve some equations of several types.</p>
<p> For instance, the procedures <strong>fsolve </strong>and <strong>RootOf </strong>are very effective and should be used in the following examples.</p>
<p> </p>
<p><em>Keywords: </em>fsolve, RootOf, polynomials of degree n > 3, orthopoly, <em>HERMITE, LEGENDRE, </em></p>
<p><em> LAGUERRE, CHEBYSHEV, </em>transcendental equations</p>
<p> </p>
<p><em><br /></em></p><img src="/applications/images/app_image_blank_lg.jpg" alt="Solving Equations with Maple" align="left"/><p>This worksheet is concerned with methods implemented in Maple to solve some equations of several types.</p>
<p> For instance, the procedures <strong>fsolve </strong>and <strong>RootOf </strong>are very effective and should be used in the following examples.</p>
<p> </p>
<p><em>Keywords: </em>fsolve, RootOf, polynomials of degree n > 3, orthopoly, <em>HERMITE, LEGENDRE, </em></p>
<p><em> LAGUERRE, CHEBYSHEV, </em>transcendental equations</p>
<p> </p>
<p><em><br /></em></p>130644Mon, 13 Feb 2012 05:00:00 ZProf. Josef BettenProf. Josef BettenClassroom Tips and Techniques: An Undamped Coupled Oscillator
http://www.maplesoft.com/applications/view.aspx?SID=129521&ref=Feed
<p>Even for just three degrees of freedom, an undamped coupled oscillator modeled by the ODE system <em>M</em> ü + <em>K</em> u = 0 is difficult to solve analytically because, ultimately, a cubic characteristic equation has to be solve exactly. Instead, we simultaneously diagonalize <em>M</em> and <em>K</em>, the mass and stiffness matrices, thereby uncoupling the equations, and obtaining an explicit solution.</p><img src="/view.aspx?si=129521/thumb.jpg" alt="Classroom Tips and Techniques: An Undamped Coupled Oscillator" align="left"/><p>Even for just three degrees of freedom, an undamped coupled oscillator modeled by the ODE system <em>M</em> ü + <em>K</em> u = 0 is difficult to solve analytically because, ultimately, a cubic characteristic equation has to be solve exactly. Instead, we simultaneously diagonalize <em>M</em> and <em>K</em>, the mass and stiffness matrices, thereby uncoupling the equations, and obtaining an explicit solution.</p>129521Tue, 10 Jan 2012 05:00:00 ZDr. Robert LopezDr. Robert LopezClassroom Tips and Techniques: Simultaneous Diagonalization and the Generalized Eigenvalue Problem
http://www.maplesoft.com/applications/view.aspx?SID=128444&ref=Feed
<p>This article explores the connections between the generalized eigenvalue problem and the problem of simultaneously diagonalizing a pair of <em>n × n</em> matrices.</p>
<p>Given the <em>n × n</em> matrices <em>A</em> and <em>B</em>, the <em>generalized eigenvalue problem</em> seeks the eigenpairs <em>(lambda<sub>k</sub>, x<sub>k</sub>)</em>, solutions of the equation <em>Ax = lambda Bx</em>, or <em>(A - lambda B) x = 0</em>. If <em>B</em> is nonsingular, the eigenpairs of <em>B<sup>-1</sup> A</em> are solutions. If a matrix <em>S</em> exists for which<em> S<sup>T</sup> A S = Lambda</em>, and <em>S<sup>T</sup> B S = I</em>, where <em>Lambda</em> is a diagonal matrix and <em>I</em> is the <em>n × n</em> identity, then <em>A</em> and <em>B</em> are said to be <em>diagonalized simultaneously</em>, in which case the diagonal entries of <em>Lambda</em> are the generalized eigenvalues for <em>A</em> and <em>B</em>. Such a matrix <em>S</em> exists if <em>A</em> is symmetric and <em>B</em> is positive definite. (Our definition of positive definite includes symmetry.)</p><img src="/view.aspx?si=128444/thumb.jpg" alt="Classroom Tips and Techniques: Simultaneous Diagonalization and the Generalized Eigenvalue Problem" align="left"/><p>This article explores the connections between the generalized eigenvalue problem and the problem of simultaneously diagonalizing a pair of <em>n × n</em> matrices.</p>
<p>Given the <em>n × n</em> matrices <em>A</em> and <em>B</em>, the <em>generalized eigenvalue problem</em> seeks the eigenpairs <em>(lambda<sub>k</sub>, x<sub>k</sub>)</em>, solutions of the equation <em>Ax = lambda Bx</em>, or <em>(A - lambda B) x = 0</em>. If <em>B</em> is nonsingular, the eigenpairs of <em>B<sup>-1</sup> A</em> are solutions. If a matrix <em>S</em> exists for which<em> S<sup>T</sup> A S = Lambda</em>, and <em>S<sup>T</sup> B S = I</em>, where <em>Lambda</em> is a diagonal matrix and <em>I</em> is the <em>n × n</em> identity, then <em>A</em> and <em>B</em> are said to be <em>diagonalized simultaneously</em>, in which case the diagonal entries of <em>Lambda</em> are the generalized eigenvalues for <em>A</em> and <em>B</em>. Such a matrix <em>S</em> exists if <em>A</em> is symmetric and <em>B</em> is positive definite. (Our definition of positive definite includes symmetry.)</p>128444Tue, 06 Dec 2011 05:00:00 ZDr. Robert LopezDr. Robert LopezShock Response Spectrum
http://www.maplesoft.com/applications/view.aspx?SID=125009&ref=Feed
<p>This worksheet calculates the shock response spectrum based on some input data.</p><img src="/view.aspx?si=125009/SRS.jpg" alt="Shock Response Spectrum" align="left"/><p>This worksheet calculates the shock response spectrum based on some input data.</p>125009Mon, 22 Aug 2011 04:00:00 ZSurak PereraSurak PereraSignal Processing in Maple
http://www.maplesoft.com/applications/view.aspx?SID=102646&ref=Feed
Consider the problem of evaluating the impact of a structure against a hard surface. The resulting acceleration will typically consist of the actual physical transient acceleration signal plus high frequency sensor resonance. Below we define a few simple analytical functions to model these responses. The effect of adjusting the sampling rate will be explored.<img src="/view.aspx?si=102646/thumb.jpg" alt="Signal Processing in Maple" align="left"/>Consider the problem of evaluating the impact of a structure against a hard surface. The resulting acceleration will typically consist of the actual physical transient acceleration signal plus high frequency sensor resonance. Below we define a few simple analytical functions to model these responses. The effect of adjusting the sampling rate will be explored.102646Fri, 18 Mar 2011 04:00:00 ZMaplesoftMaplesoftHarmonic Analysis
http://www.maplesoft.com/applications/view.aspx?SID=96900&ref=Feed
<p>Harmonic Analysis combines innovative numerical tools for signal processing with rich analytical tools for studying problems of physics and the mathematics of complex variables. Harmonic Analysis provides a Maple package with worked examples in signal filtering, finance, and conformal mapping. The rich documentation includes an in-depth explanation of the theory of harmonic analysis. <br /> <br /> The algorithms in Harmonic Analysis are the culmination of new research by the author in the field of harmonic analysis. They have a US Patent pending (#10/856,453), and a paper on the methods behind the technology is published in the September 2004 issue of IEEE Explorer.</p><img src="/view.aspx?si=96900/harmoniclogo.gif" alt="Harmonic Analysis" align="left"/><p>Harmonic Analysis combines innovative numerical tools for signal processing with rich analytical tools for studying problems of physics and the mathematics of complex variables. Harmonic Analysis provides a Maple package with worked examples in signal filtering, finance, and conformal mapping. The rich documentation includes an in-depth explanation of the theory of harmonic analysis. <br /> <br /> The algorithms in Harmonic Analysis are the culmination of new research by the author in the field of harmonic analysis. They have a US Patent pending (#10/856,453), and a paper on the methods behind the technology is published in the September 2004 issue of IEEE Explorer.</p>96900Wed, 15 Sep 2010 04:00:00 ZVladimir ClueVladimir ClueDesign of logarithmic spiral gear by closed complex function in to DXF format
http://www.maplesoft.com/applications/view.aspx?SID=95483&ref=Feed
The present worksheet deals with the complex algebraic representation of the gear tooth contact principles. The formulae deduced with the help of Maple software environment are closed form solution equations of the contact gear profile to a given rack profile. The worksheet make the final result of gear contour in DXF formatum directly.<img src="/view.aspx?si=95483/278843\30d63f44452b5fdc481d0e802c3751be.gif" alt="Design of logarithmic spiral gear by closed complex function in to DXF format" align="left"/>The present worksheet deals with the complex algebraic representation of the gear tooth contact principles. The formulae deduced with the help of Maple software environment are closed form solution equations of the contact gear profile to a given rack profile. The worksheet make the final result of gear contour in DXF formatum directly.95483Tue, 27 Jul 2010 04:00:00 ZDr. Laczik BálintDr. Laczik BálintCalculate time difference
http://www.maplesoft.com/applications/view.aspx?SID=35404&ref=Feed
<p>This small application calculates the difference between two given time points.</p><img src="/applications/images/app_image_blank_lg.jpg" alt="Calculate time difference" align="left"/><p>This small application calculates the difference between two given time points.</p>35404Tue, 20 Apr 2010 04:00:00 ZHarald KammererHarald KammererConstruction and movement of the centrodes of a slider crank mechanism
http://www.maplesoft.com/applications/view.aspx?SID=35401&ref=Feed
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<p class="MsoNormal"><span lang="EN-US">The movement of the general planar linkage mechanism with one degree of freedom matches exactly the rolling of two centrode curves on each other without slipping.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">The first centrode is fixed to the frame of the linkage and the second centrode is fixed to the moving element of the mechanism.<o:p></o:p></span></p>
<p><span lang="EN-US">The example illustrates the analytic calculation and geometric construction of the centrodes for a slider crank mechanism.</span></p><img src="/view.aspx?si=35401/0\images\linkmech_1.gif" alt="Construction and movement of the centrodes of a slider crank mechanism" align="left"/><p>
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<p class="MsoNormal"><span lang="EN-US">The movement of the general planar linkage mechanism with one degree of freedom matches exactly the rolling of two centrode curves on each other without slipping.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">The first centrode is fixed to the frame of the linkage and the second centrode is fixed to the moving element of the mechanism.<o:p></o:p></span></p>
<p><span lang="EN-US">The example illustrates the analytic calculation and geometric construction of the centrodes for a slider crank mechanism.</span></p>35401Mon, 19 Apr 2010 04:00:00 ZDr. Laczik BálintDr. Laczik BálintQuaternions, Octonions and Sedenions
http://www.maplesoft.com/applications/view.aspx?SID=35196&ref=Feed
<p>This Hypercomplex package provides the algebra of the quaternion, octonion and sedenion hypercomplex numbers.</p><img src="/applications/images/app_image_blank_lg.jpg" alt="Quaternions, Octonions and Sedenions" align="left"/><p>This Hypercomplex package provides the algebra of the quaternion, octonion and sedenion hypercomplex numbers.</p>35196Fri, 16 Apr 2010 04:00:00 ZDr. Michael Angel CarterDr. Michael Angel CarterFracture Propogation in the Internal Pressurized Vessel
http://www.maplesoft.com/applications/view.aspx?SID=35194&ref=Feed
<p>** Abstract : -Calculating the maximum value Pmax that causes the fracture propagation while applying the internal static pressure . -Evaluating the time-limit for applying the continous / discrete form of internal dynamic pressure for the round metal vessel under conditions given by series expansion and curve -fitting method . ** Subjects: Fracture Mechanics , The stress intensity factor KI . This worksheet demonstrates Maple's capabilities in estimating the maximum pressure and the time-limit for applying static or dynamic pressure on the surface of a round metal vessel which has an internal semi-elliptical surface crack .</p><img src="/view.aspx?si=35194/thumb.jpg" alt="Fracture Propogation in the Internal Pressurized Vessel" align="left"/><p>** Abstract : -Calculating the maximum value Pmax that causes the fracture propagation while applying the internal static pressure . -Evaluating the time-limit for applying the continous / discrete form of internal dynamic pressure for the round metal vessel under conditions given by series expansion and curve -fitting method . ** Subjects: Fracture Mechanics , The stress intensity factor KI . This worksheet demonstrates Maple's capabilities in estimating the maximum pressure and the time-limit for applying static or dynamic pressure on the surface of a round metal vessel which has an internal semi-elliptical surface crack .</p>35194Sat, 20 Feb 2010 05:00:00 ZDr. Co TranDr. Co TranViscoplastic Materials
http://www.maplesoft.com/applications/view.aspx?SID=35104&ref=Feed
<p>Abstract</p>
<p>This worksheet is concerned with the <em>linear </em>and <em>nonlinear </em>theory of viscoplasticity. For example, in the following the rate-dependent deformation of a Fe-0.05 weight percent carbon steel at temperatures in excess of a homologous temperature of 0.5 has been discussed in coparison with suitable experiments.</p>
<p> In order to describe the tensile tests at elevated temperatures, a viscoplastic constitutive eqution with three parametrs has been proposed. These parameters can be determined by using the <em>LEVENBERG-MARQUARDT algorithm.</em></p>
<p> </p>
<p><em>Keywords: </em>linear and nomlinear viscoplasticity; tensile tests at elevated temperature; viscoplastic constitutive equation; parameter identification; L-one and L-two error norms </p>
<p> </p><img src="/view.aspx?si=35104/thumb.jpg" alt="Viscoplastic Materials" align="left"/><p>Abstract</p>
<p>This worksheet is concerned with the <em>linear </em>and <em>nonlinear </em>theory of viscoplasticity. For example, in the following the rate-dependent deformation of a Fe-0.05 weight percent carbon steel at temperatures in excess of a homologous temperature of 0.5 has been discussed in coparison with suitable experiments.</p>
<p> In order to describe the tensile tests at elevated temperatures, a viscoplastic constitutive eqution with three parametrs has been proposed. These parameters can be determined by using the <em>LEVENBERG-MARQUARDT algorithm.</em></p>
<p> </p>
<p><em>Keywords: </em>linear and nomlinear viscoplasticity; tensile tests at elevated temperature; viscoplastic constitutive equation; parameter identification; L-one and L-two error norms </p>
<p> </p>35104Wed, 27 Jan 2010 05:00:00 ZProf. Josef BettenProf. Josef BettenTable Plot Procedure
http://www.maplesoft.com/applications/view.aspx?SID=35032&ref=Feed
<p>The procedure TablePlot is used to plot a surface given a 2D table. To use this procedure, a matrix is entered with the independent variables located along the first row and column in increasing order. The corresponding dependent variables are located in the remainder of the matrix. TablePlot uses the procedure LinearInterpolate2D to interpolate values between the known values in the matrix, and then plot3d produces the surface plot.</p><img src="/view.aspx?si=35032/thumb.jpg" alt="Table Plot Procedure" align="left"/><p>The procedure TablePlot is used to plot a surface given a 2D table. To use this procedure, a matrix is entered with the independent variables located along the first row and column in increasing order. The corresponding dependent variables are located in the remainder of the matrix. TablePlot uses the procedure LinearInterpolate2D to interpolate values between the known values in the matrix, and then plot3d produces the surface plot.</p>35032Wed, 06 Jan 2010 05:00:00 ZMaplesoftMaplesoftCreep Curves for Concrete
http://www.maplesoft.com/applications/view.aspx?SID=34931&ref=Feed
<p>This worksheet is concerned with the viscoelastic creep behaviour of concrete. It has been illustrated that linear rheological models are not suitable to describe the creep behaviour in comparison with experimental data. Therefore, a nonlinear model has been proposed in finding a satisfactory approximation to experimental data.</p>
<p>Keywords: Experimental Data of Concrete; Standard Solid Model; LEVENBERG-MARQUARDT algotithm; Nonlinear Theory; Sqrt(t)-Law; PRONY Series; L-two Error Norm; MAXWELL Distribution Function and a Modified Form as Creep Spectra</p>
<p> </p><img src="/view.aspx?si=34931/0\images\Creep_Curve_for_Conc_11.gif" alt="Creep Curves for Concrete" align="left"/><p>This worksheet is concerned with the viscoelastic creep behaviour of concrete. It has been illustrated that linear rheological models are not suitable to describe the creep behaviour in comparison with experimental data. Therefore, a nonlinear model has been proposed in finding a satisfactory approximation to experimental data.</p>
<p>Keywords: Experimental Data of Concrete; Standard Solid Model; LEVENBERG-MARQUARDT algotithm; Nonlinear Theory; Sqrt(t)-Law; PRONY Series; L-two Error Norm; MAXWELL Distribution Function and a Modified Form as Creep Spectra</p>
<p> </p>34931Fri, 11 Dec 2009 05:00:00 ZProf. Josef BettenProf. Josef BettenTHE SOLUTION STABILITY OF VAN DER POL’S EQUATION .
http://www.maplesoft.com/applications/view.aspx?SID=33153&ref=Feed
<p>We consider the Van Der Pol differential equation and two topics that we will be in discussion are <br />
<br />
- Finding the steady state solution of this equation by averaging method .<br />
<br />
- Estimating the stability of solution obtained . <br />
This worksheet demonstrates Maple's capabilities in finding the graphical solution and dealing with the stability of the steady state solution of Van der Pol 's differential equation</p><img src="/view.aspx?si=33153/image.jpg" alt="THE SOLUTION STABILITY OF VAN DER POL’S EQUATION ." align="left"/><p>We consider the Van Der Pol differential equation and two topics that we will be in discussion are <br />
<br />
- Finding the steady state solution of this equation by averaging method .<br />
<br />
- Estimating the stability of solution obtained . <br />
This worksheet demonstrates Maple's capabilities in finding the graphical solution and dealing with the stability of the steady state solution of Van der Pol 's differential equation</p>33153Wed, 24 Jun 2009 04:00:00 ZDr. Co TranDr. Co TranCalculation of B6 Bridge Losses of a power stage driven by space vector modulation scheme
http://www.maplesoft.com/applications/view.aspx?SID=33154&ref=Feed
<p>In many applications inverter fed electrical machines are used. In this paper the switching losses of an inverter with a B6 power stage built of IGBTs and freewheeling diodes are calculated.</p>
<p>First the power loss models for the IGBTs and the freewheeling diodes are defined. Then the switching times are determined by mathematically describing the space vector modulation scheme.</p>
<p>In part one the losses are calculated for one operating point to get the reader familiar with the calculation scheme.</p>
<p>in part two the formulation is more generic to perform the following calculations for a field of operating points. The surfaces of the losses are displayed depending on several input variables influencing the losses of the B6 power stage.</p><img src="/view.aspx?si=33154/0\images\B6-Bridge_losses_IGB_26.gif" alt="Calculation of B6 Bridge Losses of a power stage driven by space vector modulation scheme" align="left"/><p>In many applications inverter fed electrical machines are used. In this paper the switching losses of an inverter with a B6 power stage built of IGBTs and freewheeling diodes are calculated.</p>
<p>First the power loss models for the IGBTs and the freewheeling diodes are defined. Then the switching times are determined by mathematically describing the space vector modulation scheme.</p>
<p>In part one the losses are calculated for one operating point to get the reader familiar with the calculation scheme.</p>
<p>in part two the formulation is more generic to perform the following calculations for a field of operating points. The surfaces of the losses are displayed depending on several input variables influencing the losses of the B6 power stage.</p>33154Wed, 24 Jun 2009 04:00:00 ZAndreas SchrammAndreas SchrammThe “Gray Box” Approach
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<p>The proverbial "black box" refers to computing tools where the user is shielded from the inner algorithms and interacts with the system from a purely and input and output point of view. Most modern engineering modeling and simulation software are based on this notion. The "gray box" is a term that describes the symbolic approach to engineering computation that offers distinct benefits in education and research. This paper offers an introduction to the tools and techniques of successfully deploying symbolic tools. The Maple system will be used as the software context.</p><img src="/view.aspx?si=32963/thumb.jpg" alt="The “Gray Box” Approach" align="left"/><p>The proverbial "black box" refers to computing tools where the user is shielded from the inner algorithms and interacts with the system from a purely and input and output point of view. Most modern engineering modeling and simulation software are based on this notion. The "gray box" is a term that describes the symbolic approach to engineering computation that offers distinct benefits in education and research. This paper offers an introduction to the tools and techniques of successfully deploying symbolic tools. The Maple system will be used as the software context.</p>32963Fri, 08 May 2009 04:00:00 ZMaplesoftMaplesoft