Engineering Mathematics: New Applications
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en-us2016 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemTue, 27 Sep 2016 15:34:05 GMTTue, 27 Sep 2016 15:34:05 GMTNew applications in the Engineering Mathematics categoryhttp://www.mapleprimes.com/images/mapleapps.gifEngineering Mathematics: New Applications
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Pulsdruckwerte aus Langzeitmessung
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During a period of nearly 24 hours the blood pressure of a patient at a Hospital in Aachen has been measured. Thus, we have a lot of Systole-, Diastole-, Pulse Pressure-, and Pulse-Values important for a medical doctor treating sick patients. This worksheet is concerned with the mathematical analysis of this data.<img src="/view.aspx?si=154144/pressure.PNG" alt="Pulsdruckwerte aus Langzeitmessung" align="left"/>During a period of nearly 24 hours the blood pressure of a patient at a Hospital in Aachen has been measured. Thus, we have a lot of Systole-, Diastole-, Pulse Pressure-, and Pulse-Values important for a medical doctor treating sick patients. This worksheet is concerned with the mathematical analysis of this data.154144Tue, 06 Sep 2016 04:00:00 ZProf. Josef BettenProf. Josef BettenAplicativo de Ecuaciones en primer orden
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With this application you can develop your equations without the need to worry about the difficult calculation. Save calculation time and you will increase the time in interpreting the results. It was developed in Maple 2016 and can be executed in maple player.
In Spanish.<img src="/view.aspx?si=154139/appec.png" alt="Aplicativo de Ecuaciones en primer orden" align="left"/>With this application you can develop your equations without the need to worry about the difficult calculation. Save calculation time and you will increase the time in interpreting the results. It was developed in Maple 2016 and can be executed in maple player.
In Spanish.154139Sun, 07 Aug 2016 04:00:00 ZProf. Lenin Araujo CastilloProf. Lenin Araujo CastilloPulse Values from Long Term Measurement
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Long term measurement of heart rate furnishes important information of cardiac anomalies. During a period of about 24 hours pulse rate of a patient at the University Hospital Aachen has been measured. Thus, we have a lots of pulse values, which are important for a medical doctor treating sick patients. We use Maple to analyze this data. At first the given data have been interpolated by cubic spline functions. Then, these functions have been approximated by nonlinear regression and also by Fourier series.<img src="/view.aspx?si=154087/pulsevalues.png" alt="Pulse Values from Long Term Measurement" align="left"/>Long term measurement of heart rate furnishes important information of cardiac anomalies. During a period of about 24 hours pulse rate of a patient at the University Hospital Aachen has been measured. Thus, we have a lots of pulse values, which are important for a medical doctor treating sick patients. We use Maple to analyze this data. At first the given data have been interpolated by cubic spline functions. Then, these functions have been approximated by nonlinear regression and also by Fourier series.154087Wed, 20 Apr 2016 04:00:00 ZProf. Josef BettenProf. Josef BettenVectors in the plane.
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If an object is subjected to several forces having different magnitudes and act in different directions, how can determine the magnitude and direction of the resultant total force on the object? Forces are vectors and should be added according to the definition of the vector sum. Engineering dealing with many quantities that have both magnitude and direction and can be expressed and analyzed as vectors.
<BR><BR>
In Spanish.<img src="/view.aspx?si=154071/vp.png" alt="Vectors in the plane." align="left"/>If an object is subjected to several forces having different magnitudes and act in different directions, how can determine the magnitude and direction of the resultant total force on the object? Forces are vectors and should be added according to the definition of the vector sum. Engineering dealing with many quantities that have both magnitude and direction and can be expressed and analyzed as vectors.
<BR><BR>
In Spanish.154071Fri, 01 Apr 2016 04:00:00 ZProf. Lenin Araujo CastilloProf. Lenin Araujo CastilloThe Schwarz-Christoffel panel method: a computational kit
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The so-called Schwarz-Christoffel Panel Method devised and developed by Prof. E. Morishita for the analysis of aerodynamics of airfoils with arbitrary geometry is built as a hidden code in this document. Given the airfoil geometry, the Schwarz-Christoffel transform that maps the unit circle onto the polygon that represents the airfoil, is obtained. Some Maple resources are included to handle and visualize the computed results.<img src="/view.aspx?si=153963/temporaryAirfoils.png" alt="The Schwarz-Christoffel panel method: a computational kit" align="left"/>The so-called Schwarz-Christoffel Panel Method devised and developed by Prof. E. Morishita for the analysis of aerodynamics of airfoils with arbitrary geometry is built as a hidden code in this document. Given the airfoil geometry, the Schwarz-Christoffel transform that maps the unit circle onto the polygon that represents the airfoil, is obtained. Some Maple resources are included to handle and visualize the computed results.153963Wed, 03 Feb 2016 05:00:00 ZLuis Sainz de los TerrerosLuis Sainz de los TerrerosDemo Worksheet for Numerical Delay Differential Equation Solution
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<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 WittkopfNonlinear Viscoelastic Behaviour of Brain Tissue
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In this worksheet the relaxation of Brain Tissue has been calculated to experimental data by two nonlinear model functions:
a five parameters PRONY-Series and compared with a three parameters Sqrt(t)-Law due to BETTEN, Creep Mechanics, 3rd edtion, 2008 Springer-Verlag Berlin / Heidelberg.<img src="/applications/images/app_image_blank_lg.jpg" alt="Nonlinear Viscoelastic Behaviour of Brain Tissue" align="left"/>In this worksheet the relaxation of Brain Tissue has been calculated to experimental data by two nonlinear model functions:
a five parameters PRONY-Series and compared with a three parameters Sqrt(t)-Law due to BETTEN, Creep Mechanics, 3rd edtion, 2008 Springer-Verlag Berlin / Heidelberg.153923Tue, 01 Dec 2015 05:00:00 ZProf. Josef BettenProf. Josef BettenNonlinear Regression with Maple
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Many Authors have discussed Nonlinear Regression based upon the LEVENBERG-MARQUART algorithm. Often the SIGMAPLOT Program is very useful, too.
In this worksheet the Maple routine NonlinearFit [Statistics] has been preferred, to fit nonlinear model functions to given data. This routine is very effective and simple to use. Examples in this document include the envelopes of FRENEL's integrals and the hardening of an aluminium alloy.<img src="/applications/images/app_image_blank_lg.jpg" alt="Nonlinear Regression with Maple" align="left"/>Many Authors have discussed Nonlinear Regression based upon the LEVENBERG-MARQUART algorithm. Often the SIGMAPLOT Program is very useful, too.
In this worksheet the Maple routine NonlinearFit [Statistics] has been preferred, to fit nonlinear model functions to given data. This routine is very effective and simple to use. Examples in this document include the envelopes of FRENEL's integrals and the hardening of an aluminium alloy.153895Wed, 14 Oct 2015 04:00:00 ZProf. Josef BettenProf. Josef BettenApproximation von BESSEL-Funktionen durch FOURIER-Reihen
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Mit Hilfe der Maplesoftware können BESSEL-Funktionen bequem dargestellt werden. Beispielsweise werden BESSEL-Funktionen erster Art für gerade und ungerade Ordnung n diskutiert und durch FOURIER-Reihen beliebiger Gliederanzahl approximiert. Nach dem gleichen Muster können auch BESSEL-Funktionen zweiter Art oder beispielsweise FRESNELsche Integrale approximiert werden.<img src="/view.aspx?si=153835/6d6089d907c5cd7d58f85af2a82d634c.gif" alt="Approximation von BESSEL-Funktionen durch FOURIER-Reihen" align="left"/>Mit Hilfe der Maplesoftware können BESSEL-Funktionen bequem dargestellt werden. Beispielsweise werden BESSEL-Funktionen erster Art für gerade und ungerade Ordnung n diskutiert und durch FOURIER-Reihen beliebiger Gliederanzahl approximiert. Nach dem gleichen Muster können auch BESSEL-Funktionen zweiter Art oder beispielsweise FRESNELsche Integrale approximiert werden.153835Fri, 17 Jul 2015 04:00:00 ZProf. Josef BettenProf. Josef BettenBlutdruckwerte aus Langzeitmessung
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<p>During a period of 24 hours the blood pressure of a patient at the University Hospital Aachen has been measured. Thus, we have a lot of Systole-, Diastole-, and Pulse-Values important for medical doctors teating sick patients. To analyse these "data" the Maple Program 16 has been used.</p><img src="/view.aspx?si=153813/9eba1a814642633a6f07c19980f3a0e8.gif" alt="Blutdruckwerte aus Langzeitmessung" align="left"/><p>During a period of 24 hours the blood pressure of a patient at the University Hospital Aachen has been measured. Thus, we have a lot of Systole-, Diastole-, and Pulse-Values important for medical doctors teating sick patients. To analyse these "data" the Maple Program 16 has been used.</p>153813Thu, 04 Jun 2015 04:00:00 ZProf. Josef Professor BettenProf. Josef Professor BettenSplinefunktion als FOURIER-Reihen
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<p>Zunächst werden experimentelle Daten durch eine kubische <em>Splinefunktion </em>interpoliert. Die stückweise stetige <em>Splinefunktion</em> wird als <em>FOURIER-Reihe </em>dargestellt Dabei wird festgestellt, dass sich die <em>FOURIER-Reihe </em>mit steigender Anzahl der Reihenglieder immer szärker an die <em>Splinefunktion </em>anschmiegt. Bei unendlicher Anzahl der Reihenglieder fällt die <em>FOURIER-Reihe </em>mit der <em>Splinefunktion zusammen.</em></p><img src="/applications/images/app_image_blank_lg.jpg" alt="Splinefunktion als FOURIER-Reihen" align="left"/><p>Zunächst werden experimentelle Daten durch eine kubische <em>Splinefunktion </em>interpoliert. Die stückweise stetige <em>Splinefunktion</em> wird als <em>FOURIER-Reihe </em>dargestellt Dabei wird festgestellt, dass sich die <em>FOURIER-Reihe </em>mit steigender Anzahl der Reihenglieder immer szärker an die <em>Splinefunktion </em>anschmiegt. Bei unendlicher Anzahl der Reihenglieder fällt die <em>FOURIER-Reihe </em>mit der <em>Splinefunktion zusammen.</em></p>153796Mon, 18 May 2015 04:00:00 ZProf. Josef BettenProf. Josef BettenEconomic Pipe Sizer for Process Plants
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<p>Pipework is a large part of the cost of a process plant. Plant designers need to minimize the total cost of this pipework across the lifetime of the plant. The total overall cost is a combination of individual costs related to the:</p>
<ul>
<li>pipe material,</li>
<li>installation, </li>
<li>maintenance, </li>
<li>depreciation, </li>
<li>energy costs for pumping, </li>
<li>liquid parameters, </li>
<li>required flowrate,</li>
<li>pumping efficiencies,</li>
<li>taxes,</li>
<li>and more.</li>
</ul>
<p>The total cost is not a simple linear sum of the individual costs; a more complex relationship is needed.</p>
<p>This application uses the approach described in [1] to find the pipe diameter that minimizes the total lifetime cost. The method involves the iterative solution of an empirical equation using <a href="/support/help/Maple/view.aspx?path=fsolve">Maple’s fsolve function</a> (the code for the application is in the Startup code region).</p>
<p>Users can choose the pipe material (carbon steel, stainless steel, aluminum or brass), and specify the desired fluid flowrate, fluid viscosity and density. The application then solves the empirical equation (using Maple’s fsolve() function) and returns the economically optimal pipe diameter.</p>
<p>Bear in mind that the empirical parameters used in the application vary as economic conditions change. Those used in this application are correct for 1998 and 2008.</p>
<p><em>[1]: "Updating the Rules for Pipe Sizing", Durand et al., Chemical Engineering, January 2010</em></p><img src="/applications/images/app_image_blank_lg.jpg" alt="Economic Pipe Sizer for Process Plants" align="left"/><p>Pipework is a large part of the cost of a process plant. Plant designers need to minimize the total cost of this pipework across the lifetime of the plant. The total overall cost is a combination of individual costs related to the:</p>
<ul>
<li>pipe material,</li>
<li>installation, </li>
<li>maintenance, </li>
<li>depreciation, </li>
<li>energy costs for pumping, </li>
<li>liquid parameters, </li>
<li>required flowrate,</li>
<li>pumping efficiencies,</li>
<li>taxes,</li>
<li>and more.</li>
</ul>
<p>The total cost is not a simple linear sum of the individual costs; a more complex relationship is needed.</p>
<p>This application uses the approach described in [1] to find the pipe diameter that minimizes the total lifetime cost. The method involves the iterative solution of an empirical equation using <a href="/support/help/Maple/view.aspx?path=fsolve">Maple’s fsolve function</a> (the code for the application is in the Startup code region).</p>
<p>Users can choose the pipe material (carbon steel, stainless steel, aluminum or brass), and specify the desired fluid flowrate, fluid viscosity and density. The application then solves the empirical equation (using Maple’s fsolve() function) and returns the economically optimal pipe diameter.</p>
<p>Bear in mind that the empirical parameters used in the application vary as economic conditions change. Those used in this application are correct for 1998 and 2008.</p>
<p><em>[1]: "Updating the Rules for Pipe Sizing", Durand et al., Chemical Engineering, January 2010</em></p>153659Fri, 15 Aug 2014 04:00:00 ZSamir KhanSamir KhanWelded Beam Design Optimization
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<p>A rigid member is welded onto a beam, with a load applied to the end of the member. The total cost of production is equal to the labor costs (a function of the weld dimensions) plus the cost of the weld and beam material.</p>
<p>The design of the beam is optimized to minimize the production costs by varying the weld and member dimensions.</p>
<p>The constraints include limits on the shear stress, bending stress, buckling load and end deflection, and several size constraints.</p>
<p>The application uses Maple’s non-linear optimizers</p><img src="/view.aspx?si=153592/0621a9aba622112f66506495e21f68d9.gif" alt="Welded Beam Design Optimization" align="left"/><p>A rigid member is welded onto a beam, with a load applied to the end of the member. The total cost of production is equal to the labor costs (a function of the weld dimensions) plus the cost of the weld and beam material.</p>
<p>The design of the beam is optimized to minimize the production costs by varying the weld and member dimensions.</p>
<p>The constraints include limits on the shear stress, bending stress, buckling load and end deflection, and several size constraints.</p>
<p>The application uses Maple’s non-linear optimizers</p>153592Fri, 30 May 2014 04:00:00 ZSamir KhanSamir KhanVisualization Free and Forced Harmonic Oscillations
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<p>This worksheet focuses on how the symbolic,numerical and graphical power of CAS, maple can be used to explore and visualize with animation free harmonic.</p><img src="/applications/images/app_image_blank_lg.jpg" alt="Visualization Free and Forced Harmonic Oscillations" align="left"/><p>This worksheet focuses on how the symbolic,numerical and graphical power of CAS, maple can be used to explore and visualize with animation free harmonic.</p>153558Thu, 01 May 2014 04:00:00 ZAli Abu OamAli Abu OamAutomatic Speech Segmentation
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<p>This worksheet demonstrates the use of the Forward-Backward Divergence model (FBD) in Automatic Speech Segmentation, and how it detects discontinuities in the voice signal. It illustrates in the example below how it is possible to enlarge some segments of the speech (vowels enlargement for instance). To realize this result, it is possible to visually and acoustically perceive the stationary segments of the speech signal.</p><img src="/view.aspx?si=153553/speech.png" alt="Automatic Speech Segmentation" align="left"/><p>This worksheet demonstrates the use of the Forward-Backward Divergence model (FBD) in Automatic Speech Segmentation, and how it detects discontinuities in the voice signal. It illustrates in the example below how it is possible to enlarge some segments of the speech (vowels enlargement for instance). To realize this result, it is possible to visually and acoustically perceive the stationary segments of the speech signal.</p>153553Thu, 17 Apr 2014 04:00:00 ZJocelyn MagneJocelyn MagneThe House Warming Model
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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 MonaganCollision detection between toolholder and workpiece on ball nut grinding
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<p>In this worksheet a collision detection performed to determine the minimum safety distance between a tool holder and ball nut on grinding manufacturing. A nonlinear quartic equation system have to be solved by <em>Newton's</em> and <em>Broyden's</em> methods and results are compared with <em>Maple fsolve()</em> command. Users can check the different results by embedded components and animated 3D surface plot.</p><img src="/view.aspx?si=153477/Collision_Detection_image1.jpg" alt="Collision detection between toolholder and workpiece on ball nut grinding" align="left"/><p>In this worksheet a collision detection performed to determine the minimum safety distance between a tool holder and ball nut on grinding manufacturing. A nonlinear quartic equation system have to be solved by <em>Newton's</em> and <em>Broyden's</em> methods and results are compared with <em>Maple fsolve()</em> command. Users can check the different results by embedded components and animated 3D surface plot.</p>153477Mon, 23 Dec 2013 05:00:00 ZGyörgy HegedûsGyörgy HegedûsClassroom Tips and Techniques: Mathematical Thoughts on the Root Locus
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Under suitable assumptions, the roots of the equation <em>f</em>(<em>z, c</em>) = 0, namely, <em>z</em> = <em>z</em>(<em>c</em>), trace a curve in the complex plane. In engineering feedback-control, such curves are called a <em>root locus</em>. This article examines the parameter-dependence of roots of polynomial and transcendental equations.<img src="/view.aspx?si=153452/thumb.jpg" alt="Classroom Tips and Techniques: Mathematical Thoughts on the Root Locus" align="left"/>Under suitable assumptions, the roots of the equation <em>f</em>(<em>z, c</em>) = 0, namely, <em>z</em> = <em>z</em>(<em>c</em>), trace a curve in the complex plane. In engineering feedback-control, such curves are called a <em>root locus</em>. This article examines the parameter-dependence of roots of polynomial and transcendental equations.153452Tue, 29 Oct 2013 04:00:00 ZDr. Robert LopezDr. Robert LopezClassroom Tips and Techniques: Gems 31-35 from the Red Book of Maple Magic
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Five additional "gems" from the Red Book of Maple Magic are detailed. Gem 31 shows how the updated Explore command can be applied to the numeric solution of an initial-value problem containing parameters. Gem 32 shows some list manipulations. Gem 33 clarifies some issues with the contourplot command, while Gem 34 clarifies some issues with the sample option in the plot command. Finally, Gem 36 examines the Equate command, and its alternatives.<img src="/view.aspx?si=147092/thumb.jpg" alt="Classroom Tips and Techniques: Gems 31-35 from the Red Book of Maple Magic" align="left"/>Five additional "gems" from the Red Book of Maple Magic are detailed. Gem 31 shows how the updated Explore command can be applied to the numeric solution of an initial-value problem containing parameters. Gem 32 shows some list manipulations. Gem 33 clarifies some issues with the contourplot command, while Gem 34 clarifies some issues with the sample option in the plot command. Finally, Gem 36 examines the Equate command, and its alternatives.147092Fri, 10 May 2013 04:00:00 ZDr. Robert LopezDr. Robert LopezClassroom Tips and Techniques: Least-Squares Fits
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<p><span id="ctl00_mainContent__documentViewer" ><span ><span class="body summary">The least-squares fitting of functions to data can be done in Maple with eleven different commands from four different packages. The <em>CurveFitting</em> and LinearAlgebra packages each have a LeastSquares command; the Optimization package has the LSSolve and NLPSolve commands; and the Statistics package has the seven commands Fit, LinearFit, PolynomialFit, ExponentialFit, LogarithmicFit, PowerFit, and NonlinearFit, which can return some measure of regression analysis.</span></span></span></p><img src="/view.aspx?si=140942/image.jpg" alt="Classroom Tips and Techniques: Least-Squares Fits" align="left"/><p><span id="ctl00_mainContent__documentViewer" ><span ><span class="body summary">The least-squares fitting of functions to data can be done in Maple with eleven different commands from four different packages. The <em>CurveFitting</em> and LinearAlgebra packages each have a LeastSquares command; the Optimization package has the LSSolve and NLPSolve commands; and the Statistics package has the seven commands Fit, LinearFit, PolynomialFit, ExponentialFit, LogarithmicFit, PowerFit, and NonlinearFit, which can return some measure of regression analysis.</span></span></span></p>140942Wed, 28 Nov 2012 05:00:00 ZDr. Robert LopezDr. Robert Lopez