Engineering Mathematics: New Applications
http://www.maplesoft.com/applications/category.aspx?cid=138
en-us2017 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemSat, 18 Nov 2017 21:15:01 GMTSat, 18 Nov 2017 21:15:01 GMTNew applications in the Engineering Mathematics categoryhttp://www.mapleprimes.com/images/mapleapps.gifEngineering Mathematics: New Applications
http://www.maplesoft.com/applications/category.aspx?cid=138
Moment of a force using vectors
https://www.maplesoft.com/applications/view.aspx?SID=154345&ref=Feed
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="/view.aspx?si=154345/moment of force.PNG" alt="Moment of a force using vectors" 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.154345Tue, 26 Sep 2017 04:00:00 ZProf. Lenin Araujo CastilloProf. Lenin Araujo CastilloVector space with projections and forces
https://www.maplesoft.com/applications/view.aspx?SID=154294&ref=Feed
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="/view.aspx?si=154294/vectors.PNG" alt="Vector space with projections and forces" 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.154294Mon, 11 Sep 2017 04:00:00 ZProf. Lenin Araujo CastilloProf. Lenin Araujo CastilloDisplacement and distance traveled with vectors
https://www.maplesoft.com/applications/view.aspx?SID=154293&ref=Feed
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="/view.aspx?si=154293/desplvp.png" alt="Displacement and distance traveled with vectors" 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.154293Mon, 28 Aug 2017 04:00:00 ZProf. Lenin Araujo CastilloProf. Lenin Araujo CastilloEigenpairs: What are they and how they are found
https://www.maplesoft.com/applications/view.aspx?SID=154291&ref=Feed
Clearly, Maple can compute eigenpairs (eigenvalues and eigenvectors) for a matrix, but of what help is Maple in getting across the concept of an eigenpair, and relating that insight to the standard algorithms students are expected to use to find them? This application is the companion Maple document to the webinar “Eigenpairs in Maple”, presented by Dr. Robert Lopez. In both the webinar and this application, he demonstrates how Maple can enhance the task of teaching the eigenpair concept, and shows how Maple bridges the gap between the concept and the algorithms.
<BR><BR>
<B>View the Recorded Webinar:</B><BR>
<A HREF="/webinars/recorded/featured.aspx?id=1181">Eigenpairs in Maple</A><img src="/view.aspx?si=154291/eigenpair.jpg" alt="Eigenpairs: What are they and how they are found" align="left"/>Clearly, Maple can compute eigenpairs (eigenvalues and eigenvectors) for a matrix, but of what help is Maple in getting across the concept of an eigenpair, and relating that insight to the standard algorithms students are expected to use to find them? This application is the companion Maple document to the webinar “Eigenpairs in Maple”, presented by Dr. Robert Lopez. In both the webinar and this application, he demonstrates how Maple can enhance the task of teaching the eigenpair concept, and shows how Maple bridges the gap between the concept and the algorithms.
<BR><BR>
<B>View the Recorded Webinar:</B><BR>
<A HREF="/webinars/recorded/featured.aspx?id=1181">Eigenpairs in Maple</A>154291Fri, 25 Aug 2017 04:00:00 ZDr. Robert LopezDr. Robert LopezPlot of Position Vector
https://www.maplesoft.com/applications/view.aspx?SID=154290&ref=Feed
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="/view.aspx?si=154290/bnrvp.png" alt="Plot of Position Vector" 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.154290Thu, 10 Aug 2017 04:00:00 ZProf. Lenin Araujo CastilloProf. Lenin Araujo CastilloClassroom Tips and Techniques: Roles for the Laplace Transform's Shifting Laws
https://www.maplesoft.com/applications/view.aspx?SID=1723&ref=Feed
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="/view.aspx?si=1723/laplace.PNG" alt="Classroom Tips and Techniques: Roles for the Laplace Transform's Shifting Laws" 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)1723Tue, 25 Apr 2017 04:00:00 ZDr. Robert LopezDr. Robert LopezUniversal method of kinematic analysis of spatial and planar link mechanisms
https://www.maplesoft.com/applications/view.aspx?SID=154228&ref=Feed
The application of idea Draghilev method of solving systems of nonlinear equations for the kinematic analysis of link mechanisms with any number degrees of freedom.<img src="/view.aspx?si=154228/fig_2.jpg" alt="Universal method of kinematic analysis of spatial and planar link mechanisms" align="left"/>The application of idea Draghilev method of solving systems of nonlinear equations for the kinematic analysis of link mechanisms with any number degrees of freedom.154228Wed, 08 Mar 2017 05:00:00 ZAlexey IvanovAlexey IvanovPulsdruckwerte aus Langzeitmessung
https://www.maplesoft.com/applications/view.aspx?SID=154144&ref=Feed
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
https://www.maplesoft.com/applications/view.aspx?SID=154139&ref=Feed
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
https://www.maplesoft.com/applications/view.aspx?SID=154087&ref=Feed
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.
https://www.maplesoft.com/applications/view.aspx?SID=154071&ref=Feed
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/vpThumb.jpg" 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
https://www.maplesoft.com/applications/view.aspx?SID=153963&ref=Feed
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
https://www.maplesoft.com/applications/view.aspx?SID=153939&ref=Feed
<P>This application shows several examples of modeling using delay differential equations in Maple. These examples are from the webinar <A HREF="http://www.maplesoft.com/products/maple/demo/player/2015/solvingdelaydiffeq.aspx">Solving Delay Differential Equations</A>.</P>
<P>Note: Requires Maple 2015.2 or later.</P><img src="/view.aspx?si=153939/dde.PNG" alt="Demo Worksheet for Numerical Delay Differential Equation Solution" align="left"/><P>This application shows several examples of modeling using delay differential equations in Maple. These examples are from the webinar <A HREF="http://www.maplesoft.com/products/maple/demo/player/2015/solvingdelaydiffeq.aspx">Solving Delay Differential Equations</A>.</P>
<P>Note: Requires Maple 2015.2 or later.</P>153939Wed, 16 Dec 2015 05:00:00 ZAllan WittkopfAllan WittkopfNonlinear Viscoelastic Behaviour of Brain Tissue
https://www.maplesoft.com/applications/view.aspx?SID=153923&ref=Feed
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
https://www.maplesoft.com/applications/view.aspx?SID=153895&ref=Feed
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
https://www.maplesoft.com/applications/view.aspx?SID=153835&ref=Feed
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
https://www.maplesoft.com/applications/view.aspx?SID=153813&ref=Feed
<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
https://www.maplesoft.com/applications/view.aspx?SID=153796&ref=Feed
<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
https://www.maplesoft.com/applications/view.aspx?SID=153659&ref=Feed
<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
https://www.maplesoft.com/applications/view.aspx?SID=153592&ref=Feed
<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 Khan