New Editor's Choice Applications
http://www.maplesoft.com/applications/EditorsChoice
en-us2016 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemWed, 26 Oct 2016 09:22:25 GMTWed, 26 Oct 2016 09:22:25 GMTThe latest Editor's Choice applications added to the Application Centerhttp://www.mapleprimes.com/images/mapleapps.gifNew Editor's Choice Applications
http://www.maplesoft.com/applications/EditorsChoice
Interactive Country Data Explorer
http://www.maplesoft.com/applications/view.aspx?SID=154181&ref=Feed
This application allows you to choose a set of countries, and then select three of the more than 50 types of statistical data available for those counties, such as life expectancy, literacy rates, health expenditures, and more. You then can visualize how these factors change over time using a BubblePlot. For example, you can select several countries and then visualize how their overall number of internet users has changed along with their gross domestic product, using the x-y axis, while the bubble size shows relative population sizes.<BR><BR>Related MaplePrimes blog post: <A HREF="http://www.mapleprimes.com/maplesoftblog/203857-An-Interactive-Application-For-Exploring">An Interactive Application for Exploring Country Data</A><img src="/view.aspx?si=154181/countrybubble3.PNG" alt="Interactive Country Data Explorer" align="left"/>This application allows you to choose a set of countries, and then select three of the more than 50 types of statistical data available for those counties, such as life expectancy, literacy rates, health expenditures, and more. You then can visualize how these factors change over time using a BubblePlot. For example, you can select several countries and then visualize how their overall number of internet users has changed along with their gross domestic product, using the x-y axis, while the bubble size shows relative population sizes.<BR><BR>Related MaplePrimes blog post: <A HREF="http://www.mapleprimes.com/maplesoftblog/203857-An-Interactive-Application-For-Exploring">An Interactive Application for Exploring Country Data</A>154181Wed, 19 Oct 2016 04:00:00 ZDaniel SkoogDaniel SkoogMatrix Representation of Quantum Entangled States: Understanding Bell's Inequality and Teleportation
http://www.maplesoft.com/applications/view.aspx?SID=154100&ref=Feed
In 1935, Einstein, Podolsky and Rosen published a paper revealing a counter-intuitive situation in quantum mechanics which was later known as the EPR paradox. The phenomenon involved an entangled state., which Schrodinger called "not one but the characteristic trait of quantum mechanics." In textbooks, entanglement is often presented in abstract notations. In popular accounts of quantum mechanics, entanglement is sometimes portrayed as a mystery or even distorted in a nearly pseudoscientific fashion. In this worksheet, we use Maple's LinearAlgebra package to represent quantum states and measurements in matrix form. The famous Bell's inequality and teleportation can be understood using elementary matrix operations.<img src="/view.aspx?si=154100/8df7b465a1583cedab7e3e6452644591.gif" alt="Matrix Representation of Quantum Entangled States: Understanding Bell's Inequality and Teleportation" align="left"/>In 1935, Einstein, Podolsky and Rosen published a paper revealing a counter-intuitive situation in quantum mechanics which was later known as the EPR paradox. The phenomenon involved an entangled state., which Schrodinger called "not one but the characteristic trait of quantum mechanics." In textbooks, entanglement is often presented in abstract notations. In popular accounts of quantum mechanics, entanglement is sometimes portrayed as a mystery or even distorted in a nearly pseudoscientific fashion. In this worksheet, we use Maple's LinearAlgebra package to represent quantum states and measurements in matrix form. The famous Bell's inequality and teleportation can be understood using elementary matrix operations.154100Mon, 09 May 2016 04:00:00 ZDr. Frank WangDr. Frank WangOrdinary differential equation with Laplace Transform
http://www.maplesoft.com/applications/view.aspx?SID=154063&ref=Feed
Here the development of an ordinary differential equation using Laplace transforms, using interactive components. This worksheet is shown for teaching purposes. You can download the file to be used in a class for engineering students. <br/><br/> In Spanish.<img src="/view.aspx?si=154063/tl.png" alt="Ordinary differential equation with Laplace Transform" align="left"/>Here the development of an ordinary differential equation using Laplace transforms, using interactive components. This worksheet is shown for teaching purposes. You can download the file to be used in a class for engineering students. <br/><br/> In Spanish.154063Sat, 19 Mar 2016 04:00:00 ZProf. Lenin Araujo CastilloProf. Lenin Araujo CastilloWorking with Thermophysical Data: Dew-Point and Wet-Bulb Temperature of Air
http://www.maplesoft.com/applications/view.aspx?SID=154054&ref=Feed
Maple can perform calculations and generate visualizations involving thermophysical properties of pure fluids, humid air, and mixtures. Using the dew-point and web-bulb temperature of air as an example, this Tips and Techniques application demonstrates how to access thermophysical properties data, perform calculations that include units, and visualize the results on a psychrometric chart.
<BR><BR>
Atmospheric air contains varying levels of water vapor. Weather reports often quantify the water content of air with its relative humidity; this is the amount of water in air, divided by the maximum amount of water air can hold at the same temperature.
<BR><BR>
Given the temperature and the relative humidity of air, you can calculate:
<UL>
<LI>the temperature below which water condenses out of air - this is known as the dew-point
<LI>the coldest temperature you can achieve through evaporative cooling - this is known as the wet-bulb temperature
</UL><img src="/view.aspx?si=154054/webbulb.PNG" alt="Working with Thermophysical Data: Dew-Point and Wet-Bulb Temperature of Air" align="left"/>Maple can perform calculations and generate visualizations involving thermophysical properties of pure fluids, humid air, and mixtures. Using the dew-point and web-bulb temperature of air as an example, this Tips and Techniques application demonstrates how to access thermophysical properties data, perform calculations that include units, and visualize the results on a psychrometric chart.
<BR><BR>
Atmospheric air contains varying levels of water vapor. Weather reports often quantify the water content of air with its relative humidity; this is the amount of water in air, divided by the maximum amount of water air can hold at the same temperature.
<BR><BR>
Given the temperature and the relative humidity of air, you can calculate:
<UL>
<LI>the temperature below which water condenses out of air - this is known as the dew-point
<LI>the coldest temperature you can achieve through evaporative cooling - this is known as the wet-bulb temperature
</UL>154054Wed, 09 Mar 2016 05:00:00 ZSamir KhanSamir KhanStatically Indeterminate Structure
http://www.maplesoft.com/applications/view.aspx?SID=153940&ref=Feed
The application allows you to determine the constraint reactions, build diagrams of the normal forces N, shear forces Q and bending moments M for beams and frames with any number of sections and degree of static indefinability.
The application calculates the deformation (displacements) of the structure in millimeters and displays the displacements of nodes in the horizontal and vertical. It is also possible to calculate the displacement of any point of the structure.<img src="/view.aspx?si=153940/391e24e981ea8d11454375def604a185.gif" alt="Statically Indeterminate Structure" align="left"/>The application allows you to determine the constraint reactions, build diagrams of the normal forces N, shear forces Q and bending moments M for beams and frames with any number of sections and degree of static indefinability.
The application calculates the deformation (displacements) of the structure in millimeters and displays the displacements of nodes in the horizontal and vertical. It is also possible to calculate the displacement of any point of the structure.153940Wed, 09 Mar 2016 05:00:00 ZDr. Aleksey ShirkoDr. Aleksey ShirkoLattice: A package to model accelerator lattices and beam lines
http://www.maplesoft.com/applications/view.aspx?SID=153970&ref=Feed
The Lattice package is a Maple package to design and analyze charged-particle beam lines and circular machines. It employs a beam-line description using the standard elements (dipoles, quadrupoles and so on) and retains the algebraic power of Maple. Beam-line elements are described using the equations governing the particle motion in algebraic form. In this way it is possible to compute expressions for beam-line parameters like Twiss functions, dispersion and such, for beam
lines or rings, and to perform analysis on these expressions using the full power of Maple.<img src="/view.aspx?si=153970/Lattice.png" alt="Lattice: A package to model accelerator lattices and beam lines" align="left"/>The Lattice package is a Maple package to design and analyze charged-particle beam lines and circular machines. It employs a beam-line description using the standard elements (dipoles, quadrupoles and so on) and retains the algebraic power of Maple. Beam-line elements are described using the equations governing the particle motion in algebraic form. In this way it is possible to compute expressions for beam-line parameters like Twiss functions, dispersion and such, for beam
lines or rings, and to perform analysis on these expressions using the full power of Maple.153970Tue, 01 Mar 2016 05:00:00 ZUli WienandsUli WienandsNonlinear Model Predictive Control
http://www.maplesoft.com/applications/view.aspx?SID=153555&ref=Feed
<p>Nonlinear model predictive control (NMPC) has attracted attention in recent years. The continuation method combined with the generalized minimal residual method (C/GMRES) is well known to be a fast algorithm and is generally suitable for real-time implementation. This package provides a symbolic computation tool that automatically generates code for use in nonlinear predictive control design environment based on C/GMRES. Interaction with the package is done through an easy-to-use document interface.</p>
<p>Note: Requires Maple 17 or later and a C compiler.</p>
<p>Version 1.0.3</p><img src="/view.aspx?si=153555/Capture.PNG" alt="Nonlinear Model Predictive Control" align="left"/><p>Nonlinear model predictive control (NMPC) has attracted attention in recent years. The continuation method combined with the generalized minimal residual method (C/GMRES) is well known to be a fast algorithm and is generally suitable for real-time implementation. This package provides a symbolic computation tool that automatically generates code for use in nonlinear predictive control design environment based on C/GMRES. Interaction with the package is done through an easy-to-use document interface.</p>
<p>Note: Requires Maple 17 or later and a C compiler.</p>
<p>Version 1.0.3</p>153555Fri, 12 Feb 2016 16:38:11 ZCybernet Systems Co.Cybernet Systems Co.The Schwarz-Christoffel panel method: a computational kit
http://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 TerrerosCampo de direcciones: Un caso de estudio.
http://www.maplesoft.com/applications/view.aspx?SID=153954&ref=Feed
En esta hoja se aplica el campo de direcciones al estudio cualitativo de las soluciones de una ecuación diferencial que describe, utilizando un modelo sencillo, el fenómeno de la pesca.
En el modelo se asume que puede exitir sobrepoblación y/o captura, lo que da oportunidad al estudiante de lograr una mayor comprensión del fenómeno, así como de aprender cómo extraer información cualitativa de los campos de direcciones.<img src="/view.aspx?si=153954/Captura.PNG" alt="Campo de direcciones: Un caso de estudio." align="left"/>En esta hoja se aplica el campo de direcciones al estudio cualitativo de las soluciones de una ecuación diferencial que describe, utilizando un modelo sencillo, el fenómeno de la pesca.
En el modelo se asume que puede exitir sobrepoblación y/o captura, lo que da oportunidad al estudiante de lograr una mayor comprensión del fenómeno, así como de aprender cómo extraer información cualitativa de los campos de direcciones.153954Sat, 23 Jan 2016 05:00:00 ZDr. Ranferi GutierrezDr. Ranferi GutierrezHoliday Greetings and Tupper’s Self-Referential Formula
http://www.maplesoft.com/applications/view.aspx?SID=153935&ref=Feed
Want to send a Holiday greeting to a fellow Maple user? Then send them this worksheet - it's a seasonal spin on the classic Tupper’s Self-Referential Formula.<img src="/view.aspx?si=153935/teaserimage.png" alt="Holiday Greetings and Tupper’s Self-Referential Formula" align="left"/>Want to send a Holiday greeting to a fellow Maple user? Then send them this worksheet - it's a seasonal spin on the classic Tupper’s Self-Referential Formula.153935Fri, 11 Dec 2015 05:00:00 ZSamir KhanSamir KhanThe SHA-3 Family of Cryptographic Hash Functions and Extendable-Output Functions
http://www.maplesoft.com/applications/view.aspx?SID=153903&ref=Feed
The National Institute of Standards and Technology (NIST) has released the final version of its "Secure Hash Algorithm-3" (SHA-3) standard in August 2015. The new standard ("Federal Information Processing Standard (FIPS) 202") specifies four cryptographic hash functions, called SHA3-224, SHA3-256, SHA3-384 and SHA3-512, as well as two Extendable-Output Functions (XOFs), called SHAKE128 and SHAKE256. These functions are based on the Keccak sponge function, designed by G. Bertoni, J. Daemen, M. Peeters and G. Van Assche. The hash functions are an essential tool for securing the integrity of electronic information and the XOFs offer the added flexibility of having a variable output length. This application contains an implementation of these functions and also of the SHA-3-based Message Authentication Code HMAC.<img src="/view.aspx?si=153903/keccak.jpg" alt="The SHA-3 Family of Cryptographic Hash Functions and Extendable-Output Functions" align="left"/>The National Institute of Standards and Technology (NIST) has released the final version of its "Secure Hash Algorithm-3" (SHA-3) standard in August 2015. The new standard ("Federal Information Processing Standard (FIPS) 202") specifies four cryptographic hash functions, called SHA3-224, SHA3-256, SHA3-384 and SHA3-512, as well as two Extendable-Output Functions (XOFs), called SHAKE128 and SHAKE256. These functions are based on the Keccak sponge function, designed by G. Bertoni, J. Daemen, M. Peeters and G. Van Assche. The hash functions are an essential tool for securing the integrity of electronic information and the XOFs offer the added flexibility of having a variable output length. This application contains an implementation of these functions and also of the SHA-3-based Message Authentication Code HMAC.153903Fri, 16 Oct 2015 04:00:00 ZJosé Luis Gómez PardoJosé Luis Gómez PardoEscapeTime Fractals
http://www.maplesoft.com/applications/view.aspx?SID=153882&ref=Feed
<P>
The <A HREF="/support/help/Maple/view.aspx?path=Fractals/EscapeTime">Fractals</A> package in Maple makes it easier to create and explore popular fractals, including the Mandelbrot, Julia, Newton, and other time-iterative fractals. The Fractals package can quickly apply various escape time iterative maps over rectangular regions in the complex plane, the results of which consist of images that approximate well-known fractal sets. In the following application, you can explore escape time fractals by manipulating parameters pertaining to the generation of Mandelbrot, Julia, Newton and Burning Ship fractals.</P>
<P>
<B>Also:</B> You can <A HREF="http://maplecloud.maplesoft.com/application.jsp?appId=5690839489576960">interact with this application</A> in the MapleCloud!</P><img src="/view.aspx?si=153882/escapetimefractal.png" alt="EscapeTime Fractals" align="left"/><P>
The <A HREF="/support/help/Maple/view.aspx?path=Fractals/EscapeTime">Fractals</A> package in Maple makes it easier to create and explore popular fractals, including the Mandelbrot, Julia, Newton, and other time-iterative fractals. The Fractals package can quickly apply various escape time iterative maps over rectangular regions in the complex plane, the results of which consist of images that approximate well-known fractal sets. In the following application, you can explore escape time fractals by manipulating parameters pertaining to the generation of Mandelbrot, Julia, Newton and Burning Ship fractals.</P>
<P>
<B>Also:</B> You can <A HREF="http://maplecloud.maplesoft.com/application.jsp?appId=5690839489576960">interact with this application</A> in the MapleCloud!</P>153882Fri, 25 Sep 2015 04:00:00 ZMaplesoftMaplesoftThe SEIR model with births and deaths
http://www.maplesoft.com/applications/view.aspx?SID=153879&ref=Feed
<P>This interactive application explores the SEIR model for the spread of disease. The SEIR model is an extension of the classical SIR (Susceptibles, Infected, Recovered) model, where a fourth compartment is added that contains exposed persons which are infected but are not yet infectious. The SEIR (Susceptibles, Exposed, Infectious, Recovered) model as presented here covers also births and deaths.</P>
<P>
<B>Also:</B> <A HREF="http://maplecloud.maplesoft.com/application.jsp?appId=6407056173039616">View and interact with this app in the MapleCloud!</A></P><img src="/view.aspx?si=153879/seir.png" alt="The SEIR model with births and deaths" align="left"/><P>This interactive application explores the SEIR model for the spread of disease. The SEIR model is an extension of the classical SIR (Susceptibles, Infected, Recovered) model, where a fourth compartment is added that contains exposed persons which are infected but are not yet infectious. The SEIR (Susceptibles, Exposed, Infectious, Recovered) model as presented here covers also births and deaths.</P>
<P>
<B>Also:</B> <A HREF="http://maplecloud.maplesoft.com/application.jsp?appId=6407056173039616">View and interact with this app in the MapleCloud!</A></P>153879Wed, 16 Sep 2015 04:00:00 ZGünter EdenharterGünter EdenharterFitting Wave Height Data to a Probability Distribution
http://www.maplesoft.com/applications/view.aspx?SID=153864&ref=Feed
<p>The University of Maine records real-time accelerometer data from buoys deployed in the Gulf of Maine and Caribbean (http://gyre.umeoce.maine.edu/buoyhome.php). The data can be downloaded from their website, and includes the significant wave height recorded at regular intervals for the last few months.</p>
<p>This application:</p>
<ul>
<li>downloads accelerometer data for Buoy PR206 (located just off the coast of Puerto Rico at a latitude of 18° 28.46' N and a longitude of 66° 5.94' W),</li>
</ul>
<ul>
<li>fits the significant wave height to a Weibull distribution via two methods: maximum likelihood estimation and moment matching,</li>
</ul>
<ul>
<li>and plots the fitted distributions on top of a histogram of the experimental data</li>
</ul>
<p>The location of buoy PR206 is given in a Google Maps component.</p><img src="/view.aspx?si=153864/distribution.jpg" alt="Fitting Wave Height Data to a Probability Distribution" align="left"/><p>The University of Maine records real-time accelerometer data from buoys deployed in the Gulf of Maine and Caribbean (http://gyre.umeoce.maine.edu/buoyhome.php). The data can be downloaded from their website, and includes the significant wave height recorded at regular intervals for the last few months.</p>
<p>This application:</p>
<ul>
<li>downloads accelerometer data for Buoy PR206 (located just off the coast of Puerto Rico at a latitude of 18° 28.46' N and a longitude of 66° 5.94' W),</li>
</ul>
<ul>
<li>fits the significant wave height to a Weibull distribution via two methods: maximum likelihood estimation and moment matching,</li>
</ul>
<ul>
<li>and plots the fitted distributions on top of a histogram of the experimental data</li>
</ul>
<p>The location of buoy PR206 is given in a Google Maps component.</p>153864Wed, 09 Sep 2015 04:00:00 ZSamir KhanSamir KhanTime Series Analysis: Forecasting Average Global Temperatures
http://www.maplesoft.com/applications/view.aspx?SID=153791&ref=Feed
Maple includes powerful tools for accessing, analyzing, and visualizing time series data. This application works with global temperature data to demonstrate techniques for analyzing time series data sets using the TimeSeriesAnalysis package, including visualizing trends and modeling future global temperatures.<img src="/view.aspx?si=153791/thumb.jpg" alt="Time Series Analysis: Forecasting Average Global Temperatures" align="left"/>Maple includes powerful tools for accessing, analyzing, and visualizing time series data. This application works with global temperature data to demonstrate techniques for analyzing time series data sets using the TimeSeriesAnalysis package, including visualizing trends and modeling future global temperatures.153791Tue, 21 Apr 2015 04:00:00 ZDaniel SkoogDaniel SkoogCalibrating Response Curves for the Concentration of Melatonin Sulfate in Human Urine
http://www.maplesoft.com/applications/view.aspx?SID=153783&ref=Feed
<p>This application calibrates response curves against data from an immunoassay that records the concentration of melatonin in human urine and its optical density.</p>
<p>Melatonin is excreted by the pineal gland and regulates human circadian rhythms. Deviations outside of normal boundaries may indicate sleep disorders, depression, schizophrenia, or a range of other conditions.</p><img src="/view.aspx?si=153783/melatonin.png" alt="Calibrating Response Curves for the Concentration of Melatonin Sulfate in Human Urine" align="left"/><p>This application calibrates response curves against data from an immunoassay that records the concentration of melatonin in human urine and its optical density.</p>
<p>Melatonin is excreted by the pineal gland and regulates human circadian rhythms. Deviations outside of normal boundaries may indicate sleep disorders, depression, schizophrenia, or a range of other conditions.</p>153783Thu, 09 Apr 2015 04:00:00 ZSamir KhanSamir KhanInteraural Time Delay
http://www.maplesoft.com/applications/view.aspx?SID=153780&ref=Feed
<p>Humans locate the origin of a sound with several cues. One technique employs the small difference in the time taken for the sound to reach either ear; this is known as the interaural time delay (ITD). This application modifies a single-channel audio file so that the sound appears to originate at an angle from the observer. It does this by introducing an extra channel of sound. Despite both channels having the same amplitude, the sound appears to come from an angle simply by delaying one channel.</p><img src="/view.aspx?si=153780/interaural.png" alt="Interaural Time Delay" align="left"/><p>Humans locate the origin of a sound with several cues. One technique employs the small difference in the time taken for the sound to reach either ear; this is known as the interaural time delay (ITD). This application modifies a single-channel audio file so that the sound appears to originate at an angle from the observer. It does this by introducing an extra channel of sound. Despite both channels having the same amplitude, the sound appears to come from an angle simply by delaying one channel.</p>153780Tue, 31 Mar 2015 04:00:00 ZSamir KhanSamir KhanIs a Stock Overvalued or Undervalued?
http://www.maplesoft.com/applications/view.aspx?SID=153740&ref=Feed
<p>This application calculates the fair value of a stock, given the current market prices and several growth assumptions. Simply pick an industry, stock exchange, and then a company.</p>
<p>Maple then downloads the current market share price, EPS (for the trailing 12 months) and dividends (for the trailing 12 months) from Yahoo Finance (hence a connection to the web is needed). Given a series of growth assumptions, a fair value is then calculated. The valuation process is described at the bottom of this application, and is most appropriate for stable companies with a history of dividend payments.</p>
<p>The stock is undervalued If the fair value is greater than the current market price, and vice-versa.</p>
<p>This application comes with an Excel spreadsheet with a list of over 25000 companies across multiple industries and international exchanges, and their corresponding ticker symbols. This spreadsheet is used to populate the interface with industries, exchanges and companies, and must be saved in the same location as the Maple worksheet.</p><img src="/view.aspx?si=153740/stockovervalued.png" alt="Is a Stock Overvalued or Undervalued?" align="left"/><p>This application calculates the fair value of a stock, given the current market prices and several growth assumptions. Simply pick an industry, stock exchange, and then a company.</p>
<p>Maple then downloads the current market share price, EPS (for the trailing 12 months) and dividends (for the trailing 12 months) from Yahoo Finance (hence a connection to the web is needed). Given a series of growth assumptions, a fair value is then calculated. The valuation process is described at the bottom of this application, and is most appropriate for stable companies with a history of dividend payments.</p>
<p>The stock is undervalued If the fair value is greater than the current market price, and vice-versa.</p>
<p>This application comes with an Excel spreadsheet with a list of over 25000 companies across multiple industries and international exchanges, and their corresponding ticker symbols. This spreadsheet is used to populate the interface with industries, exchanges and companies, and must be saved in the same location as the Maple worksheet.</p>153740Tue, 20 Jan 2015 05:00:00 ZSamir KhanSamir KhanOrbitals Package
http://www.maplesoft.com/applications/view.aspx?SID=4865&ref=Feed
The Orbitals package evaluates, plots and calculates atomic orbitals, overlap integrals, and atomic four-electron integrals for hydrogenic or Slater-type orbitals. This is an update of an earlier 2007 version.<img src="/view.aspx?si=4865/orbits.jpg" alt="Orbitals Package" align="left"/>The Orbitals package evaluates, plots and calculates atomic orbitals, overlap integrals, and atomic four-electron integrals for hydrogenic or Slater-type orbitals. This is an update of an earlier 2007 version.4865Tue, 06 Jan 2015 05:00:00 ZDavid HarringtonDavid HarringtonCalculating Gaussian Curvature Using Differential Forms
http://www.maplesoft.com/applications/view.aspx?SID=153720&ref=Feed
<p>Riemannian geometry is customarily developed by tensor methods, which is not necessarily the most computationally efficient approach. Using the language of differential forms, Elie Cartan's formulation of the Riemannian geometry can be elegantly summarized in two structural equations. Essentially, the local curvature of the manifold is a measure of how the connection varies from point to point. This Maple worksheet uses the <strong>DifferentialGeometry</strong> package to solves three problems in Harley Flanders' book on differential forms to demonstrate the implementation of Cartan's method. </p><img src="/view.aspx?si=153720/c119c404932805fdc4af274016b48a13.gif" alt="Calculating Gaussian Curvature Using Differential Forms" align="left"/><p>Riemannian geometry is customarily developed by tensor methods, which is not necessarily the most computationally efficient approach. Using the language of differential forms, Elie Cartan's formulation of the Riemannian geometry can be elegantly summarized in two structural equations. Essentially, the local curvature of the manifold is a measure of how the connection varies from point to point. This Maple worksheet uses the <strong>DifferentialGeometry</strong> package to solves three problems in Harley Flanders' book on differential forms to demonstrate the implementation of Cartan's method. </p>153720Tue, 09 Dec 2014 05:00:00 ZDr. Frank WangDr. Frank Wang