Linear Algebra: New Applications
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en-us2020 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemThu, 13 Aug 2020 17:48:09 GMTThu, 13 Aug 2020 17:48:09 GMTNew applications in the Linear Algebra categoryhttps://www.maplesoft.com/images/Application_center_hp.jpgLinear Algebra: New Applications
https://www.maplesoft.com/applications/category.aspx?cid=2882
Eigenpairs: What are they and how they are found
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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.
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<B>View the Recorded Webinar:</B><BR>
<A HREF="/webinars/recorded/featured.aspx?id=1181">Eigenpairs in Maple</A><img src="https://www.maplesoft.com/view.aspx?si=154291/eigenpair.jpg" alt="Eigenpairs: What are they and how they are found" style="max-width: 25%;" 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.
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<B>View the Recorded Webinar:</B><BR>
<A HREF="/webinars/recorded/featured.aspx?id=1181">Eigenpairs in Maple</A>https://www.maplesoft.com/applications/view.aspx?SID=154291&ref=FeedFri, 25 Aug 2017 04:00:00 ZDr. Robert LopezDr. Robert LopezMathematics for Chemistry
https://www.maplesoft.com/applications/view.aspx?SID=154267&ref=Feed
This interactive electronic textbook in the form of Maple worksheets comprises two parts.
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Part I, mathematics for chemistry, is supposed to cover all mathematics that an instructor of chemistry might hope and expect that his students would learn, understand and be able to apply as a result of sufficient courses typically, but not exclusively, presented in departments of mathematics. Its nine chapters include (0) a summary and illustration of useful Maple commands, (1) arithmetic, algebra and elementary functions, (2) plotting, descriptive geometry, trigonometry, series, complex functions, (3) differential calculus of one variable, (4) integral calculus of one variable, (5) multivariate calculus, (6) linear algebra including matrix, vector, eigenvector, vector calculus, tensor, spreadsheet, (7) differential and integral equations, and (8) probability, distribution, treatment of laboratory data, linear and non-linear regression and optimization.
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Part II presents mathematical topics typically taught within chemistry courses, including (9) chemical equilibrium, (10) group theory, (11) graph theory, (12a) introduction to quantum mechanics and quantum chemistry, (14) applications of Fourier transforms in chemistry including electron diffraction, x-ray diffraction, microwave spectra, infrared and Raman spectra and nuclear-magnetic-resonance spectra, and (18) dielectric and magnetic properties of chemical matter.
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Other chapters are in preparation and will be released in due course.
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Last updated on March 19, 2019<img src="https://www.maplesoft.com/view.aspx?si=154267/molecule.PNG" alt="Mathematics for Chemistry" style="max-width: 25%;" align="left"/>This interactive electronic textbook in the form of Maple worksheets comprises two parts.
<BR><BR>
Part I, mathematics for chemistry, is supposed to cover all mathematics that an instructor of chemistry might hope and expect that his students would learn, understand and be able to apply as a result of sufficient courses typically, but not exclusively, presented in departments of mathematics. Its nine chapters include (0) a summary and illustration of useful Maple commands, (1) arithmetic, algebra and elementary functions, (2) plotting, descriptive geometry, trigonometry, series, complex functions, (3) differential calculus of one variable, (4) integral calculus of one variable, (5) multivariate calculus, (6) linear algebra including matrix, vector, eigenvector, vector calculus, tensor, spreadsheet, (7) differential and integral equations, and (8) probability, distribution, treatment of laboratory data, linear and non-linear regression and optimization.
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Part II presents mathematical topics typically taught within chemistry courses, including (9) chemical equilibrium, (10) group theory, (11) graph theory, (12a) introduction to quantum mechanics and quantum chemistry, (14) applications of Fourier transforms in chemistry including electron diffraction, x-ray diffraction, microwave spectra, infrared and Raman spectra and nuclear-magnetic-resonance spectra, and (18) dielectric and magnetic properties of chemical matter.
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Other chapters are in preparation and will be released in due course.
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Last updated on March 19, 2019https://www.maplesoft.com/applications/view.aspx?SID=154267&ref=FeedTue, 30 May 2017 04:00:00 ZJohn OgilvieJohn OgilvieInternet Page Ranking Algorithms
https://www.maplesoft.com/applications/view.aspx?SID=153532&ref=Feed
In this guest article in the Tips and Techniques series, Dr. Michael Monagan explains how internet pages are ranked.<img src="https://www.maplesoft.com/view.aspx?si=153532/thumb.jpg" alt="Internet Page Ranking Algorithms" style="max-width: 25%;" align="left"/>In this guest article in the Tips and Techniques series, Dr. Michael Monagan explains how internet pages are ranked.https://www.maplesoft.com/applications/view.aspx?SID=153532&ref=FeedThu, 20 Mar 2014 04:00:00 ZProf. Michael MonaganProf. Michael MonaganApplication of the Modified Gram-Schmidt Algorithm
https://www.maplesoft.com/applications/view.aspx?SID=152382&ref=Feed
<p>Maple's QRDecomposition command basically utilizes one of two routines for generating the Q and R matrices. If the matrix contains only integers and/or symbolic expressions, then Maple performs a QR decomposition using the Classical Gram-Schmidt algorithm. If however, the matrix contains a mixture of integers and floating point decimals or only floating point decimals, then Maple carries out the QR decomposition of the matrix using Householder transformations. My approach below uses a third alternative, the Modified Gram-Schmidt algorithm, which I read about in Chapter 8 of the textbook, NUMERICAL LINEAR ALGEBRA, by Lloyd N. Trefethen and David Bau III.</p><img src="https://www.maplesoft.com/view.aspx?si=152382/05160ad08a75a6b7948e889b5999f0ea.gif" alt="Application of the Modified Gram-Schmidt Algorithm" style="max-width: 25%;" align="left"/><p>Maple's QRDecomposition command basically utilizes one of two routines for generating the Q and R matrices. If the matrix contains only integers and/or symbolic expressions, then Maple performs a QR decomposition using the Classical Gram-Schmidt algorithm. If however, the matrix contains a mixture of integers and floating point decimals or only floating point decimals, then Maple carries out the QR decomposition of the matrix using Householder transformations. My approach below uses a third alternative, the Modified Gram-Schmidt algorithm, which I read about in Chapter 8 of the textbook, NUMERICAL LINEAR ALGEBRA, by Lloyd N. Trefethen and David Bau III.</p>https://www.maplesoft.com/applications/view.aspx?SID=152382&ref=FeedTue, 01 Oct 2013 04:00:00 ZDouglas LewitDouglas Lewit