John Ogilvie: New Applications
https://www.maplesoft.com/applications/author.aspx?mid=152
en-us2020 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemWed, 15 Jul 2020 09:26:34 GMTWed, 15 Jul 2020 09:26:34 GMTNew applications published by John Ogilviehttps://www.maplesoft.com/images/Application_center_hp.jpgJohn Ogilvie: New Applications
https://www.maplesoft.com/applications/author.aspx?mid=152
Mathematics 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.
<BR><BR>
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.
<BR><BR>
Other chapters are in preparation and will be released in due course.
<BR><BR>
Last updated on March 19, 2019https://www.maplesoft.com/applications/view.aspx?SID=154267&ref=FeedTue, 30 May 2017 04:00:00 ZJohn OgilvieJohn OgilvieOptimization with sequential simplex of variable size
https://www.maplesoft.com/applications/view.aspx?SID=4289&ref=Feed
We present an algorithm for unconstrained optimization of experimental data in chemical kinetics using as method a sequential simplex of variable size. An animated plot of progress of a triangular simplex descending across a surface of to converge to an absolute minimum illustrates an implementation of this approach.<img src="https://www.maplesoft.com/view.aspx?si=4289//applications/images/app_image_blank_lg.jpg" alt="Optimization with sequential simplex of variable size" style="max-width: 25%;" align="left"/>We present an algorithm for unconstrained optimization of experimental data in chemical kinetics using as method a sequential simplex of variable size. An animated plot of progress of a triangular simplex descending across a surface of to converge to an absolute minimum illustrates an implementation of this approach.https://www.maplesoft.com/applications/view.aspx?SID=4289&ref=FeedWed, 31 Jul 2002 16:59:27 ZProf. J. OgilvieProf. J. OgilvieTrajectory Near a Black Hole: an application of Lagrangian mechanics
https://www.maplesoft.com/applications/view.aspx?SID=4240&ref=Feed
The lagrangian formulation of mechanics has great advantages in practical use. Calculations of this type require finding the derivative of a function with respect to another function. Although our method is a pedagogic approach that might involve longer steps, it is a straightforward attack on this problem, and practically all problems in classical mechanics can be solved once the lagrangian is found. In most real physics problems, there are no analytic solutions to differential equations. We particularly emphasize forming plots numerically. We introduce an example in general relativity, to find the trajectory of a particle near a black hole, which corresponds to the shortest path between two points in a curved space.<img src="https://www.maplesoft.com/view.aspx?si=4240//applications/images/app_image_blank_lg.jpg" alt="Trajectory Near a Black Hole: an application of Lagrangian mechanics " style="max-width: 25%;" align="left"/>The lagrangian formulation of mechanics has great advantages in practical use. Calculations of this type require finding the derivative of a function with respect to another function. Although our method is a pedagogic approach that might involve longer steps, it is a straightforward attack on this problem, and practically all problems in classical mechanics can be solved once the lagrangian is found. In most real physics problems, there are no analytic solutions to differential equations. We particularly emphasize forming plots numerically. We introduce an example in general relativity, to find the trajectory of a particle near a black hole, which corresponds to the shortest path between two points in a curved space.https://www.maplesoft.com/applications/view.aspx?SID=4240&ref=FeedTue, 12 Mar 2002 11:24:18 ZProf. J. OgilvieProf. J. OgilvieMotion of a Heavy Symmetric Top
https://www.maplesoft.com/applications/view.aspx?SID=4161&ref=Feed
Calculus of variations involves finding a derivative of a function with respect to a function, which Maple does not directly support. With simple substitution, we can, however, solve easily a problem of this type without invoking an external library. We use a problem in classical mechanics to illustrate a procedure to solve the Euler-Lagrange equation, which is the most important application of calculus of variations.<img src="https://www.maplesoft.com/view.aspx?si=4161//applications/images/app_image_blank_lg.jpg" alt="Motion of a Heavy Symmetric Top" style="max-width: 25%;" align="left"/>Calculus of variations involves finding a derivative of a function with respect to a function, which Maple does not directly support. With simple substitution, we can, however, solve easily a problem of this type without invoking an external library. We use a problem in classical mechanics to illustrate a procedure to solve the Euler-Lagrange equation, which is the most important application of calculus of variations.https://www.maplesoft.com/applications/view.aspx?SID=4161&ref=FeedMon, 05 Nov 2001 10:42:57 ZProf. J. OgilvieProf. J. OgilvieVibrational and rotational spectra of diatomic molecules
https://www.maplesoft.com/applications/view.aspx?SID=3891&ref=Feed
This Maple work sheet contains procedures in four suites described in journal MapleTech [volume 5 , 1998, No. 1, pages 42 - 46] for symbolic computation in Maple 6 to form the principal expressions required to undertake a comprehensive analysis of vibration-rotational spectra of diatomic molecules in an electronic state according to conventional analytic treatment in the spirit of Dunham (cf. J. F. Ogilvie, The Vibrational and Rotational Spectrometry of Diatomic Molecules , Academic Press, London, 1998).<img src="https://www.maplesoft.com/view.aspx?si=3891//applications/images/app_image_blank_lg.jpg" alt="Vibrational and rotational spectra of diatomic molecules " style="max-width: 25%;" align="left"/>This Maple work sheet contains procedures in four suites described in journal MapleTech [volume 5 , 1998, No. 1, pages 42 - 46] for symbolic computation in Maple 6 to form the principal expressions required to undertake a comprehensive analysis of vibration-rotational spectra of diatomic molecules in an electronic state according to conventional analytic treatment in the spirit of Dunham (cf. J. F. Ogilvie, The Vibrational and Rotational Spectrometry of Diatomic Molecules , Academic Press, London, 1998).https://www.maplesoft.com/applications/view.aspx?SID=3891&ref=FeedWed, 20 Jun 2001 00:00:00 ZF. FernandezF. FernandezDiatomic anharmonic oscillator
https://www.maplesoft.com/applications/view.aspx?SID=3878&ref=Feed
The calculation undertaken here employs perturbation theory of multiple orders; the extent of the calculation, according to the order, is adjustable by a user within limitations of machine capacity and acceptable duration of calculation.<img src="https://www.maplesoft.com/view.aspx?si=3878//applications/images/app_image_blank_lg.jpg" alt="Diatomic anharmonic oscillator" style="max-width: 25%;" align="left"/>The calculation undertaken here employs perturbation theory of multiple orders; the extent of the calculation, according to the order, is adjustable by a user within limitations of machine capacity and acceptable duration of calculation.https://www.maplesoft.com/applications/view.aspx?SID=3878&ref=FeedWed, 20 Jun 2001 00:00:00 ZMichael MonaganMichael MonaganVibrational and rotational spectrometry of diatomic molecules
https://www.maplesoft.com/applications/view.aspx?SID=3877&ref=Feed
This Maple work sheet contains procedures in four suites for symbolic computation in Maple 6 to form the principal expressions required to undertake a comprehensive analysis of vibration-rotational spectra of diatomic molecules in an electronic state according to conventional analytic treatment in the spirit of Dunham.<img src="https://www.maplesoft.com/view.aspx?si=3877//applications/images/app_image_blank_lg.jpg" alt="Vibrational and rotational spectrometry of diatomic molecules" style="max-width: 25%;" align="left"/>This Maple work sheet contains procedures in four suites for symbolic computation in Maple 6 to form the principal expressions required to undertake a comprehensive analysis of vibration-rotational spectra of diatomic molecules in an electronic state according to conventional analytic treatment in the spirit of Dunham.https://www.maplesoft.com/applications/view.aspx?SID=3877&ref=FeedWed, 20 Jun 2001 00:00:00 ZF. FernandezF. FernandezEstimation of Franck-Condon factors with model wave functions
https://www.maplesoft.com/applications/view.aspx?SID=3856&ref=Feed
The integrated intensity of each band in a system corresponding to transitions between two electronic states of a diatomic molecule is proportional to the square of a matrix element that one can form according to wave mechanics by integration of electronic and vibrational wave functions over electronic and nuclear coordinates. This matrix element can be taken to be a product of a factor involving electronic wave functions and a factor that is the square of an integral of wave functions of vibrational states; this squared integral is called a Franck-Condon factor, and this worksheet enables estimation of this quantity using vibrational wave functions of either an harmonic oscillator or a Morse oscillator.
<img src="https://www.maplesoft.com/view.aspx?si=3856//applications/images/app_image_blank_lg.jpg" alt="Estimation of Franck-Condon factors with model wave functions " style="max-width: 25%;" align="left"/>The integrated intensity of each band in a system corresponding to transitions between two electronic states of a diatomic molecule is proportional to the square of a matrix element that one can form according to wave mechanics by integration of electronic and vibrational wave functions over electronic and nuclear coordinates. This matrix element can be taken to be a product of a factor involving electronic wave functions and a factor that is the square of an integral of wave functions of vibrational states; this squared integral is called a Franck-Condon factor, and this worksheet enables estimation of this quantity using vibrational wave functions of either an harmonic oscillator or a Morse oscillator.
https://www.maplesoft.com/applications/view.aspx?SID=3856&ref=FeedWed, 20 Jun 2001 00:00:00 ZGreg FeeGreg Fee