Calculus III: New Applications
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en-us2021 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemMon, 27 Sep 2021 17:00:07 GMTMon, 27 Sep 2021 17:00:07 GMTNew applications in the Calculus III categoryhttps://www.maplesoft.com/images/Application_center_hp.jpgCalculus III: New Applications
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Mathematics for Chemistry
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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,b,c) introduction to quantum mechanics and quantum chemistry, (13) optical molecular spectrometry, (14) applications of Fourier transforms in chemistry including electron diffraction, x-ray diffraction, microwave spectra, infrared and Raman spectra and nuclear-magnetic-resonance spectra, (15) advanced chemical kinetics, and (16) dielectric and magnetic properties of chemical matter.
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Also included in this collection are an essay on Teaching Mathematics to Chemistry Students with Symbolic Computation and a periodic chart of the chemical elements incorporating various
data on elemental properties.
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Edition 6.
Last updated Aug. 15, 2021.<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,b,c) introduction to quantum mechanics and quantum chemistry, (13) optical molecular spectrometry, (14) applications of Fourier transforms in chemistry including electron diffraction, x-ray diffraction, microwave spectra, infrared and Raman spectra and nuclear-magnetic-resonance spectra, (15) advanced chemical kinetics, and (16) dielectric and magnetic properties of chemical matter.
<br><br>
Also included in this collection are an essay on Teaching Mathematics to Chemistry Students with Symbolic Computation and a periodic chart of the chemical elements incorporating various
data on elemental properties.
<br><br>
Edition 6.
Last updated Aug. 15, 2021.https://www.maplesoft.com/applications/view.aspx?SID=154267&ref=FeedThu, 19 Aug 2021 14:22:04 ZJohn OgilvieJohn OgilvieIntegration by Pullback
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The calculus of differential forms is a powerful tool that unifies and simplifies many mathematical concepts. We use the Pullback command in Maple's DifferentialGeometry package to perform double, triple, line and surface integrals in James Stewart's Calculus to demonstrate the method differential forms and show the connection among these integrals.<img src="https://www.maplesoft.com/view.aspx?si=154643/flux.png" alt="Integration by Pullback" style="max-width: 25%;" align="left"/>The calculus of differential forms is a powerful tool that unifies and simplifies many mathematical concepts. We use the Pullback command in Maple's DifferentialGeometry package to perform double, triple, line and surface integrals in James Stewart's Calculus to demonstrate the method differential forms and show the connection among these integrals.https://www.maplesoft.com/applications/view.aspx?SID=154643&ref=FeedSun, 24 May 2020 04:00:00 ZDr. Frank WangDr. Frank WangApplications of Differential Forms in Thermodynamics
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We use Maple's DifferentialGeometry package to derive Maxwell and other mathematical identities in thermodynamics.<img src="https://www.maplesoft.com/view.aspx?si=154631/gradS.png" alt="Applications of Differential Forms in Thermodynamics" style="max-width: 25%;" align="left"/>We use Maple's DifferentialGeometry package to derive Maxwell and other mathematical identities in thermodynamics.https://www.maplesoft.com/applications/view.aspx?SID=154631&ref=FeedSat, 11 Apr 2020 04:00:00 ZDr. Frank WangDr. Frank WangFirst equilibrium condition
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With this application our students of science and engineering in the areas of physics will check the first condition of balance using Maple technology. Only with entering mass and angles we obtain graphs and data for a better interpretation.<img src="https://www.maplesoft.com/view.aspx?si=154624/first_eq.png" alt="First equilibrium condition" style="max-width: 25%;" align="left"/>With this application our students of science and engineering in the areas of physics will check the first condition of balance using Maple technology. Only with entering mass and angles we obtain graphs and data for a better interpretation.https://www.maplesoft.com/applications/view.aspx?SID=154624&ref=FeedWed, 01 Apr 2020 04:00:00 ZLenin Araujo CastilloLenin Araujo CastilloPole simulation with tensions
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Application developed using Maple and MapleSim. You can observe the vector analysis using Maple and the simulation using MapleSim. Also included a video of the result. It is a simple structure. A pole fastened by two cables and a force applied to the top. The results are to calculate tensions one and two. Consider the mass of each rope. In Spanish.<img src="https://www.maplesoft.com/view.aspx?si=154577/structure.png" alt="Pole simulation with tensions" style="max-width: 25%;" align="left"/>Application developed using Maple and MapleSim. You can observe the vector analysis using Maple and the simulation using MapleSim. Also included a video of the result. It is a simple structure. A pole fastened by two cables and a force applied to the top. The results are to calculate tensions one and two. Consider the mass of each rope. In Spanish.https://www.maplesoft.com/applications/view.aspx?SID=154577&ref=FeedMon, 14 Oct 2019 04:00:00 ZProf. Lenin Araujo CastilloProf. Lenin Araujo CastilloIdentificacion de ecuaciones de paraboloides
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Esta hoja permite al alumno entrenar su razonamiento para identificar la ecuación correspondiente a cada uno de los distintos paraboloides mostrados en la misma, entre un conjunto de opciones de respuesta.
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Se enfatiza, a través de un ejemplo, que el estudiante debe observar aspectos como orientación del paraboloide, coordenadas del vértice, entre otros, para tratar de deducir la ecuación que le corresponde, entre un conjunto de opciones.
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Al final de la hoja se proporcionan las respuestas a los ejercicios propuestos.<img src="https://www.maplesoft.com/view.aspx?si=154490/Figura_12.png" alt="Identificacion de ecuaciones de paraboloides" style="max-width: 25%;" align="left"/>Esta hoja permite al alumno entrenar su razonamiento para identificar la ecuación correspondiente a cada uno de los distintos paraboloides mostrados en la misma, entre un conjunto de opciones de respuesta.
<BR><BR>
Se enfatiza, a través de un ejemplo, que el estudiante debe observar aspectos como orientación del paraboloide, coordenadas del vértice, entre otros, para tratar de deducir la ecuación que le corresponde, entre un conjunto de opciones.
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Al final de la hoja se proporcionan las respuestas a los ejercicios propuestos.https://www.maplesoft.com/applications/view.aspx?SID=154490&ref=FeedTue, 18 Sep 2018 04:00:00 ZRanferi GutierrezRanferi GutierrezPlot of curvature and radius of curvature
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This app is basically made for engineering students. Calculate the curvature and radius of curvature of two trajectories given its vector position for times greater than zero seconds. You will observe the graphs Curvature vs time and also radius of curvature vs time and finally the graphs of the two trajectories. A student of civil engineering can use this app without problem to compare if the two highways are parallel and optimal for its construction. Each graph with its corresponding data table and its respective equation. In spanish.<img src="https://www.maplesoft.com/view.aspx?si=154486/radcurv.png" alt="Plot of curvature and radius of curvature" style="max-width: 25%;" align="left"/>This app is basically made for engineering students. Calculate the curvature and radius of curvature of two trajectories given its vector position for times greater than zero seconds. You will observe the graphs Curvature vs time and also radius of curvature vs time and finally the graphs of the two trajectories. A student of civil engineering can use this app without problem to compare if the two highways are parallel and optimal for its construction. Each graph with its corresponding data table and its respective equation. In spanish.https://www.maplesoft.com/applications/view.aspx?SID=154486&ref=FeedMon, 03 Sep 2018 04:00:00 ZLenin Araujo CastilloLenin Araujo CastilloInterpretación geométrica del proceso de solución de una ecuación trigonométrica
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Esta aplicación tiene como objetivo ayudar al estudiante a comprender el significado geométrico de resolver la ecuación trigonométrica sen(theta) = c en un intervalo de longitud 2Pi.
La barra deslizante de la aplicación permite variar el valor de c, mientras que los gráficos ayudan al estudiante a visualizar y comprender el proceso de búsqueda de soluciones de la ecuación trigonométrica de interés.<img src="https://www.maplesoft.com/view.aspx?si=154110/app.png" alt="Interpretación geométrica del proceso de solución de una ecuación trigonométrica" style="max-width: 25%;" align="left"/>Esta aplicación tiene como objetivo ayudar al estudiante a comprender el significado geométrico de resolver la ecuación trigonométrica sen(theta) = c en un intervalo de longitud 2Pi.
La barra deslizante de la aplicación permite variar el valor de c, mientras que los gráficos ayudan al estudiante a visualizar y comprender el proceso de búsqueda de soluciones de la ecuación trigonométrica de interés.https://www.maplesoft.com/applications/view.aspx?SID=154110&ref=FeedWed, 06 Jun 2018 04:00:00 ZRanferi GutierrezRanferi GutierrezSolving 2nd Order Differential Equations
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This worksheet illustrates how to use Maple to solve examples of homogeneous and non-homogeneous second order differential equations, including several different methods for visualizing solutions.<img src="https://www.maplesoft.com/view.aspx?si=154426/2nd_order_des.PNG" alt="Solving 2nd Order Differential Equations" style="max-width: 25%;" align="left"/>This worksheet illustrates how to use Maple to solve examples of homogeneous and non-homogeneous second order differential equations, including several different methods for visualizing solutions.https://www.maplesoft.com/applications/view.aspx?SID=154426&ref=FeedMon, 26 Mar 2018 04:00:00 ZEmilee CarsonEmilee CarsonSolving ODEs using Maple: An Introduction
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In Maple it is easy to solve a differential equation. In this worksheet, we show the basic syntax. With this you should be able to use the same basic commands to solve many second-order DEs.<img src="https://www.maplesoft.com/view.aspx?si=154422/ode.PNG" alt="Solving ODEs using Maple: An Introduction" style="max-width: 25%;" align="left"/>In Maple it is easy to solve a differential equation. In this worksheet, we show the basic syntax. With this you should be able to use the same basic commands to solve many second-order DEs.https://www.maplesoft.com/applications/view.aspx?SID=154422&ref=FeedFri, 23 Mar 2018 04:00:00 ZDr. Francis PoulinDr. Francis PoulinGenerator of exercises with vectors
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Application created for teachers. This works to evaluate the students on the blackboard simultaneously on the topics of vector sum, direction, unit vector and projections. Perform the generation of exercises through patterns so that teachers can rescue their answers. Created professors of universities and engineering students. In Spanish.<img src="https://www.maplesoft.com/view.aspx?si=154371/appteach.png" alt="Generator of exercises with vectors" style="max-width: 25%;" align="left"/>Application created for teachers. This works to evaluate the students on the blackboard simultaneously on the topics of vector sum, direction, unit vector and projections. Perform the generation of exercises through patterns so that teachers can rescue their answers. Created professors of universities and engineering students. In Spanish.https://www.maplesoft.com/applications/view.aspx?SID=154371&ref=FeedSun, 03 Dec 2017 05:00:00 ZProf. Lenin Araujo CastilloProf. Lenin Araujo CastilloMultiple integrals over sets defined by inequalities
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The aim of this worksheet is to present a method for computing multiple integrals of a function in n variables over a set defined by inequalities.<img src="https://www.maplesoft.com/view.aspx?si=154350/nint.png" alt="Multiple integrals over sets defined by inequalities" style="max-width: 25%;" align="left"/>The aim of this worksheet is to present a method for computing multiple integrals of a function in n variables over a set defined by inequalities.https://www.maplesoft.com/applications/view.aspx?SID=154350&ref=FeedWed, 25 Oct 2017 04:00:00 ZProf. Valeriu AnisiuProf. Valeriu AnisiuMoment of a force using vectors
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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="https://www.maplesoft.com/view.aspx?si=154345/moment of force.PNG" alt="Moment of a force using vectors" style="max-width: 25%;" 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.https://www.maplesoft.com/applications/view.aspx?SID=154345&ref=FeedTue, 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="https://www.maplesoft.com/view.aspx?si=154294/vectors.PNG" alt="Vector space with projections and forces" style="max-width: 25%;" 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.https://www.maplesoft.com/applications/view.aspx?SID=154294&ref=FeedMon, 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="https://www.maplesoft.com/view.aspx?si=154293/desplvp.png" alt="Displacement and distance traveled with vectors" style="max-width: 25%;" 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.https://www.maplesoft.com/applications/view.aspx?SID=154293&ref=FeedMon, 28 Aug 2017 04:00:00 ZProf. Lenin Araujo CastilloProf. Lenin Araujo CastilloPlot 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="https://www.maplesoft.com/view.aspx?si=154290/bnrvp.png" alt="Plot of Position Vector" style="max-width: 25%;" 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.https://www.maplesoft.com/applications/view.aspx?SID=154290&ref=FeedThu, 10 Aug 2017 04:00:00 ZProf. Lenin Araujo CastilloProf. Lenin Araujo CastilloKinematics using syntax
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In this file you will be able to observe and analyze how the exercises and problems of Kinematics and Dynamics are solved using the commands and operators through a very well-structured syntax. Allowing me to save time and use it in interpretation. I hope you can share and spread to break the traditional and unnecessary myths. Only for Engineering and Science. Share if you like.
In Spanish.<img src="https://www.maplesoft.com/view.aspx?si=154271/kinematicssint.png" alt="Kinematics using syntax" style="max-width: 25%;" align="left"/>In this file you will be able to observe and analyze how the exercises and problems of Kinematics and Dynamics are solved using the commands and operators through a very well-structured syntax. Allowing me to save time and use it in interpretation. I hope you can share and spread to break the traditional and unnecessary myths. Only for Engineering and Science. Share if you like.
In Spanish.https://www.maplesoft.com/applications/view.aspx?SID=154271&ref=FeedWed, 14 Jun 2017 04:00:00 ZProf. Lenin Araujo CastilloProf. Lenin Araujo CastilloVector Force
https://www.maplesoft.com/applications/view.aspx?SID=154245&ref=Feed
This worksheet is designed to develop engineering exercises with Maple applications. You should know the theory before using these applications. It is designed to solve problems faster. This is an easy-to-use interactive application. In Spanish.<img src="https://www.maplesoft.com/view.aspx?si=154245/vecfza.png" alt="Vector Force" style="max-width: 25%;" align="left"/>This worksheet is designed to develop engineering exercises with Maple applications. You should know the theory before using these applications. It is designed to solve problems faster. This is an easy-to-use interactive application. In Spanish.https://www.maplesoft.com/applications/view.aspx?SID=154245&ref=FeedTue, 09 May 2017 04:00:00 ZProf. Lenin Araujo CastilloProf. Lenin Araujo CastilloClassroom Tips and Techniques: Roles for the Laplace Transform's Shifting Laws
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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="https://www.maplesoft.com/view.aspx?si=1723/laplace.PNG" alt="Classroom Tips and Techniques: Roles for the Laplace Transform's Shifting Laws" style="max-width: 25%;" 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)https://www.maplesoft.com/applications/view.aspx?SID=1723&ref=FeedTue, 25 Apr 2017 04:00:00 ZDr. Robert LopezDr. Robert LopezThe Comet 67P/Churyumov-Gerasimenko, Rosetta & Philae
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<p> Abstract<br /><br />The Rosetta space probe launched 10 years ago by the European Space Agency (ESA) arrived recently (November 12, 2014) at the site of the comet known as 67P/Churyumov-Gerasimenco after a trip of 4 billions miles from Earth. After circling the comet, Rosetta released its precious load : the lander Philae packed with 21 different scientific instruments for the study of the comet with the main purpose : the origin of our solar system and possibly the origin of life on our planet.<br /><br />Our plan is rather a modest one since all we want is to get , by calculations, specific data concerning the comet and its lander.<br />We shall take a simplified model and consider the comet as a perfect solid sphere to which we can apply Newton's laws.<br /><br />We want to find:<br /><br />I- the acceleration on the comet surface ,<br />II- its radius,<br />III- its density,<br />IV- the velocity of Philae just after the 1st bounce off the comet (it has bounced twice),<br />V- the time for Philae to reach altitude of 1000 m above the comet .<br /><br />We shall compare our findings with the already known data to see how close our simplified mathematical model findings are to the duck-shaped comet already known results.<br />It turned out that our calculations for a sphere shaped comet are very close to the already known data.<br /><br />Conclusion<br /><br />Even with a shape that defies the application of any mechanical laws we can always get very close to reality by adopting a simplified mathematical model in any preliminary study of a complicated problem.<br /><br /></p><img src="https://www.maplesoft.com/applications/images/app_image_blank_lg.jpg" alt="The Comet 67P/Churyumov-Gerasimenko, Rosetta & Philae" style="max-width: 25%;" align="left"/><p> Abstract<br /><br />The Rosetta space probe launched 10 years ago by the European Space Agency (ESA) arrived recently (November 12, 2014) at the site of the comet known as 67P/Churyumov-Gerasimenco after a trip of 4 billions miles from Earth. After circling the comet, Rosetta released its precious load : the lander Philae packed with 21 different scientific instruments for the study of the comet with the main purpose : the origin of our solar system and possibly the origin of life on our planet.<br /><br />Our plan is rather a modest one since all we want is to get , by calculations, specific data concerning the comet and its lander.<br />We shall take a simplified model and consider the comet as a perfect solid sphere to which we can apply Newton's laws.<br /><br />We want to find:<br /><br />I- the acceleration on the comet surface ,<br />II- its radius,<br />III- its density,<br />IV- the velocity of Philae just after the 1st bounce off the comet (it has bounced twice),<br />V- the time for Philae to reach altitude of 1000 m above the comet .<br /><br />We shall compare our findings with the already known data to see how close our simplified mathematical model findings are to the duck-shaped comet already known results.<br />It turned out that our calculations for a sphere shaped comet are very close to the already known data.<br /><br />Conclusion<br /><br />Even with a shape that defies the application of any mechanical laws we can always get very close to reality by adopting a simplified mathematical model in any preliminary study of a complicated problem.<br /><br /></p>https://www.maplesoft.com/applications/view.aspx?SID=153706&ref=FeedMon, 17 Nov 2014 05:00:00 ZDr. Ahmed BaroudyDr. Ahmed Baroudy