Vector Calculus: New Applications
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en-us2021 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemSun, 17 Oct 2021 10:27:22 GMTSun, 17 Oct 2021 10:27:22 GMTNew applications in the Vector Calculus categoryhttps://www.maplesoft.com/images/Application_center_hp.jpgVector Calculus: 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.
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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.https://www.maplesoft.com/applications/view.aspx?SID=154267&ref=FeedThu, 19 Aug 2021 14:22:04 ZJohn OgilvieJohn OgilvieFirst 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 CastilloPlot 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 CastilloGenerator 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 CastilloKinematics Curvilinear
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With this application you can calculate the components of the acceleration. The scalar and vector components of the tangent and the normal. In addition to curvilinear kinetics in polar coordinates. It can be used in different engineers, especially mechanical, civil and more.
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In Spanish.<img src="https://www.maplesoft.com/view.aspx?si=154269/kc.png" alt="Kinematics Curvilinear" style="max-width: 25%;" align="left"/>With this application you can calculate the components of the acceleration. The scalar and vector components of the tangent and the normal. In addition to curvilinear kinetics in polar coordinates. It can be used in different engineers, especially mechanical, civil and more.
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In Spanish.https://www.maplesoft.com/applications/view.aspx?SID=154269&ref=FeedTue, 14 Nov 2017 05:00:00 ZProf. Lenin Araujo CastilloProf. Lenin Araujo CastilloPlot of equation impulse-momentum
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In this application you can visualize the impulse generated by a constant and variable force for the interaction of a particle with an object in a state of rest or movement. It is also the calculation of the momentum-momentum equation by entering the mass of the particle to solve initial and final velocities respectively according to the case study. Engineering students can quickly display the calculations and then their interpretation.<img src="https://www.maplesoft.com/view.aspx?si=154347/mivis.png" alt="Plot of equation impulse-momentum" style="max-width: 25%;" align="left"/>In this application you can visualize the impulse generated by a constant and variable force for the interaction of a particle with an object in a state of rest or movement. It is also the calculation of the momentum-momentum equation by entering the mass of the particle to solve initial and final velocities respectively according to the case study. Engineering students can quickly display the calculations and then their interpretation.https://www.maplesoft.com/applications/view.aspx?SID=154347&ref=FeedTue, 17 Oct 2017 04:00:00 ZProf. Lenin Araujo CastilloProf. Lenin Araujo CastilloMoment 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
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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
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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
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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 CastilloClassroom Tips and Techniques: The Lagrange Multiplier Method
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Maple has a number of graphical and analytical tools for studying and implementing the method of Lagrange multipliers. In this article, we demonstrate a number of these tools, indicating how they might be used pedagogically.<img src="https://www.maplesoft.com/view.aspx?si=4811/lagrange.PNG" alt="Classroom Tips and Techniques: The Lagrange Multiplier Method" style="max-width: 25%;" align="left"/>Maple has a number of graphical and analytical tools for studying and implementing the method of Lagrange multipliers. In this article, we demonstrate a number of these tools, indicating how they might be used pedagogically.https://www.maplesoft.com/applications/view.aspx?SID=4811&ref=FeedTue, 23 May 2017 04:00:00 ZDr. Robert LopezDr. Robert LopezVector Force
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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 CastilloVectors in the plane.
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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.
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In Spanish.<img src="https://www.maplesoft.com/view.aspx?si=154071/vpThumb.jpg" alt="Vectors in the plane." style="max-width: 25%;" 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.
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In Spanish.https://www.maplesoft.com/applications/view.aspx?SID=154071&ref=FeedFri, 01 Apr 2016 04:00:00 ZProf. Lenin Araujo CastilloProf. Lenin Araujo CastilloDescartes & Mme La Marquise du Chatelet And The Elastic Collision of Two Bodies
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<p><strong><em> ABSTRACT<br /> <br /> The Marquise</em></strong> <strong><em>du Chatelet in her book " Les Institutions Physiques" published in 1740, stated on page 36, that Descartes, when formulating his laws of motion in an elastic collision of two bodies B & C (B being more massive than C) <span >having the same speed v</span>, said that t<span >he smaller one C will reverse its course </span>while <span >the more massive body B will continue its course in the same direction as before</span> and <span >both will have again the same speed v.<br /> <br /> </span>Mme du Chatelet, basing her judgment on theoretical considerations using <span >the principle of continuity</span> , declared that Descartes was <span >wrong</span> in his statement. For Mme du Chatelet the larger mass B should reverse its course and move in the opposite direction. She mentioned nothing about both bodies B & C as <span >having the same velocity after collision as Descartes did</span>.<br /> <br /> At the time of Descartes, some 300 years ago, the concept of kinetic energy & momentum as we know today was not yet well defined, let alone considered in any physical problem.<br /> <br /> Actually both Descartes & Mme du Chatelet may have been right in some special cases but not in general as the discussion that follows will show.</em></strong></p><img src="https://www.maplesoft.com/applications/images/app_image_blank_lg.jpg" alt="Descartes & Mme La Marquise du Chatelet And The Elastic Collision of Two Bodies" style="max-width: 25%;" align="left"/><p><strong><em> ABSTRACT<br /> <br /> The Marquise</em></strong> <strong><em>du Chatelet in her book " Les Institutions Physiques" published in 1740, stated on page 36, that Descartes, when formulating his laws of motion in an elastic collision of two bodies B & C (B being more massive than C) <span >having the same speed v</span>, said that t<span >he smaller one C will reverse its course </span>while <span >the more massive body B will continue its course in the same direction as before</span> and <span >both will have again the same speed v.<br /> <br /> </span>Mme du Chatelet, basing her judgment on theoretical considerations using <span >the principle of continuity</span> , declared that Descartes was <span >wrong</span> in his statement. For Mme du Chatelet the larger mass B should reverse its course and move in the opposite direction. She mentioned nothing about both bodies B & C as <span >having the same velocity after collision as Descartes did</span>.<br /> <br /> At the time of Descartes, some 300 years ago, the concept of kinetic energy & momentum as we know today was not yet well defined, let alone considered in any physical problem.<br /> <br /> Actually both Descartes & Mme du Chatelet may have been right in some special cases but not in general as the discussion that follows will show.</em></strong></p>https://www.maplesoft.com/applications/view.aspx?SID=153515&ref=FeedFri, 07 Mar 2014 05:00:00 ZDr. Ahmed BaroudyDr. Ahmed BaroudyCollision detection between toolholder and workpiece on ball nut grinding
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<p>In this worksheet a collision detection performed to determine the minimum safety distance between a tool holder and ball nut on grinding manufacturing. A nonlinear quartic equation system have to be solved by <em>Newton's</em> and <em>Broyden's</em> methods and results are compared with <em>Maple fsolve()</em> command. Users can check the different results by embedded components and animated 3D surface plot.</p><img src="https://www.maplesoft.com/view.aspx?si=153477/0320a66eb812382755a045a5251b1390.gif" alt="Collision detection between toolholder and workpiece on ball nut grinding" style="max-width: 25%;" align="left"/><p>In this worksheet a collision detection performed to determine the minimum safety distance between a tool holder and ball nut on grinding manufacturing. A nonlinear quartic equation system have to be solved by <em>Newton's</em> and <em>Broyden's</em> methods and results are compared with <em>Maple fsolve()</em> command. Users can check the different results by embedded components and animated 3D surface plot.</p>https://www.maplesoft.com/applications/view.aspx?SID=153477&ref=FeedMon, 23 Dec 2013 05:00:00 ZGyörgy HegedûsGyörgy HegedûsClassroom Tips and Techniques: Drawing a Normal and Tangent Plane on a Surface
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Four different techniques are given for obtaining a graph showing a surface with a normal and tangent plane attached. The work is a response to <a href="http://www.mapleprimes.com/questions/147681-A-Problem-About-Plot-The-Part-Of-The-Surface">a MaplePrimes question asked on May 25, 2013</a>.<img src="https://www.maplesoft.com/view.aspx?si=150722/thumb.jpg" alt="Classroom Tips and Techniques: Drawing a Normal and Tangent Plane on a Surface" style="max-width: 25%;" align="left"/>Four different techniques are given for obtaining a graph showing a surface with a normal and tangent plane attached. The work is a response to <a href="http://www.mapleprimes.com/questions/147681-A-Problem-About-Plot-The-Part-Of-The-Surface">a MaplePrimes question asked on May 25, 2013</a>.https://www.maplesoft.com/applications/view.aspx?SID=150722&ref=FeedTue, 20 Aug 2013 04:00:00 ZDr. Robert LopezDr. Robert LopezClassroom Tips and Techniques: New Tools for Lines and Planes
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The fifteen new "Lines and Planes" commands in the Student MultivariateCalculus package are detailed, and then illustrated via a collection of examples from a typical calculus course. These new commands can also be implemented through the Context Menu system, as shown by parallel solutions in the set of examples.<img src="https://www.maplesoft.com/view.aspx?si=144642/thumb.jpg" alt="Classroom Tips and Techniques: New Tools for Lines and Planes" style="max-width: 25%;" align="left"/>The fifteen new "Lines and Planes" commands in the Student MultivariateCalculus package are detailed, and then illustrated via a collection of examples from a typical calculus course. These new commands can also be implemented through the Context Menu system, as shown by parallel solutions in the set of examples.https://www.maplesoft.com/applications/view.aspx?SID=144642&ref=FeedThu, 14 Mar 2013 04:00:00 ZDr. Robert LopezDr. Robert LopezClassroom Tips and Techniques: Animated Trace of a Curve Drawn by Radius Vector
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A plane curve <strong>R</strong>(<em>t</em>) = <em>x</em>(<em>t</em>) <strong>i</strong> + <em>y</em>(<em>t</em>) <strong>j</strong> is traced by a "moving" radius vector <strong>R</strong>(<em>t</em>). Code for this animation is explored in this article.<img src="https://www.maplesoft.com/view.aspx?si=143371/thumb.jpg" alt="Classroom Tips and Techniques: Animated Trace of a Curve Drawn by Radius Vector" style="max-width: 25%;" align="left"/>A plane curve <strong>R</strong>(<em>t</em>) = <em>x</em>(<em>t</em>) <strong>i</strong> + <em>y</em>(<em>t</em>) <strong>j</strong> is traced by a "moving" radius vector <strong>R</strong>(<em>t</em>). Code for this animation is explored in this article.https://www.maplesoft.com/applications/view.aspx?SID=143371&ref=FeedMon, 11 Feb 2013 05:00:00 ZDr. Robert LopezDr. Robert Lopez