Precalculus: New Applications
http://www.maplesoft.com/applications/category.aspx?cid=300
en-us2015 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemTue, 31 Mar 2015 23:56:39 GMTTue, 31 Mar 2015 23:56:39 GMTNew applications in the Precalculus categoryhttp://www.mapleprimes.com/images/mapleapps.gifPrecalculus: New Applications
http://www.maplesoft.com/applications/category.aspx?cid=300
Descartes & Mme La Marquise du Chatelet And The Elastic Collision of Two Bodies
http://www.maplesoft.com/applications/view.aspx?SID=153515&ref=Feed
<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="/view.aspx?si=153515/Elastic_Collision_image1.jpg" alt="Descartes & Mme La Marquise du Chatelet And The Elastic Collision of Two Bodies" 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>153515Fri, 07 Mar 2014 05:00:00 ZDr. Ahmed BaroudyDr. Ahmed BaroudyHohmann Elliptic Transfer Orbit with Animation
http://www.maplesoft.com/applications/view.aspx?SID=151351&ref=Feed
<p>Abstract<br /><br />The main purpose of this article is to show how to use Hohmann elliptic transfer in two situations:<br />a- When one manned spaceship is trying to catch up with an other one <br />on the same circular orbit around Earth.<br />b- When delivering a payload from Earth to a space station on a circular <br />orbit around Earth using 2-stage rocket .<br /><br />The way we set up the problem is as follows:<br />Consider two manned spaceships with astronauts Sally & Igor , the latter<br />lagging behind Sally by a given angle = 4.5 degrees while both are on the same<br />circular orbit C2 about Earth. A 2d lower circular orbit C1 is given. <br />Find the Hohmann elliptic orbit that is tangent to both orbits which allows<br />Sally to maneuver on C1 then to get back to the circular orbit C2 alongside Igor.<br /><br />Though the math was correct , however the final result we found was not !! <br />It was somehow tricky to find the culprit!<br />We have to restate the problem to get the correct answer. <br />The animation was then set up using the correct data. <br />The animation is a good teaching help for two reasons:<br />1- it gives a 'hand on' experience for anyone who wants to fully understand it,<br />2- it is a good lesson in Maple programming with many loops of the type 'if..then'.<br /><br />Warning<br /><br />This particular animation is a hog for the CPU memory since data accumulated <br />for plotting reached 20 MB! This is the size of this article when animation is <br />executed. For this reason and to be able to upload it I left the animation <br />procedure non executed which drops the size of the article to 300KB.<br /><br />Conclusion<br /><br />If I can get someone interested in the subject of this article in such away that he or <br />she would seek further information for learning from other sources, my efforts<br />would be well rewarded.</p><img src="/view.aspx?si=151351/Elliptic_image1.jpg" alt="Hohmann Elliptic Transfer Orbit with Animation" align="left"/><p>Abstract<br /><br />The main purpose of this article is to show how to use Hohmann elliptic transfer in two situations:<br />a- When one manned spaceship is trying to catch up with an other one <br />on the same circular orbit around Earth.<br />b- When delivering a payload from Earth to a space station on a circular <br />orbit around Earth using 2-stage rocket .<br /><br />The way we set up the problem is as follows:<br />Consider two manned spaceships with astronauts Sally & Igor , the latter<br />lagging behind Sally by a given angle = 4.5 degrees while both are on the same<br />circular orbit C2 about Earth. A 2d lower circular orbit C1 is given. <br />Find the Hohmann elliptic orbit that is tangent to both orbits which allows<br />Sally to maneuver on C1 then to get back to the circular orbit C2 alongside Igor.<br /><br />Though the math was correct , however the final result we found was not !! <br />It was somehow tricky to find the culprit!<br />We have to restate the problem to get the correct answer. <br />The animation was then set up using the correct data. <br />The animation is a good teaching help for two reasons:<br />1- it gives a 'hand on' experience for anyone who wants to fully understand it,<br />2- it is a good lesson in Maple programming with many loops of the type 'if..then'.<br /><br />Warning<br /><br />This particular animation is a hog for the CPU memory since data accumulated <br />for plotting reached 20 MB! This is the size of this article when animation is <br />executed. For this reason and to be able to upload it I left the animation <br />procedure non executed which drops the size of the article to 300KB.<br /><br />Conclusion<br /><br />If I can get someone interested in the subject of this article in such away that he or <br />she would seek further information for learning from other sources, my efforts<br />would be well rewarded.</p>151351Wed, 04 Sep 2013 04:00:00 ZDr. Ahmed BaroudyDr. Ahmed BaroudyMath Apps in Maple
http://www.maplesoft.com/applications/view.aspx?SID=132220&ref=Feed
Math Apps in Maple have give students and teachers the ability to explore and illustrate a wide variety of mathematical and scientific concepts. These fun and easy to use educational demonstrations are designed to illustrate various mathematical and physical concepts. This application contains a sampling of some of the many Math Apps available in Maple: drawing the graph of a quadratic, epicycloids, monte carlo approximations of pi, and throwing coconuts.<img src="/view.aspx?si=132220/mathapps_thumb.png" alt="Math Apps in Maple" align="left"/>Math Apps in Maple have give students and teachers the ability to explore and illustrate a wide variety of mathematical and scientific concepts. These fun and easy to use educational demonstrations are designed to illustrate various mathematical and physical concepts. This application contains a sampling of some of the many Math Apps available in Maple: drawing the graph of a quadratic, epicycloids, monte carlo approximations of pi, and throwing coconuts.132220Tue, 27 Mar 2012 04:00:00 ZMaplesoftMaplesoftWhy I Needed Maple to Make Cream Cheese Frosting
http://www.maplesoft.com/applications/view.aspx?SID=125069&ref=Feed
<p>A recipe for cream cheese frosting I was making called for 8 oz. (about 240 grams) of cream cheese. Unfortunately, I didn't have a kitchen scale, and the product I bought came in a 400 gram tub in the shape of a<strong> truncated cone</strong>, which has a rather cumbersome volume formula. <br />Given the geometry of this tub, how deep into the tub should I scoop to get 240 grams? The mathematics is trickier than you might think but lots of fun! And the final, tasty result is worth the effort!</p><img src="/view.aspx?si=125069/philly_thumb.png" alt="Why I Needed Maple to Make Cream Cheese Frosting" align="left"/><p>A recipe for cream cheese frosting I was making called for 8 oz. (about 240 grams) of cream cheese. Unfortunately, I didn't have a kitchen scale, and the product I bought came in a 400 gram tub in the shape of a<strong> truncated cone</strong>, which has a rather cumbersome volume formula. <br />Given the geometry of this tub, how deep into the tub should I scoop to get 240 grams? The mathematics is trickier than you might think but lots of fun! And the final, tasty result is worth the effort!</p>125069Tue, 23 Aug 2011 04:00:00 ZDr. Jason SchattmanDr. Jason SchattmanClassroom Tips and Techniques: Factoring a Quadratic Polynomial
http://www.maplesoft.com/applications/view.aspx?SID=120328&ref=Feed
Factoring a quadratic polynomial by inspection - is this a necessary skill, and if it is, how can students be helped to master it?<img src="/view.aspx?si=120328/thumb.jpg" alt="Classroom Tips and Techniques: Factoring a Quadratic Polynomial" align="left"/>Factoring a quadratic polynomial by inspection - is this a necessary skill, and if it is, how can students be helped to master it?120328Tue, 24 May 2011 04:00:00 ZDr. Robert LopezDr. Robert LopezClassroom Tips and Techniques: Yet More Gems from the Little Red Book of Maple Magic
http://www.maplesoft.com/applications/view.aspx?SID=102692&ref=Feed
Five more bits of accumulated "Maple magic" are shared: the limit of Picard iterates, combining radicals, factoring, yet another trig identity, and sorting strategies.<img src="/view.aspx?si=102692/thumb.jpg" alt="Classroom Tips and Techniques: Yet More Gems from the Little Red Book of Maple Magic" align="left"/>Five more bits of accumulated "Maple magic" are shared: the limit of Picard iterates, combining radicals, factoring, yet another trig identity, and sorting strategies.102692Mon, 21 Mar 2011 04:00:00 ZDr. Robert LopezDr. Robert LopezPrueba
http://www.maplesoft.com/applications/view.aspx?SID=87671&ref=Feed
<p>Una prueba de este servicio para ver si es posible publicar algunos archivos de forma gratuita con fines educativas, espero me permitan hacerlo y disculpen las molestias.</p>
<p> </p>
<p>Abrazos</p><img src="/applications/images/app_image_blank_lg.jpg" alt="Prueba" align="left"/><p>Una prueba de este servicio para ver si es posible publicar algunos archivos de forma gratuita con fines educativas, espero me permitan hacerlo y disculpen las molestias.</p>
<p> </p>
<p>Abrazos</p>87671Tue, 18 May 2010 04:00:00 ZDr. Diogenes OjedaDr. Diogenes OjedaWhy Slopes of Perpendicular Lines Are Negative Reciprocals
http://www.maplesoft.com/applications/view.aspx?SID=35264&ref=Feed
<p>In this application, Robert Lopez explains why slopes of perpendicular Lines are negative reciprocals</p><img src="/applications/images/app_image_blank_lg.jpg" alt="Why Slopes of Perpendicular Lines Are Negative Reciprocals" align="left"/><p>In this application, Robert Lopez explains why slopes of perpendicular Lines are negative reciprocals</p>35264Wed, 17 Mar 2010 04:00:00 ZDr. Robert LopezDr. Robert LopezClassroom Tips and Techniques: Stepwise Solutions in Maple - Part 1
http://www.maplesoft.com/applications/view.aspx?SID=35165&ref=Feed
<p>In Maple, there are commands, Assistants, Tutors, and Task Templates that show stepwise calculations in algebra, calculus (single-variable, multivariable, vector), and linear algebra. In this article we discuss Maple's functionality for providing these stepwise solutions to mathematical problems in algebra and calculus (both of one and several variables).</p><img src="/view.aspx?si=35165/thumb2.jpg" alt="Classroom Tips and Techniques: Stepwise Solutions in Maple - Part 1" align="left"/><p>In Maple, there are commands, Assistants, Tutors, and Task Templates that show stepwise calculations in algebra, calculus (single-variable, multivariable, vector), and linear algebra. In this article we discuss Maple's functionality for providing these stepwise solutions to mathematical problems in algebra and calculus (both of one and several variables).</p>35165Wed, 10 Feb 2010 05:00:00 ZDr. Robert LopezDr. Robert LopezMEANS
http://www.maplesoft.com/applications/view.aspx?SID=34930&ref=Feed
<p>Elementary calculations of means with classroom examples, showing proofs of inequalities between means, theoretical and by geometry.</p>
<p>One solutiion for an extremely difficult puzzle illustrating inequality in three dimensions.</p>
<p>Iteration on mixed arithmetic-geometric-harmonic means</p>
<p>Calculation values of elliptic integrals by mixed iteration.</p><img src="/view.aspx?si=34930/means.png" alt="MEANS" align="left"/><p>Elementary calculations of means with classroom examples, showing proofs of inequalities between means, theoretical and by geometry.</p>
<p>One solutiion for an extremely difficult puzzle illustrating inequality in three dimensions.</p>
<p>Iteration on mixed arithmetic-geometric-harmonic means</p>
<p>Calculation values of elliptic integrals by mixed iteration.</p>34930Wed, 09 Dec 2009 05:00:00 ZRoland EngdahlRoland EngdahlWhy is the Minimum Payment on a Credit Card So Low?
http://www.maplesoft.com/applications/view.aspx?SID=6647&ref=Feed
On a monthly credit card balance of $1000, a typical credit card company will only ask for a minimum payment of $20. Why do credit card companies do that? Let's see if Maple can lead us to some insights.<img src="/view.aspx?si=6647/thumb.gif" alt="Why is the Minimum Payment on a Credit Card So Low?" align="left"/>On a monthly credit card balance of $1000, a typical credit card company will only ask for a minimum payment of $20. Why do credit card companies do that? Let's see if Maple can lead us to some insights.6647Wed, 10 Sep 2008 00:00:00 ZJason SchattmanJason SchattmanGraphing interface for A sin(Bx + C) + D
http://www.maplesoft.com/applications/view.aspx?SID=6575&ref=Feed
Provides the student with a command-free environment to experiment with the graph of the sine function in all its glory. Includes sliders for A, B, C, D and radio buttons for selecting radians or degrees. The embedded plot component automatically labels the x-axis in multiples of either Pi/2 or 90 degrees.<img src="/view.aspx?si=6575/1.jpg" alt="Graphing interface for A sin(Bx + C) + D" align="left"/>Provides the student with a command-free environment to experiment with the graph of the sine function in all its glory. Includes sliders for A, B, C, D and radio buttons for selecting radians or degrees. The embedded plot component automatically labels the x-axis in multiples of either Pi/2 or 90 degrees.6575Tue, 26 Aug 2008 00:00:00 ZJason SchattmanJason SchattmanOptimal Speed of an 18-Wheeler
http://www.maplesoft.com/applications/view.aspx?SID=6573&ref=Feed
Derives the optimal cruising speed of an 18-wheeler given the price of diesel, the weight of the truck, the distance of the delivery route, and the monetary value of the cargo. Makes use of a study by Goodyear on the fuel economy of 18-wheelers vs. speed and weight. Uses many features new to Maple 12, including code regions, filled 3-D plots, and rotary gauges. At the end, you can turn dials to set the parameters and watch a "speedometer" (a rotary gauge) display the optimal speed under those settings.<img src="/view.aspx?si=6573/thumb.jpg" alt="Optimal Speed of an 18-Wheeler" align="left"/>Derives the optimal cruising speed of an 18-wheeler given the price of diesel, the weight of the truck, the distance of the delivery route, and the monetary value of the cargo. Makes use of a study by Goodyear on the fuel economy of 18-wheelers vs. speed and weight. Uses many features new to Maple 12, including code regions, filled 3-D plots, and rotary gauges. At the end, you can turn dials to set the parameters and watch a "speedometer" (a rotary gauge) display the optimal speed under those settings.6573Tue, 26 Aug 2008 00:00:00 ZJason SchattmanJason SchattmanGeneral Triangle
http://www.maplesoft.com/applications/view.aspx?SID=6424&ref=Feed
The intent of this application is to generalize the meaning of the expression: "Solve the general triangle". Traditionally the expression means: "Given three parts of the triangle, find the remaining parts". In this application, the expression also includes other features of the triangle such as area, perimeter, height, centroid, orthocenter, incenter, and circumcenter. Because some features are "length preserving" and others are not, in the case of SAS, aBc is not the same as cBa.
Application is written using Maple 11.<img src="/view.aspx?si=6424/1.jpg" alt="General Triangle" align="left"/>The intent of this application is to generalize the meaning of the expression: "Solve the general triangle". Traditionally the expression means: "Given three parts of the triangle, find the remaining parts". In this application, the expression also includes other features of the triangle such as area, perimeter, height, centroid, orthocenter, incenter, and circumcenter. Because some features are "length preserving" and others are not, in the case of SAS, aBc is not the same as cBa.
Application is written using Maple 11.6424Thu, 10 Jul 2008 00:00:00 ZProf. P. VelezProf. P. VelezMathematics Pre-test
http://www.maplesoft.com/applications/view.aspx?SID=6324&ref=Feed
The goal of this questionnaire is to verify your level of understanding of the basic concepts necessary for success in differential calculus and integral calculus courses.<img src="/view.aspx?si=6324/thumb.gif" alt="Mathematics Pre-test" align="left"/>The goal of this questionnaire is to verify your level of understanding of the basic concepts necessary for success in differential calculus and integral calculus courses.6324Wed, 28 May 2008 00:00:00 ZProf. mario LemelinProf. mario LemelinPlotting of Polar Points
http://www.maplesoft.com/applications/view.aspx?SID=6303&ref=Feed
Given a polar point with its radial and angular component in degrees, the system demonstrates, narrates, and animates the plotting of polar points. It also includes other petinents topics related to polar points.
System is intended for high school or junior college students taking a course in either Trigonometry or Precalculus.<img src="/view.aspx?si=6303/Untitled-1.gif" alt="Plotting of Polar Points" align="left"/>Given a polar point with its radial and angular component in degrees, the system demonstrates, narrates, and animates the plotting of polar points. It also includes other petinents topics related to polar points.
System is intended for high school or junior college students taking a course in either Trigonometry or Precalculus.6303Wed, 21 May 2008 00:00:00 ZProf. P. VelezProf. P. VelezPré-test en Mathématique
http://www.maplesoft.com/applications/view.aspx?SID=5563&ref=Feed
Cette feuille de travail est un questionnaire permettant aux étudiants débutant en calcul différentiel de vérifier l'état de ses connaissances du secondaire.<img src="/view.aspx?si=5563/1.gif" alt="Pré-test en Mathématique" align="left"/>Cette feuille de travail est un questionnaire permettant aux étudiants débutant en calcul différentiel de vérifier l'état de ses connaissances du secondaire.5563Wed, 19 Dec 2007 00:00:00 ZProf. mario LemelinProf. mario LemelinClassroom Tips and Techniques: Task Templates in Maple
http://www.maplesoft.com/applications/view.aspx?SID=1763&ref=Feed
Maple comes with more than 200 built-in Task Templates. The process of creating a new Task Template, and adding it to the Table of Contents of all such tasks is relatively straightforward. In this article, we explain how to create a new Task Template and add it to the list of built-in tasks.<img src="/view.aspx?si=1763/tasktemplates.gif" alt="Classroom Tips and Techniques: Task Templates in Maple" align="left"/>Maple comes with more than 200 built-in Task Templates. The process of creating a new Task Template, and adding it to the Table of Contents of all such tasks is relatively straightforward. In this article, we explain how to create a new Task Template and add it to the list of built-in tasks.1763Thu, 20 Jul 2006 00:00:00 ZDr. Robert LopezDr. Robert LopezClassroom Tips and Techniques: Norm of a Matrix
http://www.maplesoft.com/applications/view.aspx?SID=1430&ref=Feed
The greatest benefits from bringing Maple into the classroom are realized when the static pedagogy of a printed textbook is enlivened by the interplay of symbolic, graphic, and numeric calculations made possible by technology. It is not enough merely to compute or check answers with Maple. To stop after noting that indeed, Maple can compute the correct answer is not a pedagogical breakthrough.
Getting Maple to compute the correct answer is just the first step. Using Maple to bring insights not easily realized with by-hand calculations should be the goal of everyone who sets a hand to improving the learning experiences of students.<img src="/view.aspx?si=1430/thumb.jpg" alt="Classroom Tips and Techniques: Norm of a Matrix" align="left"/>The greatest benefits from bringing Maple into the classroom are realized when the static pedagogy of a printed textbook is enlivened by the interplay of symbolic, graphic, and numeric calculations made possible by technology. It is not enough merely to compute or check answers with Maple. To stop after noting that indeed, Maple can compute the correct answer is not a pedagogical breakthrough.
Getting Maple to compute the correct answer is just the first step. Using Maple to bring insights not easily realized with by-hand calculations should be the goal of everyone who sets a hand to improving the learning experiences of students.1430Thu, 27 Jan 2005 00:00:00 ZDr. Robert LopezDr. Robert LopezComposition Tutor
http://www.maplesoft.com/applications/view.aspx?SID=4754&ref=Feed
Maple's Student package is filled with a complete set of Precalculus, Calculus I and Linear Algebra tutors. With these graphical, interactive tutors, you can analyze conics sections, translate standard functions, or single step through mathematical problems without ever seeing the underlying Maple syntax. Each of the single stepping tutors come fully equipped with a problem status window, buttons to apply applicable rules, a drop down menu to retrieve rule definitions, and more. The graphical tutors display a mathematical and graphical portrait of each concept, which makes analyzing these concepts a snap.<img src="/view.aspx?si=4754/Composition.jpg" alt="Composition Tutor" align="left"/>Maple's Student package is filled with a complete set of Precalculus, Calculus I and Linear Algebra tutors. With these graphical, interactive tutors, you can analyze conics sections, translate standard functions, or single step through mathematical problems without ever seeing the underlying Maple syntax. Each of the single stepping tutors come fully equipped with a problem status window, buttons to apply applicable rules, a drop down menu to retrieve rule definitions, and more. The graphical tutors display a mathematical and graphical portrait of each concept, which makes analyzing these concepts a snap.4754Wed, 01 Oct 2003 00:00:00 ZMaplesoftMaplesoft