Precalculus: New Applications
http://www.maplesoft.com/applications/category.aspx?cid=163
en-us2014 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemWed, 17 Sep 2014 03:37:20 GMTWed, 17 Sep 2014 03:37:20 GMTNew applications in the Precalculus categoryhttp://www.mapleprimes.com/images/mapleapps.gifPrecalculus: New Applications
http://www.maplesoft.com/applications/category.aspx?cid=163
Hohmann 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 BaroudyUnderstanding the Slope and Y-Intercept of a Line
http://www.maplesoft.com/applications/view.aspx?SID=143408&ref=Feed
<p>This is a Maple application designed to help students understand the slope and y-intercept of a line.</p>
<p>The fun and educational app includes a dynamic plot with two sliders for changing the slope and y-intercept over a range of values from -30 to 30. Enjoy!</p><img src="/view.aspx?si=143408/d1e71619e166d2f4ff49688b73f28690.gif" alt="Understanding the Slope and Y-Intercept of a Line" align="left"/><p>This is a Maple application designed to help students understand the slope and y-intercept of a line.</p>
<p>The fun and educational app includes a dynamic plot with two sliders for changing the slope and y-intercept over a range of values from -30 to 30. Enjoy!</p>143408Tue, 12 Feb 2013 05:00:00 ZDouglas LewitDouglas LewitThe Origin of Complex Numbers
http://www.maplesoft.com/applications/view.aspx?SID=126618&ref=Feed
The origin of complex numbers starts with the contributions of Scipione del Ferro, Nicolo Tartaglia, Girolamo Cardano, and Rafael Bombelli. This Maple worksheed details the methods and formulas they used. It explores these formulas using Maple and shows how they can be extended. Numerous examples, exercises and illustrations make this a useful teaching module for an introduction of complex numbers.<img src="/applications/images/app_image_blank_lg.jpg" alt="The Origin of Complex Numbers" align="left"/>The origin of complex numbers starts with the contributions of Scipione del Ferro, Nicolo Tartaglia, Girolamo Cardano, and Rafael Bombelli. This Maple worksheed details the methods and formulas they used. It explores these formulas using Maple and shows how they can be extended. Numerous examples, exercises and illustrations make this a useful teaching module for an introduction of complex numbers.126618Fri, 14 Oct 2011 04:00:00 ZDr. John MathewsDr. John MathewsWhy 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 SchattmanTerminator circle with animation
http://www.maplesoft.com/applications/view.aspx?SID=100509&ref=Feed
<p>The idea of writing this article came to me on the 25th of June 2003 when I was listening to Cairo radio announcing that Maghrib prayer is due in Cairo city while I was sitting in my home town at 400 miles North East of Cairo. What is interesting is that at exactly the same time a next door mosque, in my home town, was also calling for the Maghrib prayer. This makes me wonder : how could it be that sunset is simultaneous at two locations separated by a distance of 400 miles from each other and at different Latitudes & Longitudes. As a reminder Maghrib prayer time occurs everywhere at sunset. <br />In what follows we explore this issue and try to prove or disprove the simultaneity of sunset at two different locations. In so doing we are led to some interesting conclusions and as a bonus we got ourselves an animation of the Terminator circle on the surface of the globe. <br />Aside from its modest value and its originality ( I am not aware of anything similar to it ) this article is a good exercise in Maple programming. <br />May this article be a stimulus for some readers to get interested in Astronomy which is a science as ancient as the early human civilizations. <br /><br /></p><img src="/view.aspx?si=100509/thumb.jpg" alt="Terminator circle with animation" align="left"/><p>The idea of writing this article came to me on the 25th of June 2003 when I was listening to Cairo radio announcing that Maghrib prayer is due in Cairo city while I was sitting in my home town at 400 miles North East of Cairo. What is interesting is that at exactly the same time a next door mosque, in my home town, was also calling for the Maghrib prayer. This makes me wonder : how could it be that sunset is simultaneous at two locations separated by a distance of 400 miles from each other and at different Latitudes & Longitudes. As a reminder Maghrib prayer time occurs everywhere at sunset. <br />In what follows we explore this issue and try to prove or disprove the simultaneity of sunset at two different locations. In so doing we are led to some interesting conclusions and as a bonus we got ourselves an animation of the Terminator circle on the surface of the globe. <br />Aside from its modest value and its originality ( I am not aware of anything similar to it ) this article is a good exercise in Maple programming. <br />May this article be a stimulus for some readers to get interested in Astronomy which is a science as ancient as the early human civilizations. <br /><br /></p>100509Tue, 28 Dec 2010 05:00:00 ZDr. Ahmed BaroudyDr. Ahmed BaroudyHow Fast Does An Advent Candle Burn?
http://www.maplesoft.com/applications/view.aspx?SID=100332&ref=Feed
<p>Any kid who's ever been entranced by an advent wreath knows that a tapered advent candle shrinks faster on Sunday night when it's new and slender than on Saturday night when it's old, stubby and caked with melted wax. How much faster? As an apropos application of math during this Christmas season, <strong>we derive a formula for the height of a burning tapered candle as a function of time</strong>. Assuming the candle has the shape of a cone when it is new and that it loses volume at a constant rate as it burns, we show that the height of the candle shrinks roughly in proportion to the cube root of time.</p><img src="/view.aspx?si=100332/thumb.jpg" alt="How Fast Does An Advent Candle Burn?" align="left"/><p>Any kid who's ever been entranced by an advent wreath knows that a tapered advent candle shrinks faster on Sunday night when it's new and slender than on Saturday night when it's old, stubby and caked with melted wax. How much faster? As an apropos application of math during this Christmas season, <strong>we derive a formula for the height of a burning tapered candle as a function of time</strong>. Assuming the candle has the shape of a cone when it is new and that it loses volume at a constant rate as it burns, we show that the height of the candle shrinks roughly in proportion to the cube root of time.</p>100332Mon, 20 Dec 2010 05:00:00 ZDr. Jason SchattmanDr. Jason SchattmanClassroom Tips and Techniques: Real Distinct Roots of a Cubic
http://www.maplesoft.com/applications/view.aspx?SID=95925&ref=Feed
<p>The real distinct roots of the cubic equation z<sup>3</sup> + a z<sup>2</sup> + b z + c = 0 can be expressed compactly in terms of trig functions. However, Maple's solve command does not return this compact form, so we explore how we can interpret and compact Maple's solution of this equation.<br /><br /></p><img src="/view.aspx?si=95925/thumb.jpg" alt="Classroom Tips and Techniques: Real Distinct Roots of a Cubic" align="left"/><p>The real distinct roots of the cubic equation z<sup>3</sup> + a z<sup>2</sup> + b z + c = 0 can be expressed compactly in terms of trig functions. However, Maple's solve command does not return this compact form, so we explore how we can interpret and compact Maple's solution of this equation.<br /><br /></p>95925Tue, 10 Aug 2010 04:00:00 ZRobert LopezRobert LopezWhy 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 LopezStandard Functions Tutor
http://www.maplesoft.com/applications/view.aspx?SID=4761&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=4761//applications/images/app_image_blank_lg.jpg" alt="Standard Functions 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.4761Wed, 01 Oct 2003 00:00:00 ZMaplesoftMaplesoftPolynomial Tutor
http://www.maplesoft.com/applications/view.aspx?SID=4758&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=4758//applications/images/app_image_blank_lg.jpg" alt="Polynomial 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.4758Wed, 01 Oct 2003 00:00:00 ZMaplesoftMaplesoftCurve Analysis Tutor
http://www.maplesoft.com/applications/view.aspx?SID=4756&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=4756//applications/images/app_image_blank_lg.jpg" alt="Curve Analysis 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.4756Wed, 01 Oct 2003 00:00:00 ZMaplesoftMaplesoftPrecalculus: Complete Set of Lessons
http://www.maplesoft.com/applications/view.aspx?SID=4731&ref=Feed
This is a set of 17 Maple lessons for high school Precalculus or Elementary Analysis, developed by Gregory Moore of Orange Coast College.
They are designed so you can present each topic as you would during a normal lecture but using Maple as the main presentation tool. The students do not have to understand Maple syntax to benefit from the lessons.
With these Maple lessons, you can carry a topic far beyond what is possible on the blackboard. You can generate a new example or diagram instantly just by changing a few values in the worksheet.
You can show more interesting examples than you could on the board, where the examples always had to be planned to work out "nice". Maple computes the dirty work, so the class can focus on the thinking steps.<img src="/view.aspx?si=4731/Precalc.gif" alt="Precalculus: Complete Set of Lessons" align="left"/>This is a set of 17 Maple lessons for high school Precalculus or Elementary Analysis, developed by Gregory Moore of Orange Coast College.
They are designed so you can present each topic as you would during a normal lecture but using Maple as the main presentation tool. The students do not have to understand Maple syntax to benefit from the lessons.
With these Maple lessons, you can carry a topic far beyond what is possible on the blackboard. You can generate a new example or diagram instantly just by changing a few values in the worksheet.
You can show more interesting examples than you could on the board, where the examples always had to be planned to work out "nice". Maple computes the dirty work, so the class can focus on the thinking steps.4731Wed, 01 Oct 2003 00:00:00 ZGregory MooreGregory Moore