Calculus I: New Applications
https://www.maplesoft.com/applications/category.aspx?cid=175
en-us2019 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemSun, 17 Nov 2019 08:52:18 GMTSun, 17 Nov 2019 08:52:18 GMTNew applications in the Calculus I categoryhttps://www.maplesoft.com/images/Application_center_hp.jpgCalculus I: New Applications
https://www.maplesoft.com/applications/category.aspx?cid=175
System of Equations 2x2 and 3x3
https://www.maplesoft.com/applications/view.aspx?SID=154520&ref=Feed
This application solves a set of compatible equations of two or three variables. For two variables, it also graphs the intersection point of the variable "x" and "y". If we want to observe the intersection point closer we will use the zoom button that is activated when manipulating the graph. If we want to change the variable ("x" and "y") we enter the code of the button that solves and graphs. For three variables, the intersecting planes are shown.
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In Spanish.<img src="https://www.maplesoft.com/view.aspx?si=154520/sis_eq_dpd.png" alt="System of Equations 2x2 and 3x3" style="max-width: 25%;" align="left"/>This application solves a set of compatible equations of two or three variables. For two variables, it also graphs the intersection point of the variable "x" and "y". If we want to observe the intersection point closer we will use the zoom button that is activated when manipulating the graph. If we want to change the variable ("x" and "y") we enter the code of the button that solves and graphs. For three variables, the intersecting planes are shown.
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In Spanish.https://www.maplesoft.com/applications/view.aspx?SID=154520&ref=FeedTue, 19 Mar 2019 04:00:00 ZLenin Araujo CastilloLenin Araujo CastilloNewton’s Method
https://www.maplesoft.com/applications/view.aspx?SID=154421&ref=Feed
Newton's Method is a method of successive iteration that helps us to find the roots of an algebraic function f(x).
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Given an initial guess, x0, we can compute an x1, then an x2 and so on. This worksheet shows different ways to apply Newton’s Method in Maple.<img src="https://www.maplesoft.com/view.aspx?si=154421/newtons_method.PNG" alt="Newton’s Method" style="max-width: 25%;" align="left"/>Newton's Method is a method of successive iteration that helps us to find the roots of an algebraic function f(x).
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Given an initial guess, x0, we can compute an x1, then an x2 and so on. This worksheet shows different ways to apply Newton’s Method in Maple.https://www.maplesoft.com/applications/view.aspx?SID=154421&ref=FeedFri, 23 Mar 2018 04:00:00 ZEmilee CarsonEmilee CarsonRiemann Sums
https://www.maplesoft.com/applications/view.aspx?SID=154423&ref=Feed
This worksheet demonstrates the use of the Riemann Sums command in the <A HREF="/support/help/maple/view.aspx?path=Student/Calculus1">Student Calculus 1 package</A>.<img src="https://www.maplesoft.com/view.aspx?si=154423/riemann_sums.PNG" alt="Riemann Sums" style="max-width: 25%;" align="left"/>This worksheet demonstrates the use of the Riemann Sums command in the <A HREF="/support/help/maple/view.aspx?path=Student/Calculus1">Student Calculus 1 package</A>.https://www.maplesoft.com/applications/view.aspx?SID=154423&ref=FeedFri, 23 Mar 2018 04:00:00 ZEmilee CarsonEmilee CarsonImplementation of Maple apps for the creation of mathematical exercises in engineering
https://www.maplesoft.com/applications/view.aspx?SID=154388&ref=Feed
In this research work has allowed to show the implementation of applications developed in the Maple software for the creation of mathematical exercises given the different levels of education whether basic or higher.
For the majority of teachers in this area, it seems very difficult to implement apps in Maple; that is why we show the creation of exercises easily and permanently. The purpose is to get teachers from our institutions to use applications ready to be evaluated in the classroom. The results of these apps (applications with components made in Maple) are supported on mobile devices such as tablets and / or laptops and taken to the cloud to be executed online from any computer. The generation of patterns is a very important alternative leaving aside random numbers, which would allow us to lose results
onscreen. With this; Our teachers in schools or universities would evaluate their students in parallel on the blackboard without losing the results of any student and thus achieve the competencies proposed in the learning sessions. In Spanish.<img src="https://www.maplesoft.com/view.aspx?si=154388/genexr.png" alt="Implementation of Maple apps for the creation of mathematical exercises in engineering" style="max-width: 25%;" align="left"/>In this research work has allowed to show the implementation of applications developed in the Maple software for the creation of mathematical exercises given the different levels of education whether basic or higher.
For the majority of teachers in this area, it seems very difficult to implement apps in Maple; that is why we show the creation of exercises easily and permanently. The purpose is to get teachers from our institutions to use applications ready to be evaluated in the classroom. The results of these apps (applications with components made in Maple) are supported on mobile devices such as tablets and / or laptops and taken to the cloud to be executed online from any computer. The generation of patterns is a very important alternative leaving aside random numbers, which would allow us to lose results
onscreen. With this; Our teachers in schools or universities would evaluate their students in parallel on the blackboard without losing the results of any student and thus achieve the competencies proposed in the learning sessions. In Spanish.https://www.maplesoft.com/applications/view.aspx?SID=154388&ref=FeedFri, 26 Jan 2018 05:00:00 ZProf. Lenin Araujo CastilloProf. Lenin Araujo CastilloMathematics for Chemistry
https://www.maplesoft.com/applications/view.aspx?SID=154267&ref=Feed
This interactive electronic textbook in the form of Maple worksheets comprises two parts.
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Part I, mathematics for chemistry, is supposed to cover all mathematics that an instructor of chemistry might hope and expect that his students would learn, understand and be able to apply as a result of sufficient courses typically, but not exclusively, presented in departments of mathematics. Its nine chapters include (0) a summary and illustration of useful Maple commands, (1) arithmetic, algebra and elementary functions, (2) plotting, descriptive geometry, trigonometry, series, complex functions, (3) differential calculus of one variable, (4) integral calculus of one variable, (5) multivariate calculus, (6) linear algebra including matrix, vector, eigenvector, vector calculus, tensor, spreadsheet, (7) differential and integral equations, and (8) probability, distribution, treatment of laboratory data, linear and non-linear regression and optimization.
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Part II presents mathematical topics typically taught within chemistry courses, including (9) chemical equilibrium, (10) group theory, (11) graph theory, (12a) introduction to quantum mechanics and quantum chemistry, (14) applications of Fourier transforms in chemistry including electron diffraction, x-ray diffraction, microwave spectra, infrared and Raman spectra and nuclear-magnetic-resonance spectra, and (18) dielectric and magnetic properties of chemical matter.
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Other chapters are in preparation and will be released in due course.
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Last updated on March 19, 2019<img src="https://www.maplesoft.com/view.aspx?si=154267/molecule.PNG" alt="Mathematics for Chemistry" style="max-width: 25%;" align="left"/>This interactive electronic textbook in the form of Maple worksheets comprises two parts.
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Part I, mathematics for chemistry, is supposed to cover all mathematics that an instructor of chemistry might hope and expect that his students would learn, understand and be able to apply as a result of sufficient courses typically, but not exclusively, presented in departments of mathematics. Its nine chapters include (0) a summary and illustration of useful Maple commands, (1) arithmetic, algebra and elementary functions, (2) plotting, descriptive geometry, trigonometry, series, complex functions, (3) differential calculus of one variable, (4) integral calculus of one variable, (5) multivariate calculus, (6) linear algebra including matrix, vector, eigenvector, vector calculus, tensor, spreadsheet, (7) differential and integral equations, and (8) probability, distribution, treatment of laboratory data, linear and non-linear regression and optimization.
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Part II presents mathematical topics typically taught within chemistry courses, including (9) chemical equilibrium, (10) group theory, (11) graph theory, (12a) introduction to quantum mechanics and quantum chemistry, (14) applications of Fourier transforms in chemistry including electron diffraction, x-ray diffraction, microwave spectra, infrared and Raman spectra and nuclear-magnetic-resonance spectra, and (18) dielectric and magnetic properties of chemical matter.
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Other chapters are in preparation and will be released in due course.
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Last updated on March 19, 2019https://www.maplesoft.com/applications/view.aspx?SID=154267&ref=FeedTue, 30 May 2017 04:00:00 ZProf. John OgilvieProf. John OgilvieClassroom Tips and Techniques: Integration by Parts
https://www.maplesoft.com/applications/view.aspx?SID=1742&ref=Feed
Maple implements integration by parts with two different commands. One was designed in a pedagogical setting, and the other, for a "production" setting. In this article, we compare the functionalities of these two commands.<img src="https://www.maplesoft.com/view.aspx?si=1742/tutor.png" alt="Classroom Tips and Techniques: Integration by Parts" style="max-width: 25%;" align="left"/>Maple implements integration by parts with two different commands. One was designed in a pedagogical setting, and the other, for a "production" setting. In this article, we compare the functionalities of these two commands.https://www.maplesoft.com/applications/view.aspx?SID=1742&ref=FeedThu, 02 Mar 2017 05:00:00 ZDr. Robert LopezDr. Robert LopezClassroom Tips and Techniques: Norm of a Matrix
https://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. 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. In this article we will show how Maple can be used to gain insight on what the norm of a matrix means.<img src="https://www.maplesoft.com/view.aspx?si=1430/thumb.jpg" alt="Classroom Tips and Techniques: Norm of a Matrix" style="max-width: 25%;" 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. 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. In this article we will show how Maple can be used to gain insight on what the norm of a matrix means.https://www.maplesoft.com/applications/view.aspx?SID=1430&ref=FeedMon, 13 Feb 2017 05:00:00 ZDr. Robert LopezDr. Robert LopezGirding the Equator of Earth with a Belt
https://www.maplesoft.com/applications/view.aspx?SID=154220&ref=Feed
This is a problem that appears in many calculus texts. The problem is that of girding the equator of the earth with a belt, then extending by one unit (here, taken as the foot) the radius of the circle so formed. The question is by how much does the circumference of the belt increase. This problem usually appears in the section of the calculus text dealing with linear approximations by the differential.
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This app is also the subject of a blog post on MaplePrimes: <A HREF="http://www.mapleprimes.com/maplesoftblog/207876-Girding-The-Equator-Of-The-Earth-With-A-Belt">Girding the Equator of Earth with a Belt</A><img src="https://www.maplesoft.com/view.aspx?si=154220/b54e83a2917e82eae1adfaebd0567f9c.gif" alt="Girding the Equator of Earth with a Belt" style="max-width: 25%;" align="left"/>This is a problem that appears in many calculus texts. The problem is that of girding the equator of the earth with a belt, then extending by one unit (here, taken as the foot) the radius of the circle so formed. The question is by how much does the circumference of the belt increase. This problem usually appears in the section of the calculus text dealing with linear approximations by the differential.
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This app is also the subject of a blog post on MaplePrimes: <A HREF="http://www.mapleprimes.com/maplesoftblog/207876-Girding-The-Equator-Of-The-Earth-With-A-Belt">Girding the Equator of Earth with a Belt</A>https://www.maplesoft.com/applications/view.aspx?SID=154220&ref=FeedTue, 07 Feb 2017 05:00:00 ZDr. Robert LopezDr. Robert LopezHollywood Math 2
https://www.maplesoft.com/applications/view.aspx?SID=153681&ref=Feed
<p>Over the years, Hollywood has entertained us with many mathematical moments in film and television, often in unexpected places. In this application, you’ll find several examples of Hollywood Math, including Fermat’s Last Theorem and <em>The Simpsons</em>, the Monty Hall problem in <em>21</em>, and a discussion of just how long that runway actually was in <em>The Fast and the Furious</em>. These examples are also presented in <a href="/webinars/recorded/featured.aspx?id=782">Hollywood Math 2: The Recorded Webinar</a>.</p>
<p>For even more examples, see <a href="/applications/view.aspx?SID=6611">Hollywood Math: The Original Episode</a>.</p><img src="https://www.maplesoft.com/view.aspx?si=153681/HollywoodMath2.jpg" alt="Hollywood Math 2" style="max-width: 25%;" align="left"/><p>Over the years, Hollywood has entertained us with many mathematical moments in film and television, often in unexpected places. In this application, you’ll find several examples of Hollywood Math, including Fermat’s Last Theorem and <em>The Simpsons</em>, the Monty Hall problem in <em>21</em>, and a discussion of just how long that runway actually was in <em>The Fast and the Furious</em>. These examples are also presented in <a href="/webinars/recorded/featured.aspx?id=782">Hollywood Math 2: The Recorded Webinar</a>.</p>
<p>For even more examples, see <a href="/applications/view.aspx?SID=6611">Hollywood Math: The Original Episode</a>.</p>https://www.maplesoft.com/applications/view.aspx?SID=153681&ref=FeedTue, 23 Sep 2014 04:00:00 ZMaplesoftMaplesoftRate of Change of Surface Area on an Expanding Sphere
https://www.maplesoft.com/applications/view.aspx?SID=149511&ref=Feed
<p>An example of a related-rates problem in differential calculus that asks for the rate of change of surface area on a sphere whose volume expands at a constant rate is <a href="http://www.maplesoft.com/teachingconcepts/detail.aspx?cid=7">solved here</a> via the syntax-free paradigm in Maple. </p>
<p>Recently, after presenting the solution in a Maplesoft Webinar, I was asked if it were possible to see an animation for this process. So, after a quick presentation of a solution, this worksheet will try to answer the request for an animation. Of course, we first have to consider just what is it that is to be displayed in the animation. It's easy enough to show an expanding sphere, but the question of real interest is the varying rate of change of surface area. How is the change in surface area to be visualized, let alone animated?</p><img src="https://www.maplesoft.com/view.aspx?si=149511/related-rates.JPG" alt="Rate of Change of Surface Area on an Expanding Sphere" style="max-width: 25%;" align="left"/><p>An example of a related-rates problem in differential calculus that asks for the rate of change of surface area on a sphere whose volume expands at a constant rate is <a href="http://www.maplesoft.com/teachingconcepts/detail.aspx?cid=7">solved here</a> via the syntax-free paradigm in Maple. </p>
<p>Recently, after presenting the solution in a Maplesoft Webinar, I was asked if it were possible to see an animation for this process. So, after a quick presentation of a solution, this worksheet will try to answer the request for an animation. Of course, we first have to consider just what is it that is to be displayed in the animation. It's easy enough to show an expanding sphere, but the question of real interest is the varying rate of change of surface area. How is the change in surface area to be visualized, let alone animated?</p>https://www.maplesoft.com/applications/view.aspx?SID=149511&ref=FeedTue, 16 Jul 2013 04:00:00 ZDr. Robert LopezDr. Robert LopezClassroom Tips and Techniques: The Sliding Ladder
https://www.maplesoft.com/applications/view.aspx?SID=148714&ref=Feed
A January 10, 2013 post to <a href="http://www.mapleprimes.com/questions/142194-Sliding-Ladder-Animation" class="plainlink">MaplePrimes</a> asked for an animation of the trajectory traced by the center of a "sliding ladder." This month's article generalizes the solutions suggested by Adri van der Meer and Doug Meade, and shows the trajectory of an arbitrary point on the ladder as its top slides down a vertical wall and its bottom moves away from that wall along an orthogonal "floor." The location of the arbitrary point on the ladder is controlled by a slider, the animation being generated with the updated Explore command.<img src="https://www.maplesoft.com/view.aspx?si=148714/thumb.jpg" alt="Classroom Tips and Techniques: The Sliding Ladder" style="max-width: 25%;" align="left"/>A January 10, 2013 post to <a href="http://www.mapleprimes.com/questions/142194-Sliding-Ladder-Animation" class="plainlink">MaplePrimes</a> asked for an animation of the trajectory traced by the center of a "sliding ladder." This month's article generalizes the solutions suggested by Adri van der Meer and Doug Meade, and shows the trajectory of an arbitrary point on the ladder as its top slides down a vertical wall and its bottom moves away from that wall along an orthogonal "floor." The location of the arbitrary point on the ladder is controlled by a slider, the animation being generated with the updated Explore command.https://www.maplesoft.com/applications/view.aspx?SID=148714&ref=FeedFri, 21 Jun 2013 04:00:00 ZDr. Robert LopezDr. Robert LopezPerimeter, area and visualization of a plane figure
https://www.maplesoft.com/applications/view.aspx?SID=146470&ref=Feed
<p>The work contains three procedures that allow symbolically to calculate the perimeter and area of any plane figure bounded by <span>non-selfintersecting piecewise smooth curve</span>, and to portray this figure together with its boundary in a suitable design.</p><img src="https://www.maplesoft.com/view.aspx?si=146470/planefigure_thumb.png" alt="Perimeter, area and visualization of a plane figure" style="max-width: 25%;" align="left"/><p>The work contains three procedures that allow symbolically to calculate the perimeter and area of any plane figure bounded by <span>non-selfintersecting piecewise smooth curve</span>, and to portray this figure together with its boundary in a suitable design.</p>https://www.maplesoft.com/applications/view.aspx?SID=146470&ref=FeedTue, 30 Apr 2013 04:00:00 ZDr. Yury ZavarovskyDr. Yury ZavarovskyClassroom Tips and Techniques: Tractrix Questions - A Homework Problem from MaplePrimes
https://www.maplesoft.com/applications/view.aspx?SID=137299&ref=Feed
A May 13, 2012, post to MaplePrimes asked some interesting questions about the tractrix defined parametrically by <em>x(s)</em> = sech<em>(s), y(s)</em> = <em>s</em> - tanh(s), s ≥ 0. I answered these questions on May 14 in a worksheet that forms the basis for this month's article.</p>
<p>It behooves me to write this article because the solution given in the May 14 MaplePrimes reply wasn't completely correct, the error stemming from a confounding of the variables <em>x, y, </em>and <em>s</em>. Mea culpa.<img src="https://www.maplesoft.com/view.aspx?si=137299/thumb.jpg" alt="Classroom Tips and Techniques: Tractrix Questions - A Homework Problem from MaplePrimes" style="max-width: 25%;" align="left"/>A May 13, 2012, post to MaplePrimes asked some interesting questions about the tractrix defined parametrically by <em>x(s)</em> = sech<em>(s), y(s)</em> = <em>s</em> - tanh(s), s ≥ 0. I answered these questions on May 14 in a worksheet that forms the basis for this month's article.</p>
<p>It behooves me to write this article because the solution given in the May 14 MaplePrimes reply wasn't completely correct, the error stemming from a confounding of the variables <em>x, y, </em>and <em>s</em>. Mea culpa.https://www.maplesoft.com/applications/view.aspx?SID=137299&ref=FeedWed, 12 Sep 2012 04:00:00 ZDr. Robert LopezDr. Robert LopezMath Apps in Maple
https://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="https://www.maplesoft.com/view.aspx?si=132220/mathapps_thumb.png" alt="Math Apps in Maple" style="max-width: 25%;" 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.https://www.maplesoft.com/applications/view.aspx?SID=132220&ref=FeedTue, 27 Mar 2012 04:00:00 ZMaplesoftMaplesoftzoMbi
https://www.maplesoft.com/applications/view.aspx?SID=129642&ref=Feed
<p>Higher Mathematics for external students of biological faculty.<br />Solver-practicum.<br />1st semester.<br />300 problems (15 labs in 20 variants).<br />mw.zip</p>
<p>Before use - Shake! <br />(Click on the button and activate the program and Maplet).<br />Full version in html: <a href="http://webmath.exponenta.ru/zom/index.html">http://webmath.exponenta.ru/zom/index.html</a></p><img src="https://www.maplesoft.com/view.aspx?si=129642/zombie_3.jpg" alt="zoMbi" style="max-width: 25%;" align="left"/><p>Higher Mathematics for external students of biological faculty.<br />Solver-practicum.<br />1st semester.<br />300 problems (15 labs in 20 variants).<br />mw.zip</p>
<p>Before use - Shake! <br />(Click on the button and activate the program and Maplet).<br />Full version in html: <a href="http://webmath.exponenta.ru/zom/index.html">http://webmath.exponenta.ru/zom/index.html</a></p>https://www.maplesoft.com/applications/view.aspx?SID=129642&ref=FeedSun, 15 Jan 2012 05:00:00 ZDr. Valery CyboulkoDr. Valery CyboulkoAn Epidemic Model (for Influenza or Zombies)
https://www.maplesoft.com/applications/view.aspx?SID=127836&ref=Feed
<p>Systems of differential equations can be used to model an epidemic of influenza or of zombies. This is an interactive Maple document suitable for use in courses on mathematical biology or differential equations or calculus courses that include differential equations. No knowledge of Maple is required.</p><img src="https://www.maplesoft.com/view.aspx?si=127836/Cholera.jpg" alt="An Epidemic Model (for Influenza or Zombies)" style="max-width: 25%;" align="left"/><p>Systems of differential equations can be used to model an epidemic of influenza or of zombies. This is an interactive Maple document suitable for use in courses on mathematical biology or differential equations or calculus courses that include differential equations. No knowledge of Maple is required.</p>https://www.maplesoft.com/applications/view.aspx?SID=127836&ref=FeedThu, 17 Nov 2011 05:00:00 ZDr. Robert IsraelDr. Robert IsraelWhy I Needed Maple to Make Cream Cheese Frosting
https://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="https://www.maplesoft.com/view.aspx?si=125069/philly_thumb.png" alt="Why I Needed Maple to Make Cream Cheese Frosting" style="max-width: 25%;" 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>https://www.maplesoft.com/applications/view.aspx?SID=125069&ref=FeedTue, 23 Aug 2011 04:00:00 ZDr. Jason SchattmanDr. Jason SchattmanMapler. 05. Аlgebraic equations & Index
https://www.maplesoft.com/applications/view.aspx?SID=102285&ref=Feed
<p>Mathematical program-controlled multivariate Workshop.<br />Version without maplets and test problems. <br />Further depends on community interest.</p><img src="https://www.maplesoft.com/view.aspx?si=102285/mrs.jpg" alt="Mapler. 05. Аlgebraic equations & Index" style="max-width: 25%;" align="left"/><p>Mathematical program-controlled multivariate Workshop.<br />Version without maplets and test problems. <br />Further depends on community interest.</p>https://www.maplesoft.com/applications/view.aspx?SID=102285&ref=FeedMon, 07 Mar 2011 05:00:00 ZDr. Valery CyboulkoDr. Valery CyboulkoExotic EIE-course
https://www.maplesoft.com/applications/view.aspx?SID=102076&ref=Feed
<p>Ukraine. <br />Exotic training course for the entrance examination in mathematics.<br /><strong>External independent evaluation</strong> <br />Themes:<br />0101 Goals and rational number <br />0102 Interest. The main problem of interest <br />0103 The simplest geometric shapes on the plane and their properties <br />0201 Degree of natural and integral indicator <br />0202 Monomial and polynomials and operations on them <br />0203 Triangles and their basic properties <br />0301 Algebraic fractions and operations on them <br />0302 Square root. Real numbers <br />0303 Circle and circle, their properties <br />0401 Equations, inequalities and their systems <br />0402 Function and its basic properties <br />0403 Described and inscribed triangles <br />0501 Linear function, linear equations, inequalities and their systems <br />0502 Quadratic function, quadratic equation, inequality and their systems <br />0503 Solving square triangles <br />0601 Rational Equations, Inequalities and their sysytemy <br />0602 Numerical sequence. Arithmetic and geometric progression <br />0603 Solving arbitrary triangles <br />0701 Sine, cosine, tangent and cotangent numeric argument <br />0702 Identical transformation of trigonometric expressions <br />0703 Quadrilateral types and their basic properties <br />0801 Trigonometric and inverse trigonometric functions, their properties <br />0802 Trigonometric equations and inequalities <br />0803 Polygons and their properties <br />0901 The root of n-th degree. Degree of rational parameters <br />0902 The power functions and their properties. Irrational equations, inequalities and their systems <br />0903 Regular polygons and their properties <br />1001 Logarithms. Logarithmic function. Logarithmic equations, inequalities and their systems <br />1002 Exponential function. Indicator of equations, inequalities and their systems <br />1003 Direct and planes in space <br />1101 Derivative and its geometric and mechanical content <br />1102 Derivatives and its application <br />1103 Polyhedron. Prisms and pyramids. Regular polyhedron <br />1201 Initial and definite integral <br />1202 Application of certain integral <br />1203 Body rotation <br />1301 Compounds. Binomial theorem <br />1302 General methods for solving equations, inequalities and their systems <br />1303 Coordinates in the plane and in space <br />1401 The origins of probability theory <br />1402 Beginnings of Mathematical Statistics <br />1403 Vectors in the plane and in space <br /><strong>Maple </strong>version<br /><strong>Html-interactive</strong> version</p><img src="https://www.maplesoft.com/view.aspx?si=102076/ell.jpg" alt="Exotic EIE-course" style="max-width: 25%;" align="left"/><p>Ukraine. <br />Exotic training course for the entrance examination in mathematics.<br /><strong>External independent evaluation</strong> <br />Themes:<br />0101 Goals and rational number <br />0102 Interest. The main problem of interest <br />0103 The simplest geometric shapes on the plane and their properties <br />0201 Degree of natural and integral indicator <br />0202 Monomial and polynomials and operations on them <br />0203 Triangles and their basic properties <br />0301 Algebraic fractions and operations on them <br />0302 Square root. Real numbers <br />0303 Circle and circle, their properties <br />0401 Equations, inequalities and their systems <br />0402 Function and its basic properties <br />0403 Described and inscribed triangles <br />0501 Linear function, linear equations, inequalities and their systems <br />0502 Quadratic function, quadratic equation, inequality and their systems <br />0503 Solving square triangles <br />0601 Rational Equations, Inequalities and their sysytemy <br />0602 Numerical sequence. Arithmetic and geometric progression <br />0603 Solving arbitrary triangles <br />0701 Sine, cosine, tangent and cotangent numeric argument <br />0702 Identical transformation of trigonometric expressions <br />0703 Quadrilateral types and their basic properties <br />0801 Trigonometric and inverse trigonometric functions, their properties <br />0802 Trigonometric equations and inequalities <br />0803 Polygons and their properties <br />0901 The root of n-th degree. Degree of rational parameters <br />0902 The power functions and their properties. Irrational equations, inequalities and their systems <br />0903 Regular polygons and their properties <br />1001 Logarithms. Logarithmic function. Logarithmic equations, inequalities and their systems <br />1002 Exponential function. Indicator of equations, inequalities and their systems <br />1003 Direct and planes in space <br />1101 Derivative and its geometric and mechanical content <br />1102 Derivatives and its application <br />1103 Polyhedron. Prisms and pyramids. Regular polyhedron <br />1201 Initial and definite integral <br />1202 Application of certain integral <br />1203 Body rotation <br />1301 Compounds. Binomial theorem <br />1302 General methods for solving equations, inequalities and their systems <br />1303 Coordinates in the plane and in space <br />1401 The origins of probability theory <br />1402 Beginnings of Mathematical Statistics <br />1403 Vectors in the plane and in space <br /><strong>Maple </strong>version<br /><strong>Html-interactive</strong> version</p>https://www.maplesoft.com/applications/view.aspx?SID=102076&ref=FeedMon, 28 Feb 2011 05:00:00 ZTIMOTIMOHow Fast Does An Advent Candle Burn?
https://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="https://www.maplesoft.com/view.aspx?si=100332/thumb.jpg" alt="How Fast Does An Advent Candle Burn?" style="max-width: 25%;" 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>https://www.maplesoft.com/applications/view.aspx?SID=100332&ref=FeedMon, 20 Dec 2010 05:00:00 ZDr. Jason SchattmanDr. Jason Schattman