MaplePrimes - Maplesoft Blog
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en-us2016 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemTue, 06 Dec 2016 21:48:54 GMTTue, 06 Dec 2016 21:48:54 GMTThe latest posts on the Maplesoft Bloghttp://www.mapleprimes.com/images/mapleprimeswhite.jpgMaplePrimes - Maplesoft Blog
http://www.mapleprimes.com/maplesoftblog
Utilizing MapleSim to Improve Assisted Living Devices
http://www.mapleprimes.com/maplesoftblog/207408-Utilizing-MapleSim-To-Improve-Assisted?ref=Feed:MaplePrimes:Maplesoft Blog
<p style="margin-left: 40px;"><em>This MaplePrimes guest blog post is from Dr. James Smith, an Assistant Lecturer in the Electrical Engineering and Computer Science Department of York University’s Lassonde School of Engineering. His team has been working with Maplesim to improve the design of assistive devices.</em></p>
<p>As we go through our everyday lives, we rarely give much thought to the complex motions and movements our bodies go through on a regular basis. Motions and movements that seem so simple on the surface require more strength and coordination to execute than we realize. And these are made far more difficult as we age or when our health is in decline. So what can be done to assist us with these functions?</p>
<p>In recent years, my research team and I have been working on developing more practical and streamlined devices to assist humans with everyday movements, such as standing and sitting. Our objective was to determine if energy could be regenerated in prosthetic devices during these movements, similar to the way in which hybrid electric vehicles recover waste heat from braking and convert it into useable energy.</p>
<p align="CENTER"><iframe allowfullscreen="" height="315" src="https://www.youtube.com/embed/IpkUK5V2l4c" width="560"></iframe></p>
<p>People use – and potentially generate – more energy than they realize in carrying out common, everyday movements. Our research for this project <a href="https://www.youtube.com/watch?v=IpkUK5V2l4c#action=share">focused on the leg joints</a>, and investigated which of the three joints (ankle, knee or hip) was able to regenerate the most energy throughout a sitting or standing motion. We were confident that determining this would lead to the development of more efficient locomotive devices for people suffering from diseases or disabilities affecting the muscles around these joints.</p>
<p>In order to identify the point at which regenerative power is at its peak, <a href="http://www.maplesoft.com/company/casestudies/stories/sit2stand.aspx">we determined that MapleSim was the best tool</a> to help us gather the desired data. We took biomechanical data from actual human trials and applied them to a robotic model that mimics human movements when transitioning between sitting and standing positions. We created models to measure unique movements and energy consumption at each joint throughout the identified movements to determine where the greatest regeneration occurred.</p>
<p>To successfully carry out our research, it was essential that we were able to model the complex chemical reactions that occur within the battery needed to power the assistive device. It is a challenge finding this feature in many engineering software programs and MapleSim’s battery modeling library saved our team a great deal of time and effort during the process, as we were able to <a href="http://www.maplesoft.com/products/maplesim/ModelGallery/detail.aspx?id=250">use an existing MapleSim model</a> and simply make adjustments to fit our project.</p>
<p>Using MapleSim, we developed a simplified model of the human leg with a foot firmly planted on the ground, followed by a more complex model with a realistic human foot that could be raised off the ground. The first model was used to create a simplified model-based motion controller that was then applied to the second model. The human trials we conducted produced the necessary data for input into a multi-domain MapleSim model that was used to accurately simulate the necessary motions to properly analyze battery autonomy.</p>
<p><img src="/view.aspx?sf=207408_post/Sit2Stand_ThreeLinkPendulum.jpg"></p>
<p>The findings that resulted from our research have useful and substantial applications for prostheses and orthoses designs. If one is able to determine the most efficient battery autonomy, operation of these assistive devices can be prolonged, and smaller, lighter batteries can be used to power them. Ultimately, our simulations and the resulting data create the possibility of more efficient devices that can reduce joint loads during standing to sitting processes, and vice versa.</p>
<p style="margin-left: 40px;"><em>This MaplePrimes guest blog post is from Dr. James Smith, an Assistant Lecturer in the Electrical Engineering and Computer Science Department of York University’s Lassonde School of Engineering. His team has been working with Maplesim to improve the design of assistive devices.</em></p>
<p>As we go through our everyday lives, we rarely give much thought to the complex motions and movements our bodies go through on a regular basis. Motions and movements that seem so simple on the surface require more strength and coordination to execute than we realize. And these are made far more difficult as we age or when our health is in decline. So what can be done to assist us with these functions?</p>
<p>In recent years, my research team and I have been working on developing more practical and streamlined devices to assist humans with everyday movements, such as standing and sitting. Our objective was to determine if energy could be regenerated in prosthetic devices during these movements, similar to the way in which hybrid electric vehicles recover waste heat from braking and convert it into useable energy.</p>
<p align="CENTER"><iframe allowfullscreen="" height="315" src="https://www.youtube.com/embed/IpkUK5V2l4c" width="560"></iframe></p>
<p>People use – and potentially generate – more energy than they realize in carrying out common, everyday movements. Our research for this project <a href="https://www.youtube.com/watch?v=IpkUK5V2l4c#action=share">focused on the leg joints</a>, and investigated which of the three joints (ankle, knee or hip) was able to regenerate the most energy throughout a sitting or standing motion. We were confident that determining this would lead to the development of more efficient locomotive devices for people suffering from diseases or disabilities affecting the muscles around these joints.</p>
<p>In order to identify the point at which regenerative power is at its peak, <a href="http://www.maplesoft.com/company/casestudies/stories/sit2stand.aspx">we determined that MapleSim was the best tool</a> to help us gather the desired data. We took biomechanical data from actual human trials and applied them to a robotic model that mimics human movements when transitioning between sitting and standing positions. We created models to measure unique movements and energy consumption at each joint throughout the identified movements to determine where the greatest regeneration occurred.</p>
<p>To successfully carry out our research, it was essential that we were able to model the complex chemical reactions that occur within the battery needed to power the assistive device. It is a challenge finding this feature in many engineering software programs and MapleSim’s battery modeling library saved our team a great deal of time and effort during the process, as we were able to <a href="http://www.maplesoft.com/products/maplesim/ModelGallery/detail.aspx?id=250">use an existing MapleSim model</a> and simply make adjustments to fit our project.</p>
<p>Using MapleSim, we developed a simplified model of the human leg with a foot firmly planted on the ground, followed by a more complex model with a realistic human foot that could be raised off the ground. The first model was used to create a simplified model-based motion controller that was then applied to the second model. The human trials we conducted produced the necessary data for input into a multi-domain MapleSim model that was used to accurately simulate the necessary motions to properly analyze battery autonomy.</p>
<p><img src="/view.aspx?sf=207408_post/Sit2Stand_ThreeLinkPendulum.jpg"></p>
<p>The findings that resulted from our research have useful and substantial applications for prostheses and orthoses designs. If one is able to determine the most efficient battery autonomy, operation of these assistive devices can be prolonged, and smaller, lighter batteries can be used to power them. Ultimately, our simulations and the resulting data create the possibility of more efficient devices that can reduce joint loads during standing to sitting processes, and vice versa.</p>
207408Thu, 10 Nov 2016 15:47:01 ZOnnimikkiOnnimikkiSummary of the 2016 Maple T.A. and MÃ¶bius User Summit
http://www.mapleprimes.com/maplesoftblog/207379-Summary-Of-The-2016-Maple-TA-And-Mbius?ref=Feed:MaplePrimes:Maplesoft Blog
<p>From October 19-21, the third installment of the Maple T.A. and Möbius User Summit took place. Making the move back to Europe this year, the three-day conference was held at the beautiful Vienna University of Technology in the heart of Vienna, Austria. The scope of this year’s event expanded to include Maplesoft’s newest product, Möbius, which is designed to help academic institutions move their STEM courses online.</p>
<p>This year’s Summit brought together participants from 20 countries, including Australia, the Czech Republic, Poland, China, Norway, India, Egypt, Japan, the Netherlands, and many others. Needless to say, there is great interest in learning more about how Maple T.A. and Möbius can play a role in shaping the educational landscape.</p>
<p>Video recordings of each presentation will be made public soon, so keep an eye out for them!</p>
<p><img src="/ViewTemp.ashx?f=170335_1478289377/Summit_Attendees.jpg"><em>Conference attendees take in the sights on the veranda at TU Wien</em></p>
<p><strong><u>Getting Down to Business</u></strong></p>
<p>Presentations were divided into 5 overarching themes as they relate to Maple T.A. and Möbius: Shaping Curriculum; Content Creation; Experiences Using Möbius; Integrating with your Technology; and The Future of Online Education. Presentations were given by representatives from schools across Europe, including DTU (Denmark), TH Köln (Germany), Imperial College of London and University of Birmingham (UK), Vienna UT (Austria), KTH Royal Institute of Technology (Sweden), Université de Lausanne (Switzerland), and others.</p>
<p><img src="/ViewTemp.ashx?f=170335_1478289377/IMG_8595.jpg"></p>
<p>Many talks showcased the impressive versatility of Maple T.A. and Möbius to have practical applications in all STEM subjects, from Nuclear Engineering to Operations Management and many subjects in between.</p>
<p>Perhaps the discussion that gave Maplesoft the most feedback was led by Steve Furino from the University of Waterloo, who divided attendees up into groups to formulate a wish list of what they’d like to see in a courseware authoring environment. The list had over 40 items.</p>
<p><img src="/ViewTemp.ashx?f=170335_1478289377/Linda_in_a_group.jpg"><br>
<em>Linda Simonsen, Country Manager in the Nordic, records a group’s wish list</em></p>
<p><strong><u>Notable Quotables</u></strong></p>
<p>Many thought-provoking statements and questions were posed, but the following few stood out above the rest:</p>
<ul>
<li>“Wouldn’t it be wonderful if you could take the best course from the best instructor anywhere in the world?”</li>
<li>“With Maple T.A., we can divert resources away from grading and over to tutoring.”</li>
<li>“Möbius rescued us!”</li>
</ul>
<p><strong><u>Get the party started!</u></strong></p>
<p>While each day was full of invigorating conference discussions, evenings provided ample opportunity to ditch the suit jacket and tie, and enjoy the lively Austrian atmosphere. The first evening at the Zwölf Apostelkeller was the perfect venue to break the ice while satisfying those taste buds longing for some traditional Viennese cuisine. Once Schnitzel, Käsespätzle (a delicious German version of Mac and Cheese), Strudel, Kaiserschmarren (shredded pancake), and a glass or two of wine hit the table, people soon forgot about the pouring rain outside.</p>
<p><img src="/ViewTemp.ashx?f=170335_1478289377/Zwoelf_Apostelkeller.jpg"></p>
<p><img src="/ViewTemp.ashx?f=170335_1478289377/Jonny_and_friends.jpg"></p>
<p><img src="/ViewTemp.ashx?f=170335_1478289377/Keller.jpg"></p>
<p><em>The evening reception took place 3-4 levels under ground</em></p>
<p><img src="/ViewTemp.ashx?f=170335_1478289377/European_Service_sm.jpg"></p>
<p><em>Michael Pisapia, VP of Europe, serves digestifs to guests</em></p>
<p>It would have been hard to top the social in the Apostelkeller, but the next evening sure tried.</p>
<p>Day 2 finished with an impressive formal dining experience at the historic Gerstner Beletage in the Palace Todesco, built in 1864 and situated directly across from the Vienna State Opera House. The 500-room palace was home to Eduard Freiherr von Todesco, a well-known Viennese banker.</p>
<p><img src="/ViewTemp.ashx?f=170335_1478289377/Palace_empty_sm.jpg"></p>
<p><img src="/ViewTemp.ashx?f=170335_1478289377/Palace_reception.jpg"></p>
<p><img src="/ViewTemp.ashx?f=170335_1478289377/Opera_House.jpg"></p>
<p><em>View from the palace of the Vienna State Opera House</em></p>
<p><img src="/ViewTemp.ashx?f=170335_1478289377/Palace_Jonny.jpg"></p>
<p><i>Jonny Zivku, Maple T.A. Product Manager, g</i><em>ives opening remarks at the Gerstner Beletage im Palais Todesco</em></p>
<p><img src="/ViewTemp.ashx?f=170335_1478289377/Jonathan_and_Mike_sm.jpg"></p>
<p><em>Jonathan Watkins from the University of Birmingham and Michael Pisapia - both dressed to impress</em></p>
<p>The skies finally cleared enough to take some photos, but only after most people had gone home. Thankfully Aron Pasieka, Möbius Project Manager, was still around to get some great shots of the city. Enjoy!</p>
<p><img src="/ViewTemp.ashx?f=170335_1478289377/Vienna-1.jpg"><br>
<img src="/ViewTemp.ashx?f=170335_1478289377/Sky15.jpg"></p>
<p><em>Before the skies cleared vs. after the skies cleared</em></p>
<p><img src="/ViewTemp.ashx?f=170335_1478289377/Vienna1.jpg"></p>
<p><img src="/ViewTemp.ashx?f=170335_1478289377/Vienna2.jpg"></p>
<p><img src="/ViewTemp.ashx?f=170335_1478289377/Vienna3.jpg"></p>
<p>From beginning to end, the entire Summit was very well received by everyone who attended.</p>
<p>We would be remiss if we did not thank our incredible hosts at the Vienna University of Technology. Stefanie Winkler, Professor Andreas Körner, and Professor Felix Breitenecker were beyond helpful in bringing many of the finer details together, as well as helping many people overcome the language barrier.</p>
<p>We can’t wait to do it all again in London, England in 2017, and hope to see just as many new faces as familiar ones.</p>
<p> </p>
<p>Photo credits: A. Pasieka, A. French, H. Zunic, J. Cooper</p>
<p>From October 19-21, the third installment of the Maple T.A. and Möbius User Summit took place. Making the move back to Europe this year, the three-day conference was held at the beautiful Vienna University of Technology in the heart of Vienna, Austria. The scope of this year’s event expanded to include Maplesoft’s newest product, Möbius, which is designed to help academic institutions move their STEM courses online.</p>
<p>This year’s Summit brought together participants from 20 countries, including Australia, the Czech Republic, Poland, China, Norway, India, Egypt, Japan, the Netherlands, and many others. Needless to say, there is great interest in learning more about how Maple T.A. and Möbius can play a role in shaping the educational landscape.</p>
<p>Video recordings of each presentation will be made public soon, so keep an eye out for them!</p>
<p><img src="/ViewTemp.ashx?f=170335_1478289377/Summit_Attendees.jpg"><em>Conference attendees take in the sights on the veranda at TU Wien</em></p>
<p><strong><u>Getting Down to Business</u></strong></p>
<p>Presentations were divided into 5 overarching themes as they relate to Maple T.A. and Möbius: Shaping Curriculum; Content Creation; Experiences Using Möbius; Integrating with your Technology; and The Future of Online Education. Presentations were given by representatives from schools across Europe, including DTU (Denmark), TH Köln (Germany), Imperial College of London and University of Birmingham (UK), Vienna UT (Austria), KTH Royal Institute of Technology (Sweden), Université de Lausanne (Switzerland), and others.</p>
<p><img src="/ViewTemp.ashx?f=170335_1478289377/IMG_8595.jpg"></p>
<p>Many talks showcased the impressive versatility of Maple T.A. and Möbius to have practical applications in all STEM subjects, from Nuclear Engineering to Operations Management and many subjects in between.</p>
<p>Perhaps the discussion that gave Maplesoft the most feedback was led by Steve Furino from the University of Waterloo, who divided attendees up into groups to formulate a wish list of what they’d like to see in a courseware authoring environment. The list had over 40 items.</p>
<p><img src="/ViewTemp.ashx?f=170335_1478289377/Linda_in_a_group.jpg"><br>
<em>Linda Simonsen, Country Manager in the Nordic, records a group’s wish list</em></p>
<p><strong><u>Notable Quotables</u></strong></p>
<p>Many thought-provoking statements and questions were posed, but the following few stood out above the rest:</p>
<ul>
<li>“Wouldn’t it be wonderful if you could take the best course from the best instructor anywhere in the world?”</li>
<li>“With Maple T.A., we can divert resources away from grading and over to tutoring.”</li>
<li>“Möbius rescued us!”</li>
</ul>
<p><strong><u>Get the party started!</u></strong></p>
<p>While each day was full of invigorating conference discussions, evenings provided ample opportunity to ditch the suit jacket and tie, and enjoy the lively Austrian atmosphere. The first evening at the Zwölf Apostelkeller was the perfect venue to break the ice while satisfying those taste buds longing for some traditional Viennese cuisine. Once Schnitzel, Käsespätzle (a delicious German version of Mac and Cheese), Strudel, Kaiserschmarren (shredded pancake), and a glass or two of wine hit the table, people soon forgot about the pouring rain outside.</p>
<p><img src="/ViewTemp.ashx?f=170335_1478289377/Zwoelf_Apostelkeller.jpg"></p>
<p><img src="/ViewTemp.ashx?f=170335_1478289377/Jonny_and_friends.jpg"></p>
<p><img src="/ViewTemp.ashx?f=170335_1478289377/Keller.jpg"></p>
<p><em>The evening reception took place 3-4 levels under ground</em></p>
<p><img src="/ViewTemp.ashx?f=170335_1478289377/European_Service_sm.jpg"></p>
<p><em>Michael Pisapia, VP of Europe, serves digestifs to guests</em></p>
<p>It would have been hard to top the social in the Apostelkeller, but the next evening sure tried.</p>
<p>Day 2 finished with an impressive formal dining experience at the historic Gerstner Beletage in the Palace Todesco, built in 1864 and situated directly across from the Vienna State Opera House. The 500-room palace was home to Eduard Freiherr von Todesco, a well-known Viennese banker.</p>
<p><img src="/ViewTemp.ashx?f=170335_1478289377/Palace_empty_sm.jpg"></p>
<p><img src="/ViewTemp.ashx?f=170335_1478289377/Palace_reception.jpg"></p>
<p><img src="/ViewTemp.ashx?f=170335_1478289377/Opera_House.jpg"></p>
<p><em>View from the palace of the Vienna State Opera House</em></p>
<p><img src="/ViewTemp.ashx?f=170335_1478289377/Palace_Jonny.jpg"></p>
<p><i>Jonny Zivku, Maple T.A. Product Manager, g</i><em>ives opening remarks at the Gerstner Beletage im Palais Todesco</em></p>
<p><img src="/ViewTemp.ashx?f=170335_1478289377/Jonathan_and_Mike_sm.jpg"></p>
<p><em>Jonathan Watkins from the University of Birmingham and Michael Pisapia - both dressed to impress</em></p>
<p>The skies finally cleared enough to take some photos, but only after most people had gone home. Thankfully Aron Pasieka, Möbius Project Manager, was still around to get some great shots of the city. Enjoy!</p>
<p><img src="/ViewTemp.ashx?f=170335_1478289377/Vienna-1.jpg"><br>
<img src="/ViewTemp.ashx?f=170335_1478289377/Sky15.jpg"></p>
<p><em>Before the skies cleared vs. after the skies cleared</em></p>
<p><img src="/ViewTemp.ashx?f=170335_1478289377/Vienna1.jpg"></p>
<p><img src="/ViewTemp.ashx?f=170335_1478289377/Vienna2.jpg"></p>
<p><img src="/ViewTemp.ashx?f=170335_1478289377/Vienna3.jpg"></p>
<p>From beginning to end, the entire Summit was very well received by everyone who attended.</p>
<p>We would be remiss if we did not thank our incredible hosts at the Vienna University of Technology. Stefanie Winkler, Professor Andreas Körner, and Professor Felix Breitenecker were beyond helpful in bringing many of the finer details together, as well as helping many people overcome the language barrier.</p>
<p>We can’t wait to do it all again in London, England in 2017, and hope to see just as many new faces as familiar ones.</p>
<p> </p>
<p>Photo credits: A. Pasieka, A. French, H. Zunic, J. Cooper</p>
207379Tue, 08 Nov 2016 13:41:50 ZjarmitagejarmitageSupporting STEM Education
http://www.mapleprimes.com/maplesoftblog/207318-Supporting-STEM-Education?ref=Feed:MaplePrimes:Maplesoft Blog
<p style="margin-left: 40px;"><em>This MaplePrimes guest blog post is from Ian VanderBurgh, the Director of the Center for Education in Mathematics and Computing (CEMC) and a Lecturer in the Faculty of Mathematics at the University of Waterloo. He has been overseeing a project to develop online, interactive mathematics curriculum for high school students, and has been integral in the development of Möbius, Maplesoft's <a href="http://www.maplesoft.com/products/mobius">online courseware environment</a>.</em></p>
<p>Start with one part interest in online education, add one part increased functionality for developing online content, and mix with one part increased focus in the media and elsewhere on mathematics education. What does this produce? The perfect time to create high-quality online resources to support learning and teaching in mathematics.</p>
<p>The Centre for Education in Mathematics and Computing (CEMC) at the University of Waterloo aims to increase interest, enjoyment, confidence, and ability in mathematics and computer science among learners and educators in Canada and internationally. For more than fifty years, we have been working with teachers to support the important work that they do in the classroom. When online courses rose to prominence several years ago, we felt that this gave us the perfect opportunity to create materials to better support the curriculum being taught across Canada and around the world.</p>
<p>The content for what we now call “Phase One” was planned: Advanced Functions (Pre-Calculus) as well as Calculus & Vectors. These materials would support the education of students in their final year of secondary school, and also provide materials to reinforce concepts for students in STEM programs at the post-secondary level.</p>
<p>After deciding on the content, we needed a platform. We knew that we needed one with exceptional mathematical capabilities. Thus, we have been working hand-in-hand with Maplesoft ever since.</p>
<p>With content and platform established, the style began to take shape. It is based around what one of my colleagues calls “the five Es”: <strong>Exposition</strong> (onscreen text with synchronized audio), <strong>Experimentation</strong> (worksheets where users can manipulate mathematical objects), <strong>Evaluation</strong> (re-generating quiz questions), <strong>Exercises</strong> (with answers and solutions), and <strong>Enrichment</strong> (application and extension problems and solutions). <a href="http://courseware.cemc.uwaterloo.ca">Have a look at the materials</a> and <a href="https://www.youtube.com/watch?v=y23ZDwGDAz0">watch a video about the courseware</a>. After less than two years of “public life”, Phase One has received more than 2 million page views and usage is accelerating.</p>
<p>But why stop there? Through the development of Phase One, all of the stakeholders realized that, while what we created was great, we needed better and more efficient development tools. Thus, Möbius was born. (In the meantime, the CEMC separately launched Phase Two of this ambitious initiative: resources in computer science to support the teaching and learning of programming concepts.)</p>
<p>Now, using the full capabilities of Möbius, we are developing Phase Three, a parallel set of resources to Phase One that will support mathematics at the Grade 7/8 level. Why Grade 7/8? We believe that these are very important years in education, that it is vital to future success in STEM disciplines that students flourish in these years, and that we should do whatever we can to support this.</p>
<p>What comes next? Time will tell. But, the CEMC will be there supporting mathematics and STEM education. STEM disciplines will drive almost everything in the twenty-first century, and we have an obligation to do whatever we can to give young people every possible chance for success.</p>
<p style="margin-left: 40px;"><em>This MaplePrimes guest blog post is from Ian VanderBurgh, the Director of the Center for Education in Mathematics and Computing (CEMC) and a Lecturer in the Faculty of Mathematics at the University of Waterloo. He has been overseeing a project to develop online, interactive mathematics curriculum for high school students, and has been integral in the development of Möbius, Maplesoft's <a href="http://www.maplesoft.com/products/mobius">online courseware environment</a>.</em></p>
<p>Start with one part interest in online education, add one part increased functionality for developing online content, and mix with one part increased focus in the media and elsewhere on mathematics education. What does this produce? The perfect time to create high-quality online resources to support learning and teaching in mathematics.</p>
<p>The Centre for Education in Mathematics and Computing (CEMC) at the University of Waterloo aims to increase interest, enjoyment, confidence, and ability in mathematics and computer science among learners and educators in Canada and internationally. For more than fifty years, we have been working with teachers to support the important work that they do in the classroom. When online courses rose to prominence several years ago, we felt that this gave us the perfect opportunity to create materials to better support the curriculum being taught across Canada and around the world.</p>
<p>The content for what we now call “Phase One” was planned: Advanced Functions (Pre-Calculus) as well as Calculus & Vectors. These materials would support the education of students in their final year of secondary school, and also provide materials to reinforce concepts for students in STEM programs at the post-secondary level.</p>
<p>After deciding on the content, we needed a platform. We knew that we needed one with exceptional mathematical capabilities. Thus, we have been working hand-in-hand with Maplesoft ever since.</p>
<p>With content and platform established, the style began to take shape. It is based around what one of my colleagues calls “the five Es”: <strong>Exposition</strong> (onscreen text with synchronized audio), <strong>Experimentation</strong> (worksheets where users can manipulate mathematical objects), <strong>Evaluation</strong> (re-generating quiz questions), <strong>Exercises</strong> (with answers and solutions), and <strong>Enrichment</strong> (application and extension problems and solutions). <a href="http://courseware.cemc.uwaterloo.ca">Have a look at the materials</a> and <a href="https://www.youtube.com/watch?v=y23ZDwGDAz0">watch a video about the courseware</a>. After less than two years of “public life”, Phase One has received more than 2 million page views and usage is accelerating.</p>
<p>But why stop there? Through the development of Phase One, all of the stakeholders realized that, while what we created was great, we needed better and more efficient development tools. Thus, Möbius was born. (In the meantime, the CEMC separately launched Phase Two of this ambitious initiative: resources in computer science to support the teaching and learning of programming concepts.)</p>
<p>Now, using the full capabilities of Möbius, we are developing Phase Three, a parallel set of resources to Phase One that will support mathematics at the Grade 7/8 level. Why Grade 7/8? We believe that these are very important years in education, that it is vital to future success in STEM disciplines that students flourish in these years, and that we should do whatever we can to support this.</p>
<p>What comes next? Time will tell. But, the CEMC will be there supporting mathematics and STEM education. STEM disciplines will drive almost everything in the twenty-first century, and we have an obligation to do whatever we can to give young people every possible chance for success.</p>
207318Thu, 03 Nov 2016 18:27:18 ZIan VanderBurghIan VanderBurghUpdated Spam Detection Features
http://www.mapleprimes.com/maplesoftblog/207278-Updated-Spam-Detection-Features?ref=Feed:MaplePrimes:Maplesoft Blog
<p>As mentioned a few weeks back, we have been working on an update to MaplePrimes designed to dramatically curtail the amount of spam we have been receiving. I'm happy to say that we implemented these features earlier today, and in the hour or so since publication, they have already helped prevent multiple messages from being posted.</p>
<p>Using content posted to MaplePrimes over the past few months as a baseline, this new feature is successfully able to detect 90% of spam, while maintaining a false positive (i.e., incorrectly identifying a legitimate question or post) rate of 1%.</p>
<p>If a message is detected as spam, it is immediately quarantined and not publicly posted. Importantly, any user who posts a message seen as spam is immediately informed, and is provided with a simple mechanism to let us know so that their post can be reinstated (if it is in fact legimate.)</p>
<p>We will be closely monitoring these services to ensure that they are working as intended. In the meantime, I am very hopeful that they help improve the experience for our members, and require much less effort from our dedicated group of spam fighters.</p>
<p>As mentioned a few weeks back, we have been working on an update to MaplePrimes designed to dramatically curtail the amount of spam we have been receiving. I'm happy to say that we implemented these features earlier today, and in the hour or so since publication, they have already helped prevent multiple messages from being posted.</p>
<p>Using content posted to MaplePrimes over the past few months as a baseline, this new feature is successfully able to detect 90% of spam, while maintaining a false positive (i.e., incorrectly identifying a legitimate question or post) rate of 1%.</p>
<p>If a message is detected as spam, it is immediately quarantined and not publicly posted. Importantly, any user who posts a message seen as spam is immediately informed, and is provided with a simple mechanism to let us know so that their post can be reinstated (if it is in fact legimate.)</p>
<p>We will be closely monitoring these services to ensure that they are working as intended. In the meantime, I am very hopeful that they help improve the experience for our members, and require much less effort from our dedicated group of spam fighters.</p>
207278Wed, 02 Nov 2016 17:32:42 ZBryonBryonMaplePrimes Update - New interface, editor, notifications, and more!
http://www.mapleprimes.com/maplesoftblog/207107-MaplePrimes-Update--New-Interface?ref=Feed:MaplePrimes:Maplesoft Blog
<p>Today we have published an update to MaplePrimes that includes a variety of improvements. Many of these changes are a direct result of member feedback and suggestions, and I am very appreciative for that!</p>
<p>What follows is a brief summary of the changes. As always, we remain very interested in your thoughts and feedback, and look forward to your further suggestions.</p>
<p>Also, a note that, as mentioned in a previous post, we have already begun working on a further update to address the influx of spam we have been receiving. This update will be published within the next 2-3 weeks.</p>
<p><strong>Updated Look and feel</strong><br>
The most obvious change is the updated interface. With a few exceptions, the previous layout and functionality has been maintained, but with a cleaner, more responsive, and more appealing look.</p>
<p><strong>New message editor</strong><br>
This update includes a new text editor called CKEditor. This editor provides a simpler, cleaner experience for posting your messages and also aligns MaplePrimes more closely with the Maplesoft product suite.</p>
<p><strong>Notifications</strong><br>
You will notice a new flag icon in the upper right hand corner of the interface. This is the new MaplePrimes Notification feature, and it provides similar functionality to what we have become accustomed to on other social media sites. The icon is displayed in an orange color when you have notifications, and then when opened, your new notifications are highlighted in blue. Clicking on a notification will take you directly to the item being referenced.</p>
<p><img src="/view.aspx?sf=207107_post/notificaton.PNG"></p>
<p><strong>Improved flow for removing spam messages</strong><br>
As any MaplePrimes moderator could tell you, removing spam on MaplePrimes was a cumbersome process taking 4 clicks. In this update, this process has been streamlined to 2 clicks, which will make the process considerably faster for our legion of spam fighters. In addition, the ability to remove spam is now available on all message types – comments, replies, etc.</p>
<p><strong>Identification Badges</strong><br>
There are now 3 identification badges that are used throughout MaplePrimes wherever member information is displayed. These include:</p>
<p><img src="/view.aspx?sf=207107_post/employee.jpg"> Denotes a member who works at Maplesoft</p>
<p><img src="/view.aspx?sf=207107_post/Moderator.jpg"> Site moderators are the heart and soul of MaplePrimes, and are now identified by this new badge</p>
<p><img src="/view.aspx?sf=207107_post/ambassador.jpg"> A member who also particpates in the <a href="http://www.maplesoft.com/ambassador">Maple Ambassador Program</a></p>
<p><strong>Other fixes and improvements</strong><br>
In addition to the changes mentioned above, several other minor fixes and improvements were made.</p>
<p>Today we have published an update to MaplePrimes that includes a variety of improvements. Many of these changes are a direct result of member feedback and suggestions, and I am very appreciative for that!</p>
<p>What follows is a brief summary of the changes. As always, we remain very interested in your thoughts and feedback, and look forward to your further suggestions.</p>
<p>Also, a note that, as mentioned in a previous post, we have already begun working on a further update to address the influx of spam we have been receiving. This update will be published within the next 2-3 weeks.</p>
<p><strong>Updated Look and feel</strong><br>
The most obvious change is the updated interface. With a few exceptions, the previous layout and functionality has been maintained, but with a cleaner, more responsive, and more appealing look.</p>
<p><strong>New message editor</strong><br>
This update includes a new text editor called CKEditor. This editor provides a simpler, cleaner experience for posting your messages and also aligns MaplePrimes more closely with the Maplesoft product suite.</p>
<p><strong>Notifications</strong><br>
You will notice a new flag icon in the upper right hand corner of the interface. This is the new MaplePrimes Notification feature, and it provides similar functionality to what we have become accustomed to on other social media sites. The icon is displayed in an orange color when you have notifications, and then when opened, your new notifications are highlighted in blue. Clicking on a notification will take you directly to the item being referenced.</p>
<p><img src="/view.aspx?sf=207107_post/notificaton.PNG"></p>
<p><strong>Improved flow for removing spam messages</strong><br>
As any MaplePrimes moderator could tell you, removing spam on MaplePrimes was a cumbersome process taking 4 clicks. In this update, this process has been streamlined to 2 clicks, which will make the process considerably faster for our legion of spam fighters. In addition, the ability to remove spam is now available on all message types – comments, replies, etc.</p>
<p><strong>Identification Badges</strong><br>
There are now 3 identification badges that are used throughout MaplePrimes wherever member information is displayed. These include:</p>
<p><img src="/view.aspx?sf=207107_post/employee.jpg"> Denotes a member who works at Maplesoft</p>
<p><img src="/view.aspx?sf=207107_post/Moderator.jpg"> Site moderators are the heart and soul of MaplePrimes, and are now identified by this new badge</p>
<p><img src="/view.aspx?sf=207107_post/ambassador.jpg"> A member who also particpates in the <a href="http://www.maplesoft.com/ambassador">Maple Ambassador Program</a></p>
<p><strong>Other fixes and improvements</strong><br>
In addition to the changes mentioned above, several other minor fixes and improvements were made.</p>
207107Tue, 18 Oct 2016 16:15:25 ZBryonBryonShowing steps of a solution
http://www.mapleprimes.com/maplesoftblog/206346-Showing-Steps-Of-A-Solution?ref=Feed:MaplePrimes:Maplesoft Blog
<p>Students using Maple often have different needs than non-students. Students need more than just a final answer; they are looking to gain an understanding of the mathematical concepts behind the problems they are asked to solve and to learn how to solve problems. They need an environment that allows them to explore the concepts and break problems down into smaller steps.</p>
<p>The <a href="https://www.maplesoft.com/support/help/Maple/view.aspx?path=Student">Student</a> packages in Maple offer focused learning environments in which students can explore and reinforce fundamental concepts for courses in <a href="http://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/Precalculus">Precalculus</a>, <a href="http://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/Calculus1/Hint">Calculus</a>, <a href="http://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/LinearAlgebra">Linear Algebra</a>, <a href="http://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/Statistics">Statistics</a>, and more. For example, Maple includes step-by-step tutors that allow students to practice <a href="https://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/Calculus1/IntTutor">integration</a>, <a href="https://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/Calculus1/DiffTutor">differentiation</a>, <a href="https://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/Calculus1/LimitTutor">the finding of limits</a>, and more. The Integration Tutor, shown below, lets a student evaluate an integral by selecting an applicable rule at each step. Maple will also offer hints or show the next step, if asked. The tutor doesn't only demonstrate how to obtain the result, but is designed for practicing and learning.</p>
<p style="text-align: center;"><img src="/view.aspx?sf=206346_post/IntMethods.PNG" alt="" width="480" height="436"></p>
<p>For this blog post, I’d like to focus in on an area of great interest to students: showing step-by-step solutions for a variety of problems in Maple.</p>
<p>Several commands in the Student packages can show solution steps as either output or inline in an interactive pop-up window. The first few examples return the solution steps as output.</p>
<p><strong>Precalculus problems:</strong></p>
<p>The <a href="http://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/Basics/ExpandSteps">Student:-Basics</a> sub-package provides a collection of commands to help students and teachers explore fundamental mathematical concepts that are core to many disciplines. It features two commands, both of which return step-by-step solutions as output.</p>
<p>The <a href="http://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/Basics/ExpandSteps">ExpandSteps</a> command accepts a product of polynomials and displays the steps required to expand the expression:</p>
<pre><strong>with(Student:-Basics):</strong></pre>
<pre><strong>ExpandSteps( (a^2-1)/(a/3+1/3) );</strong></pre>
<p style="text-align: center;"><img src="/view.aspx?sf=206346_post/ExpandSteps.PNG" alt="" width="479" height="291"></p>
<p>The <a href="http://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/Basics/LinearSolveSteps">LinearSolveSteps</a> command accepts an equation in one variable and displays the steps required to solve for that variable.</p>
<pre><strong>with(Student:-Basics):</strong></pre>
<pre><strong>LinearSolveSteps( (x+1)/y = 4*y^2 + 3*x, x );</strong></pre>
<p style="text-align: center;"><img src="/view.aspx?sf=206346_post/LinearSolveSteps.PNG" alt="" width="480" height="455"></p>
<p>This command also accepts some nonlinear equations that can be reduced down to linear equations.</p>
<p><strong>Calculus problems:</strong></p>
<p>The <a href="http://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/Calculus1">Student:-Calculus1</a> sub-package is designed to cover the basic material of a standard first course in single-variable calculus. Several commands in this package provide interactive tutors where you can step through computations and step-by-step solutions can be returned as standard worksheet output.</p>
<p>Tools like the <a href="https://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/Calculus1/IntTutor">integration</a>, <a href="https://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/Calculus1/DiffTutor">differentiation</a>, and <a href="https://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/Calculus1/LimitTutor">limit</a> method tutors are interactive interfaces that allow for exploration. For example, similar to the integration-methods tutor above, the differentiation-methods tutor lets a student obtain a derivative by selecting the appropriate rule that applies at each step or by requesting a complete solution all at once. When done, pressing “Close” prints out to the Maple worksheet an annotated solution containing all of the steps.</p>
<p>For example, try entering the following into Maple:</p>
<pre><strong>with(Student:-Calculus1):</strong></pre>
<pre><strong>x*sin(x);</strong></pre>
<p>Next, right click on the Matrix and choose “<strong>Student Calculus1 -> Tutors -> Differentiation Methods…</strong>”</p>
<p style="text-align: center;"><img src="/view.aspx?sf=206346_post/DiffMethods.PNG" alt="" width="480" height="440"></p>
<p>The Student:-Calculus1 sub-package is not alone in offering this kind of step-by-step solution finding. Other commands in other Student packages are also capable of returning solutions.</p>
<p><strong>Linear Algebra Problems:</strong></p>
<p>The <a href="http://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/LinearAlgebra">Student:-LinearAlgebra</a> sub-package is designed to cover the basic material of a standard first course in linear algebra. This sub-package features similar tutors to those found in the Calculus1 sub-package. Commands such as the <a href="https://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/LinearAlgebra/GaussianEliminationTutor">Gaussian Elimination</a>, <a href="https://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/LinearAlgebra/GaussJordanEliminationTutor">Gauss-Jordan Elimination</a>, <a href="https://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/LinearAlgebra/InverseTutor">Matrix Inverse</a>, <a href="http://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/LinearAlgebra/EigenvaluesTutor">Eigenvalues</a> or <a href="http://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/LinearAlgebra/EigenvectorsTutor">Eigenvectors</a> tutors show step-by-step solutions for linear algebra problems in interactive pop-up tutor windows. Of these tutors, a personal favourite has to be the Gauss-Jordan Elimination tutor, which were I still a student, would have saved me a lot of time and effort searching for simple arithmetic errors while row-reducing matrices.</p>
<p>For example, try entering the following into Maple:</p>
<pre><strong>with(Student:-LinearAlgebra):</strong></pre>
<pre><strong>M:=<<77,9,31>|<-50,-80,43>|<25,94,12>|<20,-61,-48>>;</strong></pre>
<p>Next, right click on the Matrix and choose “<strong>Student Linear Algebra -> Tutors -> Gauss-Jordan Elimination Tutor</strong>”</p>
<p style="text-align: center;"><img src="/view.aspx?sf=206346_post/GJElimTutor.PNG" alt="" width="480" height="452"></p>
<p>This tutor makes it possible to step through row-reducing a matrix by using the controls on the right side of the pop-up window. If you are unsure where to go next, the “Next Step” button can be used to move forward one-step. Pressing “All Steps” returns all of the steps required to row reduce this matrix.</p>
<p>When this tutor is closed, it does not return results to the Maple worksheet, however it is still possible to use the Maple interface to step through performing elementary row operations and to capture the output in the Maple worksheet. By loading the Student:-LinearAlgebra package, you can simply use the right-click context menu to apply elementary row operations to a Matrix in order to step through the operations, capturing all of your steps along the way!</p>
<p><strong>An interactive application for showing steps for some problems:</strong></p>
<p>While working on this blog post, it struck me that we did not have any online interactive applications that could show solution steps, so using the commands that I’ve discussed above, I authored an application that can expand, solve linear problems, integrate, differentiate, or find limits. You can interact with this application <a href="http://maplecloud.maplesoft.com/application.jsp?appId=5651983367143424">here</a>, but note that this application is a work in progress, so feel free to email me (maplepm (at) Maplesoft.com) any strange bugs that you may encounter with it.</p>
<p>More detail on each of these commands can be found in Maple’s help pages.</p>
<p> </p><p>Students using Maple often have different needs than non-students. Students need more than just a final answer; they are looking to gain an understanding of the mathematical concepts behind the problems they are asked to solve and to learn how to solve problems. They need an environment that allows them to explore the concepts and break problems down into smaller steps.</p>
<p>The <a href="https://www.maplesoft.com/support/help/Maple/view.aspx?path=Student">Student</a> packages in Maple offer focused learning environments in which students can explore and reinforce fundamental concepts for courses in <a href="http://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/Precalculus">Precalculus</a>, <a href="http://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/Calculus1/Hint">Calculus</a>, <a href="http://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/LinearAlgebra">Linear Algebra</a>, <a href="http://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/Statistics">Statistics</a>, and more. For example, Maple includes step-by-step tutors that allow students to practice <a href="https://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/Calculus1/IntTutor">integration</a>, <a href="https://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/Calculus1/DiffTutor">differentiation</a>, <a href="https://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/Calculus1/LimitTutor">the finding of limits</a>, and more. The Integration Tutor, shown below, lets a student evaluate an integral by selecting an applicable rule at each step. Maple will also offer hints or show the next step, if asked. The tutor doesn't only demonstrate how to obtain the result, but is designed for practicing and learning.</p>
<p style="text-align: center;"><img src="/view.aspx?sf=206346_post/IntMethods.PNG" alt="" width="480" height="436"></p>
<p>For this blog post, I’d like to focus in on an area of great interest to students: showing step-by-step solutions for a variety of problems in Maple.</p>
<p>Several commands in the Student packages can show solution steps as either output or inline in an interactive pop-up window. The first few examples return the solution steps as output.</p>
<p><strong>Precalculus problems:</strong></p>
<p>The <a href="http://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/Basics/ExpandSteps">Student:-Basics</a> sub-package provides a collection of commands to help students and teachers explore fundamental mathematical concepts that are core to many disciplines. It features two commands, both of which return step-by-step solutions as output.</p>
<p>The <a href="http://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/Basics/ExpandSteps">ExpandSteps</a> command accepts a product of polynomials and displays the steps required to expand the expression:</p>
<pre><strong>with(Student:-Basics):</strong></pre>
<pre><strong>ExpandSteps( (a^2-1)/(a/3+1/3) );</strong></pre>
<p style="text-align: center;"><img src="/view.aspx?sf=206346_post/ExpandSteps.PNG" alt="" width="479" height="291"></p>
<p>The <a href="http://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/Basics/LinearSolveSteps">LinearSolveSteps</a> command accepts an equation in one variable and displays the steps required to solve for that variable.</p>
<pre><strong>with(Student:-Basics):</strong></pre>
<pre><strong>LinearSolveSteps( (x+1)/y = 4*y^2 + 3*x, x );</strong></pre>
<p style="text-align: center;"><img src="/view.aspx?sf=206346_post/LinearSolveSteps.PNG" alt="" width="480" height="455"></p>
<p>This command also accepts some nonlinear equations that can be reduced down to linear equations.</p>
<p><strong>Calculus problems:</strong></p>
<p>The <a href="http://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/Calculus1">Student:-Calculus1</a> sub-package is designed to cover the basic material of a standard first course in single-variable calculus. Several commands in this package provide interactive tutors where you can step through computations and step-by-step solutions can be returned as standard worksheet output.</p>
<p>Tools like the <a href="https://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/Calculus1/IntTutor">integration</a>, <a href="https://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/Calculus1/DiffTutor">differentiation</a>, and <a href="https://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/Calculus1/LimitTutor">limit</a> method tutors are interactive interfaces that allow for exploration. For example, similar to the integration-methods tutor above, the differentiation-methods tutor lets a student obtain a derivative by selecting the appropriate rule that applies at each step or by requesting a complete solution all at once. When done, pressing “Close” prints out to the Maple worksheet an annotated solution containing all of the steps.</p>
<p>For example, try entering the following into Maple:</p>
<pre><strong>with(Student:-Calculus1):</strong></pre>
<pre><strong>x*sin(x);</strong></pre>
<p>Next, right click on the Matrix and choose “<strong>Student Calculus1 -> Tutors -> Differentiation Methods…</strong>”</p>
<p style="text-align: center;"><img src="/view.aspx?sf=206346_post/DiffMethods.PNG" alt="" width="480" height="440"></p>
<p>The Student:-Calculus1 sub-package is not alone in offering this kind of step-by-step solution finding. Other commands in other Student packages are also capable of returning solutions.</p>
<p><strong>Linear Algebra Problems:</strong></p>
<p>The <a href="http://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/LinearAlgebra">Student:-LinearAlgebra</a> sub-package is designed to cover the basic material of a standard first course in linear algebra. This sub-package features similar tutors to those found in the Calculus1 sub-package. Commands such as the <a href="https://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/LinearAlgebra/GaussianEliminationTutor">Gaussian Elimination</a>, <a href="https://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/LinearAlgebra/GaussJordanEliminationTutor">Gauss-Jordan Elimination</a>, <a href="https://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/LinearAlgebra/InverseTutor">Matrix Inverse</a>, <a href="http://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/LinearAlgebra/EigenvaluesTutor">Eigenvalues</a> or <a href="http://www.maplesoft.com/support/help/Maple/view.aspx?path=Student/LinearAlgebra/EigenvectorsTutor">Eigenvectors</a> tutors show step-by-step solutions for linear algebra problems in interactive pop-up tutor windows. Of these tutors, a personal favourite has to be the Gauss-Jordan Elimination tutor, which were I still a student, would have saved me a lot of time and effort searching for simple arithmetic errors while row-reducing matrices.</p>
<p>For example, try entering the following into Maple:</p>
<pre><strong>with(Student:-LinearAlgebra):</strong></pre>
<pre><strong>M:=<<77,9,31>|<-50,-80,43>|<25,94,12>|<20,-61,-48>>;</strong></pre>
<p>Next, right click on the Matrix and choose “<strong>Student Linear Algebra -> Tutors -> Gauss-Jordan Elimination Tutor</strong>”</p>
<p style="text-align: center;"><img src="/view.aspx?sf=206346_post/GJElimTutor.PNG" alt="" width="480" height="452"></p>
<p>This tutor makes it possible to step through row-reducing a matrix by using the controls on the right side of the pop-up window. If you are unsure where to go next, the “Next Step” button can be used to move forward one-step. Pressing “All Steps” returns all of the steps required to row reduce this matrix.</p>
<p>When this tutor is closed, it does not return results to the Maple worksheet, however it is still possible to use the Maple interface to step through performing elementary row operations and to capture the output in the Maple worksheet. By loading the Student:-LinearAlgebra package, you can simply use the right-click context menu to apply elementary row operations to a Matrix in order to step through the operations, capturing all of your steps along the way!</p>
<p><strong>An interactive application for showing steps for some problems:</strong></p>
<p>While working on this blog post, it struck me that we did not have any online interactive applications that could show solution steps, so using the commands that I’ve discussed above, I authored an application that can expand, solve linear problems, integrate, differentiate, or find limits. You can interact with this application <a href="http://maplecloud.maplesoft.com/application.jsp?appId=5651983367143424">here</a>, but note that this application is a work in progress, so feel free to email me (maplepm (at) Maplesoft.com) any strange bugs that you may encounter with it.</p>
<p>More detail on each of these commands can be found in Maple’s help pages.</p>
<p> </p>206346Tue, 20 Sep 2016 18:42:06 ZDSkoogDSkoog