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en-us2017 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemThu, 23 Feb 2017 11:39:24 GMTThu, 23 Feb 2017 11:39:24 GMTMaple Questions and Posts on MaplePrimeshttp://www.mapleprimes.com/images/mapleprimeswhite.jpgMaplePrimes - Maple Posts and Questions
http://www.mapleprimes.com/tags/Maple
How I can find all Maxima and Minima from graph of a function ?
http://www.mapleprimes.com/questions/221268-How-I-Can-Find-All-Maxima-And-Minima?ref=Feed:MaplePrimes:Tagged With Maple
<p>Dear All</p>
<p>I have a trignometric function and I plotted it in 2D. It is visible from the graph that the function has Maxima and Minima. My question is, can I located all values<br>
</p>
<form name="worksheet_form"><input name="md.ref" type="hidden" value="D517C48AEBB37FE4501C6B244DC3D7C0">
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<p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"><img align="middle" alt="0.12981e-1+0.80285e-1*cos(.9519256799*x)+0.41370e-1*cos(1.903851360*x)+0.35690e-1*cos(2.855777040*x)+0.147e-3*cos(3.807702720*x)" height="40" src="/view.aspx?sf=221268_question/538f1fa7e3e816a6bf7823bcc0f68aeb.gif" style="vertical-align:-23px" width="768"></p>
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<p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"><img align="middle" alt="0.12981e-1+0.80285e-1*cos(.9519256799*x)+0.41370e-1*cos(1.903851360*x)+0.35690e-1*cos(2.855777040*x)+0.147e-3*cos(3.807702720*x)" height="40" src="/view.aspx?sf=221268_question/963f6b37729b17cc73722fb94fe88ed0.gif" style="vertical-align:-23px" width="738"></p>
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<td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;">(1)</td>
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<p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"><img alt="plot(diff(0.12981e-1+0.80285e-1*cos(.9519256799*x)+0.41370e-1*cos(1.903851360*x)+0.35690e-1*cos(2.855777040*x)+0.147e-3*cos(3.807702720*x), x), x = -6.2 .. 6.2)" height="23" src="/view.aspx?sf=221268_question/6062e4cf2419ec07bf47b960a740e79e.gif" style="vertical-align:-6px" width="203"></p>
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<p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"><img align="middle" height="400" src="/view.aspx?sf=221268_question/27ab020dd5b4d563516f685baf862c4b.gif" style="border:none" width="400"></p>
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<p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"><img alt="``" height="23" src="/view.aspx?sf=221268_question/418a393fef07049f2552a6bc1bf90764.gif" style="vertical-align:-6px" width="11"></p>
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<p><a href="/view.aspx?sf=221268_question/Max_Min_from_Graph.mw">Download Max_Min_from_Graph.mw</a></p>
<p>of "x" corresponding to these Max. and Min. ?</p>
<p>Dear All</p>
<p>I have a trignometric function and I plotted it in 2D. It is visible from the graph that the function has Maxima and Minima. My question is, can I located all values<br>
</p>
<form name="worksheet_form"><input name="md.ref" type="hidden" value="D517C48AEBB37FE4501C6B244DC3D7C0">
<table align="center" width="768">
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<td><span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;">> </span></td>
<td>
<p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"><img align="middle" alt="0.12981e-1+0.80285e-1*cos(.9519256799*x)+0.41370e-1*cos(1.903851360*x)+0.35690e-1*cos(2.855777040*x)+0.147e-3*cos(3.807702720*x)" height="40" src="/view.aspx?sf=221268_question/538f1fa7e3e816a6bf7823bcc0f68aeb.gif" style="vertical-align:-23px" width="768"></p>
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<p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"><img align="middle" alt="0.12981e-1+0.80285e-1*cos(.9519256799*x)+0.41370e-1*cos(1.903851360*x)+0.35690e-1*cos(2.855777040*x)+0.147e-3*cos(3.807702720*x)" height="40" src="/view.aspx?sf=221268_question/963f6b37729b17cc73722fb94fe88ed0.gif" style="vertical-align:-23px" width="738"></p>
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<td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;">(1)</td>
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<p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"><img alt="plot(diff(0.12981e-1+0.80285e-1*cos(.9519256799*x)+0.41370e-1*cos(1.903851360*x)+0.35690e-1*cos(2.855777040*x)+0.147e-3*cos(3.807702720*x), x), x = -6.2 .. 6.2)" height="23" src="/view.aspx?sf=221268_question/6062e4cf2419ec07bf47b960a740e79e.gif" style="vertical-align:-6px" width="203"></p>
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<p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"><img alt="``" height="23" src="/view.aspx?sf=221268_question/418a393fef07049f2552a6bc1bf90764.gif" style="vertical-align:-6px" width="11"></p>
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<p><a href="/view.aspx?sf=221268_question/Max_Min_from_Graph.mw">Download Max_Min_from_Graph.mw</a></p>
<p>of "x" corresponding to these Max. and Min. ?</p>
221268Thu, 23 Feb 2017 01:20:43 ZmskalsimskalsiRunge-Kutta in maple
http://www.mapleprimes.com/questions/221267-RungeKutta-In-Maple?ref=Feed:MaplePrimes:Tagged With Maple
<p>dy/dx=sqrt(1+(a*x)+(2*y))</p>
<p>for the case a=1, y=1 and x=0 construct a program for the runge-kutta method of order 2 with formulae as follows where f(x,y)=dy/dx.</p>
<p>k_1=h*f(x_n,y_n)</p>
<p>k_2=h*f(x_n+h,y_n+k_1)</p>
<p>y_(n+1)=y_n+1/2(k_1+k_2).</p>
<p> </p>
<p>After creating a program obtain value of y correct to 4 decimal places when x=1 for h=0.1 and h =0.05.</p>
<p>dy/dx=sqrt(1+(a*x)+(2*y))</p>
<p>for the case a=1, y=1 and x=0 construct a program for the runge-kutta method of order 2 with formulae as follows where f(x,y)=dy/dx.</p>
<p>k_1=h*f(x_n,y_n)</p>
<p>k_2=h*f(x_n+h,y_n+k_1)</p>
<p>y_(n+1)=y_n+1/2(k_1+k_2).</p>
<p> </p>
<p>After creating a program obtain value of y correct to 4 decimal places when x=1 for h=0.1 and h =0.05.</p>
221267Wed, 22 Feb 2017 23:45:32 Znk2016nk2016plotting for second derivative for y=0
http://www.mapleprimes.com/questions/221265-Plotting-For-Second-Derivative-For-Y0?ref=Feed:MaplePrimes:Tagged With Maple
<p>yVal := 0.01</p>
<p>xVal := 0.01</p>
<p>p8 := plot([fdiff(('rhs')((pds:-value(f(x, y)))(x, yVal)[3]), [y, y], x = z)], z = 0 .. 20, color = [red])</p>
<p>I cant seem to plot the graph for yVal, but if I were to switch it around to (xVal,y), the graph works perfectly. How should I input the code such that I can obtain the f''(x,0) graph. </p>
<p>Any help will be greatly appreciated :) thanks</p>
<p><a href="/view.aspx?sf=221265_question/fyp3.mw">fyp3.mw</a></p>
<p>yVal := 0.01</p>
<p>xVal := 0.01</p>
<p>p8 := plot([fdiff(('rhs')((pds:-value(f(x, y)))(x, yVal)[3]), [y, y], x = z)], z = 0 .. 20, color = [red])</p>
<p>I cant seem to plot the graph for yVal, but if I were to switch it around to (xVal,y), the graph works perfectly. How should I input the code such that I can obtain the f''(x,0) graph. </p>
<p>Any help will be greatly appreciated :) thanks</p>
<p><a href="/view.aspx?sf=221265_question/fyp3.mw">fyp3.mw</a></p>
221265Wed, 22 Feb 2017 19:11:13 Zktan025ktan025Inspiring Young People to be Science and Technology Leaders
http://www.mapleprimes.com/maplesoftblog/207919-Inspiring-Young-People-To-Be-Science?ref=Feed:MaplePrimes:Tagged With Maple
<p> Maplesoft aims to promote innovation in science, technology, engineering and math (STEM) in high school students by partnering with various organizations, and sponsoring initiatives in education, research and innovation. Every year, Maplesoft commits time, funds and people to enhance the quality of math-based learning and discovery and to encourage high school students to strengthen their math skills.</p>
<p> One such organization we partner with is The Perimeter Institute, a leading centre for scientific research, training and educational outreach in foundational theoretical physics. Maplesoft currently serves as its Educational Outreach Champion, supporting various initiatives that promote math learning and exploration. Perhaps the most popular of its student outreach program is the annual International Summer School for Young Physicists (ISSYP), a two-week camp that brings together 40 exceptional students from high schools across the globe. Each year students receive a complimentary copy of Maple, and use the product to practice and strengthen their math skills. The ISSYP program also uses Möbius, the comprehensive online STEM courseware platform from Maplesoft, to offer preparatory course materials to students. Completing lessons in Möbius aid in making the summer program a more productive and dynamic experience for the students.</p>
<p style="text-align: center;"><img src="/view.aspx?sf=207919_post/ISSYP2.jpg"> <img src="/view.aspx?sf=207919_post/ISSYP3.jpg"></p>
<p style="text-align: center;"><em>International Summer School for Young Scientists at Perimeter Institute</em></p>
<p> </p>
<p> Who Wants to Be a Mathematician is a competition organized by the American Mathematical Society (AMS) for high school students in North America. Maplesoft has been a sponsor of the contest for many years. Maple T.A., the testing and assessment tool by Maplesoft, is used to administer the tests online, saving significant time and money for the organizers. When Maplesoft first introduced Maple T.A. to the contest, taking the competition from pen-and-paper tests to online tests, the number of contestants doubled, with about 2000 students participating in the contest. Maplesoft also donates prizes to the games in order to promote the use and love of math by high school students. This year will be first time the competition moves international. Six students in the UK took the Round 2 qualifying test, with the use of Maple T.A., and qualified for the live, on-stage finals of the UK edition of the competition that took place at the 2017 Maths Fest in London. Maplesoft is also supporting the spread of the WWTBAM contest to Canada in 2017.</p>
<p style="text-align: center;"><br>
<img src="/view.aspx?sf=207919_post/wwtbam-jmm2017-gametwo.jpg"></p>
<p style="text-align: center;"><em>Who Wants to be a Mathematician finals</em></p>
<p>Maplesoft also sponsors two outreach initiatives in Texas A&M University. The Summer Educational Enrichment (SEE) Math Program is a summer workshop attended by gifted middle school students. Students spend two weeks exploring ideas such as algebra, geometry, graph theory, and topology. The University also conducts the Integral Bee every year, a math based contest for high school students.</p>
<p>In addition to the above key projects, throughout the year Maplesoft also sponsors and is associated with a number of other competitions, conferences, and educational initiatives. A few of these are listed below.</p>
<ul>
<li>The Connecticut Science & Engineering Fair is a yearly, statewide science and engineering fair open to all 7th through 12th grade students. An important objective of their program is to attract young people to careers in science and engineering while developing skills essential to critical thinking.</li>
<li>FIRST Robotics Competition is a high school robotics competition. Each year, teams of high school students and mentors work during a six-week period to build game-playing robots that weigh up to 120 pounds.</li>
</ul>
<p style="text-align: center;"> <img height="100" src="/view.aspx?sf=207919_post/first_robotics.jpg" style="width: 207px; height: 158px;" width="100"></p>
<p style="text-align: center;"><em>FIRSTRobotics Competition</em></p>
<ul>
<li>ScienceExpo Conference is a student-run event that engages students with STEM-related opportunities and workshops</li>
<li>SWATposium is an annual robotics conference that brings together nearly 40 First Robotic Competition teams from both Canada and the United States for a day of guest speakers, workshops and social activities.</li>
</ul>
<p style="text-align: center;"><img height="100" src="/view.aspx?sf=207919_post/SWAT1.jpg" style="width: 202px; height: 159px;" width="100"> <img height="100" src="/view.aspx?sf=207919_post/SWAT2.jpg" style="width: 182px; height: 161px;" width="100"> <img height="100" src="/view.aspx?sf=207919_post/SWAT3.jpg" style="width: 168px; height: 158px;" width="100"></p>
<p style="text-align: center;"><em>SWATposium</em></p>
<ul>
<li>FIRST LEGO League gives elementary and middle school students and their adult coaches the opportunity to work and create together to solve a common problem.</li>
</ul>
<p style="text-align: center;"><img height="100" src="/view.aspx?sf=207919_post/IMG_0223.JPG" style="width: 203px; height: 172px;" width="100"> <img height="100" src="/view.aspx?sf=207919_post/IMG_0221.JPG" style="width: 208px; height: 171px;" width="100"></p>
<p style="text-align: center;"><em>FIRST LEGO League at St. Luke's School in Waterloo</em></p>
<p> Maplesoft’s objective of these sponsorships is to support those who inspire and channel young minds to be STEM focussed. By engaging them in exciting contests and programs the hope is that they build science, engineering, and technology skills at a young age and grow to be innovators and technology leaders of tomorrow.</p>
<p> Maplesoft aims to promote innovation in science, technology, engineering and math (STEM) in high school students by partnering with various organizations, and sponsoring initiatives in education, research and innovation. Every year, Maplesoft commits time, funds and people to enhance the quality of math-based learning and discovery and to encourage high school students to strengthen their math skills.</p>
<p> One such organization we partner with is The Perimeter Institute, a leading centre for scientific research, training and educational outreach in foundational theoretical physics. Maplesoft currently serves as its Educational Outreach Champion, supporting various initiatives that promote math learning and exploration. Perhaps the most popular of its student outreach program is the annual International Summer School for Young Physicists (ISSYP), a two-week camp that brings together 40 exceptional students from high schools across the globe. Each year students receive a complimentary copy of Maple, and use the product to practice and strengthen their math skills. The ISSYP program also uses Möbius, the comprehensive online STEM courseware platform from Maplesoft, to offer preparatory course materials to students. Completing lessons in Möbius aid in making the summer program a more productive and dynamic experience for the students.</p>
<p style="text-align: center;"><img src="/view.aspx?sf=207919_post/ISSYP2.jpg"> <img src="/view.aspx?sf=207919_post/ISSYP3.jpg"></p>
<p style="text-align: center;"><em>International Summer School for Young Scientists at Perimeter Institute</em></p>
<p> </p>
<p> Who Wants to Be a Mathematician is a competition organized by the American Mathematical Society (AMS) for high school students in North America. Maplesoft has been a sponsor of the contest for many years. Maple T.A., the testing and assessment tool by Maplesoft, is used to administer the tests online, saving significant time and money for the organizers. When Maplesoft first introduced Maple T.A. to the contest, taking the competition from pen-and-paper tests to online tests, the number of contestants doubled, with about 2000 students participating in the contest. Maplesoft also donates prizes to the games in order to promote the use and love of math by high school students. This year will be first time the competition moves international. Six students in the UK took the Round 2 qualifying test, with the use of Maple T.A., and qualified for the live, on-stage finals of the UK edition of the competition that took place at the 2017 Maths Fest in London. Maplesoft is also supporting the spread of the WWTBAM contest to Canada in 2017.</p>
<p style="text-align: center;"><br>
<img src="/view.aspx?sf=207919_post/wwtbam-jmm2017-gametwo.jpg"></p>
<p style="text-align: center;"><em>Who Wants to be a Mathematician finals</em></p>
<p>Maplesoft also sponsors two outreach initiatives in Texas A&M University. The Summer Educational Enrichment (SEE) Math Program is a summer workshop attended by gifted middle school students. Students spend two weeks exploring ideas such as algebra, geometry, graph theory, and topology. The University also conducts the Integral Bee every year, a math based contest for high school students.</p>
<p>In addition to the above key projects, throughout the year Maplesoft also sponsors and is associated with a number of other competitions, conferences, and educational initiatives. A few of these are listed below.</p>
<ul>
<li>The Connecticut Science & Engineering Fair is a yearly, statewide science and engineering fair open to all 7th through 12th grade students. An important objective of their program is to attract young people to careers in science and engineering while developing skills essential to critical thinking.</li>
<li>FIRST Robotics Competition is a high school robotics competition. Each year, teams of high school students and mentors work during a six-week period to build game-playing robots that weigh up to 120 pounds.</li>
</ul>
<p style="text-align: center;"> <img height="100" src="/view.aspx?sf=207919_post/first_robotics.jpg" style="width: 207px; height: 158px;" width="100"></p>
<p style="text-align: center;"><em>FIRSTRobotics Competition</em></p>
<ul>
<li>ScienceExpo Conference is a student-run event that engages students with STEM-related opportunities and workshops</li>
<li>SWATposium is an annual robotics conference that brings together nearly 40 First Robotic Competition teams from both Canada and the United States for a day of guest speakers, workshops and social activities.</li>
</ul>
<p style="text-align: center;"><img height="100" src="/view.aspx?sf=207919_post/SWAT1.jpg" style="width: 202px; height: 159px;" width="100"> <img height="100" src="/view.aspx?sf=207919_post/SWAT2.jpg" style="width: 182px; height: 161px;" width="100"> <img height="100" src="/view.aspx?sf=207919_post/SWAT3.jpg" style="width: 168px; height: 158px;" width="100"></p>
<p style="text-align: center;"><em>SWATposium</em></p>
<ul>
<li>FIRST LEGO League gives elementary and middle school students and their adult coaches the opportunity to work and create together to solve a common problem.</li>
</ul>
<p style="text-align: center;"><img height="100" src="/view.aspx?sf=207919_post/IMG_0223.JPG" style="width: 203px; height: 172px;" width="100"> <img height="100" src="/view.aspx?sf=207919_post/IMG_0221.JPG" style="width: 208px; height: 171px;" width="100"></p>
<p style="text-align: center;"><em>FIRST LEGO League at St. Luke's School in Waterloo</em></p>
<p> Maplesoft’s objective of these sponsorships is to support those who inspire and channel young minds to be STEM focussed. By engaging them in exciting contests and programs the hope is that they build science, engineering, and technology skills at a young age and grow to be innovators and technology leaders of tomorrow.</p>
207919Wed, 22 Feb 2017 16:24:42 ZJennifer IorgulescuJennifer IorgulescuHow to increase the resolution of odeplots
http://www.mapleprimes.com/questions/221264-How-To-Increase-The-Resolution-Of-Odeplots?ref=Feed:MaplePrimes:Tagged With Maple
<p>Dear All, </p>
<p>I work on the period doubling phenomenon by integrating the dynamical system at some particular parameter values. My main commands are as follows</p>
<p>restart:<br>
with(DEtools): with(plots): with(plottools):<br>
a:=-1: b:=-3: c:=3: d:=1: omega:=1: v1:=1: f:=-4: epsilon:=0.01: <br>
sys:=diff(u1(t),t)=v1*u1(t)-(omega+u2(t)^2)*u2(t)+u1(t)*(a*(u1(t)^2+u2(t)^2)+b*z(t)^2),<br>
diff(u2(t),t)=(omega+u1(t)^2)*u1(t)+v1*u2(t)+u2(t)*(a*(u1(t)^2+u2(t)^2)+b*z(t)^2),<br>
diff(z(t),t)=z(t)*(-v1+c*(u1(t)^2+u2(t)^2)+z(t)^2)+epsilon*z(t)*(v2+f*z(t)^4):</p>
<p>solC:=dsolve({eval(sys, v2=2.0500014987),<br>
u1(0)=0.6,u2(0)=0.6,z(0)=0.1},<br>
type=numeric, method=rkf45, maxfun=10^7,<br>
range=350..750):<br>
p1:=odeplot(solC, [sqrt(u1(t)^2+u2(t)^2),z(t)],<br>
refine=2,<br>
color=burgundy,<br>
thickness=1);<br>
</p>
<p>The resulting curves are quite blurring and furry. I have tried to increase the "refine" or the "numpoints" values, but with minimal improvement. I would like to know if there a way to obtain clean and sharp integral curves? <br>
<br>
I would be very grateful if someone could help me! <br>
<br>
Thank you in advance.<br>
<br>
With kind wishes,</p>
<p>Wang Zhe</p>
<p>Dear All, </p>
<p>I work on the period doubling phenomenon by integrating the dynamical system at some particular parameter values. My main commands are as follows</p>
<p>restart:<br />
with(DEtools): with(plots): with(plottools):<br />
a:=-1: b:=-3: c:=3: d:=1: omega:=1: v1:=1: f:=-4: epsilon:=0.01: <br />
sys:=diff(u1(t),t)=v1*u1(t)-(omega+u2(t)^2)*u2(t)+u1(t)*(a*(u1(t)^2+u2(t)^2)+b*z(t)^2),<br />
diff(u2(t),t)=(omega+u1(t)^2)*u1(t)+v1*u2(t)+u2(t)*(a*(u1(t)^2+u2(t)^2)+b*z(t)^2),<br />
diff(z(t),t)=z(t)*(-v1+c*(u1(t)^2+u2(t)^2)+z(t)^2)+epsilon*z(t)*(v2+f*z(t)^4):</p>
<p>solC:=dsolve({eval(sys, v2=2.0500014987),<br />
u1(0)=0.6,u2(0)=0.6,z(0)=0.1},<br />
type=numeric, method=rkf45, maxfun=10^7,<br />
range=350..750):<br />
p1:=odeplot(solC, [sqrt(u1(t)^2+u2(t)^2),z(t)],<br />
refine=2,<br />
color=burgundy,<br />
thickness=1);<br />
</p>
<p>The resulting curves are quite blurring and furry. I have tried to increase the "refine" or the "numpoints" values, but with minimal improvement. I would like to know if there a way to obtain clean and sharp integral curves? <br />
<br />
I would be very grateful if someone could help me! <br />
<br />
Thank you in advance.<br />
<br />
With kind wishes,</p>
<p>Wang Zhe</p>
221264Wed, 22 Feb 2017 15:24:03 ZZWangZWang conservation laws of fractional differential equation with Maple
http://www.mapleprimes.com/questions/221260--Conservation-Laws-Of-Fractional-Differential?ref=Feed:MaplePrimes:Tagged With Maple
<p>How we can construct conservation laws of fractional differential equation with Maple?</p>
<p>How we can construct conservation laws of fractional differential equation with Maple?</p>
221260Wed, 22 Feb 2017 12:21:18 Zlashkarianelhamlashkarianelham