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MaplePrimes Posts are for sharing your experiences, techniques and opinions about Maple, MapleSim and related products, as well as general interests in math and computing.

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    Maple 2023 is here!

    by: Karishma 955 Maple 2023
    maplesoft release
    March 09 2023
    17  0

     

    The moment we've all been waiting for has arrived: Maple 2023 is here!

    With this release we continue to pursue our mission to provide powerful technology to explore, derive, capture, solve and disseminate mathematical problems and their applications, and to make math easier to learn, understand, and use. Bearing this in mind, our team of mathematicians and developers have dedicated the last year to adding new features and enhancements that not only improve the math engine but make that math engine more easily accessible within a user-friendly interface.

    And if you ever wonder where our team gets inspiration, you don't need to look further than Maple Primes. Many of the improvements that went into Maple 2023 came as a direct result of feedback from users. I’ll highlight a few of those user-requested features below, and you can learn more about these, and many, many other improvements, in What’s New in Maple 2023.

    • The Plot Builder in Maple 2023 now allows you to build interactive plot explorations where parameters are controlled by sliders or dials, and customize them as easily as you can other plots

    Plot Builder Explore

     

    • In Maple 2023, 2-D contour and density plots now feature a color bar to show the values of the gradations.


    • For those who write a lot of code:  You can now open your .mpl Maple code files directly in Maple’s code editor, where you can  view and edit the file from inside Maple using the editor’s syntax highlighting, command completion, and automatic indenting.

    Programming Improvements

    • Integration has been improved in many ways. Here’s one of them:  The definite integration method that works via MeijerG convolutions now does a better job of checking conditions on parameters so that they are only applied under proper assumptions. It also tells you the conditions under which the method could have produced an answer, so if your problem does meet those conditions, you can add the appropriate assumptions to get your result.
    • Many people have asked that we make it easier for them to create more complex interactive Math Apps and applications that require programming, such as interactive clickable plots, quizzes that provide feedback, examples that provide solution steps. And I’m pleased to announce that we’ve done that in Maple 2023 with the introduction of the Quiz Builder and the Canvas Scripting Gallery.
      • The new Quiz Builder comes loaded with sample quizzes and makes it easy to create your own custom quiz questions. Launch the quiz builder next time you want to author interactive quizzes with randomized questions, different response types, hints, feedback, and show the solution. It’s probably one of my favorite features in Maple 2023.

    • The Scripting Gallery in Maple 2023 provides 44 templates and modifiable examples that make it easier to create more complex Math Apps and interactive applications that require programming. The Maple code used to build each application in the scripting gallery can be easily viewed, copied and modified, so you can customize specific applications or use the code as a starting point for your own work

    • Finally, here’s one that is bound to make a lot of people happy: You can finally have more than one help page open at the same time!

    For more information about all the new features and enhancements in Maple 2023, check out the What’s New in Maple 2023.

    P.S. In case you weren’t aware - in addition to Maple, the Maplesoft Mathematics Suite includes a variety of other complementary software products, including online and mobile solutions, that help you teach and learn math and math-related courses.  Even avid Maple users may find something of interest!

    Is there an error in dsolve using method=laplace...

    by: Michael Gustafson 40 Maple 2021
    ode dsolve differential-equations
    February 21 2023
    3  5

    I was looking at symbolically solving a second-order differential equation and it looks like the method=laplace method has a sign error when the coefficients are presented in a certain way.  Below is a picture of some examples with and without method=laplace that should all have the same closed form.  Note that lines (s6) and (s8) have different signs in the exponential than they should have (which is a HUGE problem):

    > 

    restart
    > 

    s1 := dsolve([diff(x(t), t, t)+2*a*(diff(x(t), t))+a^2*x(t)], [x(t)])

    {x(t) = exp(-a*t)*(_C2*t+_C1)}

    		 (1)
    > 

    s2 := dsolve([diff(x(t), t, t)+2*a*(diff(x(t), t))+a^2*x(t)], [x(t)], method = laplace)

    x(t) = exp(-a*t)*(t*(D(x))(0)+x(0)*(a*t+1))

    		 (2)
    > 

    s3 := dsolve([diff(x(t), t, t)+2*(diff(x(t), t))/b+x(t)/b^2], [x(t)])

    {x(t) = exp(-t/b)*(_C2*t+_C1)}

    		 (3)
    > 

    s4 := dsolve([diff(x(t), t, t)+2*(diff(x(t), t))/b+x(t)/b^2], [x(t)], method = laplace)

    x(t) = exp(-t/b)*(t*(D(x))(0)+x(0)*(b+t)/b)

    		 (4)
    > 

    s5 := dsolve([diff(x(t), t, t)+2*(diff(x(t), t))/sqrt(L*C)+x(t)/(L*C)], [x(t)])

    {x(t) = exp(-(L*C)^(1/2)*t/(L*C))*(_C2*t+_C1)}

    		 (5)
    > 

    s6 := dsolve([diff(x(t), t, t)+2*(diff(x(t), t))/sqrt(L*C)+x(t)/(L*C)], [x(t)], method = laplace)

    x(t) = (t*(D(x))(0)+3*C*L*x(0)*t/(L*C)^(3/2)+x(0))*exp((L*C)^(1/2)*t/(L*C))

    		 (6)
    > 

    s7 := dsolve([L*C*(diff(x(t), t, t))+2*sqrt(L*C)*(diff(x(t), t))+x(t)], [x(t)])

    {x(t) = exp(-(L*C)^(1/2)*t/(L*C))*(_C2*t+_C1)}

    		 (7)
    > 

    s8 := dsolve([L*C*(diff(x(t), t, t))+2*sqrt(L*C)*(diff(x(t), t))+x(t)], [x(t)], method = laplace)

    x(t) = exp(t/(L*C)^(1/2))*(t*(D(x))(0)+x(0)*(L*C+3*(L*C)^(1/2)*t)/(L*C))

    		 (8)
    > 

    s9 := dsolve([diff(x(t), t, t)+2*z*wn*(diff(x(t), t))+wn^2*x(t)], [x(t)])

    {x(t) = _C1*exp((-z+(z^2-1)^(1/2))*wn*t)+_C2*exp(-(z+(z^2-1)^(1/2))*wn*t)}

    		 (9)
    > 

    s10 := dsolve([diff(x(t), t, t)+2*z*wn*(diff(x(t), t))+wn^2*x(t)], [x(t)], method = laplace)

    x(t) = exp(-wn*t*z)*(cosh((wn^2*(z^2-1))^(1/2)*t)*x(0)+(x(0)*wn*z+(D(x))(0))*sinh((wn^2*(z^2-1))^(1/2)*t)/(wn^2*(z^2-1))^(1/2))

    		 (10)
    > 

    > 

    s11 := dsolve([(diff(x(t), t, t))/wn^2+2*z*(diff(x(t), t))/wn+x(t)], [x(t)])

    {x(t) = _C1*exp((-z+(z^2-1)^(1/2))*wn*t)+_C2*exp(-(z+(z^2-1)^(1/2))*wn*t)}

    		 (11)
    > 

    s12 := dsolve([(diff(x(t), t, t))/wn^2+2*z*(diff(x(t), t))/wn+x(t)], [x(t)], method = laplace)

    x(t) = exp(-wn*t*z)*(cosh((wn^2*(z^2-1))^(1/2)*t)*x(0)+(x(0)*wn*z+(D(x))(0))*sinh((wn^2*(z^2-1))^(1/2)*t)/(wn^2*(z^2-1))^(1/2))

    		 (12)
    > 

    s13 := dsolve([(diff(x(t), t, t))/wn^2+2*z*(diff(x(t), t))/wn+x(t)], [x(t)])

    {x(t) = _C1*exp((-z+(z^2-1)^(1/2))*wn*t)+_C2*exp(-(z+(z^2-1)^(1/2))*wn*t)}

    		 (13)
    > 

    s14 := dsolve([(diff(x(t), t, t))/wn^2+2*z*(diff(x(t), t))/wn+x(t)], [x(t)], method = laplace)

    x(t) = exp(-wn*t*z)*(cosh((wn^2*(z^2-1))^(1/2)*t)*x(0)+(x(0)*wn*z+(D(x))(0))*sinh((wn^2*(z^2-1))^(1/2)*t)/(wn^2*(z^2-1))^(1/2))

    		 (14)
    > 

    NULL

    Download DsolveLaplaceIssues.mw

    Simple Interest Collection

    by: 2teachis2learn4ever 60 Maple Learn
    February 16 2023
    3  0

    Hello everyone! Alex, Sarah, and I decided to create this collection of financial literacy documents as we noticed a lack of resources for this strand in mathematics. With many curricula around the world implementing financial literacy concepts, we thought it might be useful not just for Ontario, but for many jurisdictions around the world. 

    There are 4 documents in the Simple Interest collection; Introduction, Equation Generator, Mental Calculations, and Reflection. The Introduction is designed for intermediate and advanced level students as it introduces students to the concept of interest and how to calculate it. Students get to fill in the table by filling in the calculations on the right. This provides enough scaffolding so students of various grades can participate in this activity. 

     

    The Equation Generator document uses sliders to help students investigate linear equations in the form of y=mx+b. It also relates the simple interest equation (I=Prt) to the linear equation by asking students to compare interest rates. The idea behind this document is to bridge concepts outlined in the 2021 grade 9 destreamed math curriculum; in particular, the financial literacy, and linear relations strands. The document provides some reflection questions for students to think about the relationship between the variables. 

    The third document in the collection is the mental calculations document which presents a series of questions in increasing difficulty designed to help students compare interest rates. Students are intended to choose which scenario they think is more appropriate without using a calculator. There are hints provided on the right side if students wish for a hint, as well as explanations further to the right of the hints and answers below the main questions. Through our analysis of the curricula around the world, we noticed that many jurisdictions focus on mental math as a skill that their students should develop. Students may not always have access to a calculator and it is important for them to know how to make financially sound decisions or analyze advertisements that they may see around their neighbourhood.