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Solution Steps 

Maple 2021 includes numerous new algorithms for showing step-by-step solutions for a variety of problems in mathematics. 

 

Long Division 

Factoring 

Solve 

Calculus: Integration, Differentiation, and Limits 

Differential Equations 

Matrix Inverse 

Eigenvalues 

Eigenvectors 

Gauss Jordan Elimination 

Share your solution 

Where did I go wrong? 

Long Division 

The LongDivision command gives a visual solution to an arithmetic or polynomial long division problem, showing all of the intermediate steps. 

> with(Student:-Basics); -1
 

> LongDivision(`+`(`*`(48, `*`(`^`(x, 4))), `*`(284, `*`(`^`(x, 3))), `*`(620, `*`(`^`(x, 2))), `*`(593, `*`(x)), 210), `+`(`*`(2, `*`(x)), 3));
 

(1.1)
 

> LongDivision(1001, 30, 'decimaldigits' = 4); 1
 

(1.2)
 

Factoring 

The FactorSteps command shows the steps in factoring a polynomial. 

> with(Student:-Basics); -1
 

> FactorSteps(`+`(`*`(`^`(x, 3)), `*`(6, `*`(`^`(x, 2))), `*`(12, `*`(x)), 8));
 

(2.1)
 

 

Solve 

The SolveSteps command shows the steps in solving an equation or system of equations 

> with(Student:-Basics); -1
 

> SolveSteps(`+`(`*`(5, `*`(exp(`+`(`*`(4, `*`(x))))))) = 16);
 

(3.1)
 

> SolveSteps([`+`(`*`(12, `*`(x)), y) = 18, `+`(`*`(7, `*`(x)), `-`(`*`(8, `*`(y)))) = 32]);
 

(3.2)
 

Calculus: Integration, Differentiation, and Limits 

The ShowSolution command has been improved to show more detailed steps when solving integration, differentiation, and limit problems. 

> with(Student:-Calculus1); -1
 

> ShowSolution(Int(`*`(`^`(sin(x), 2)), x));
 

(4.1)
 

> ShowSolution(Limit(`/`(`*`(sin(x)), `*`(x)), x = 0));
 

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Diff(`*`(`^`(x, 2), `*`(sin(x))), x);  

Typesetting:-mprintslash([Diff(`*`(`^`(x, 2), `*`(sin(x))), x)], [Diff(`*`(`^`(x, 2), `*`(sin(x))), x)]) (4.2)
 

> ShowSolution(Diff(`*`(`^`(x, 2), `*`(sin(x))), x));
 

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Differential Equations 

The ODESteps command provides detailed steps when solving ordinary differential equations and systems of ODEs.  

> with(Student:-ODEs); -1
 

> ode1 := `+`(`*`(`^`(t, 2), `*`(`+`(z(t), 1))), `*`(`^`(z(t), 2), `*`(`+`(t, `-`(1)), `*`(diff(z(t), t))))) = 0;
 

Typesetting:-mprintslash([ode1 := `+`(`*`(`^`(t, 2), `*`(`+`(z(t), 1))), `*`(`^`(z(t), 2), `*`(`+`(t, `-`(1)), `*`(diff(z(t), t))))) = 0], [`+`(`*`(`^`(t, 2), `*`(`+`(z(t), 1))), `*`(`^`(z(t), 2), `*`... (5.1)
 

> ODESteps(ode1);
 

(5.2)
 

> ivp2 := {`+`(diff(y(x), x, x), `-`(diff(y(x), x)), `-`(`*`(x, `*`(exp(x))))) = 0, eval(diff(y(x), x), x = 0) = 0, y(0) = 1};
 

Typesetting:-mprintslash([ivp2 := {`+`(diff(y(x), `$`(x, 2)), `-`(diff(y(x), x)), `-`(`*`(x, `*`(exp(x))))) = 0, eval(diff(y(x), x), {x = 0}) = 0, y(0) = 1}], [{`+`(diff(diff(y(x), x), x), `-`(diff(y(... (5.3)
 

> ODESteps(ivp2);
 

(5.4)
 

Matrix Inverse 

The InverseTutor command now has an option to return detailed steps for finding the matrix inverse. 

> with(Student:-LinearAlgebra); -1
 

> M := rtable(1 .. 3, 1 .. 3, [[3, -3, 7], [2, 4, 8], [-2, -4, 6]], subtype = Matrix); -1
 

> InverseTutor(M, output = steps);
 

(6.1)
 

Eigenvalues 

The EigenvaluesTutor command now has an option to return detailed steps for finding Eigenvalues.
 

> with(Student:-LinearAlgebra); -1
 

> M := rtable(1 .. 3, 1 .. 3, [[1, 2, 0], [2, 3, 2], [0, 2, 1]], subtype = Matrix); -1
 

> EigenvaluesTutor(M, output = steps);
 

(7.1)
 

 

 

Eigenvectors 

The EigenvectorsTutorcommand now has an option to return detailed steps for finding Eigenvectors.
 

> with(Student:-LinearAlgebra); -1
 

> M := rtable(1 .. 3, 1 .. 3, [[1, 2, 0], [2, 3, 2], [0, 2, 1]], subtype = Matrix); -1
 

> EigenvectorsTutor(M, output = steps);
 

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Gauss Jordan Elimination 

The GaussJordanEliminationTutor command now has an option to return detailed steps for finding Eigenvalues.
 

> with(Student:-LinearAlgebra); -1
 

> M := rtable(1 .. 3, 1 .. 4, [[1, 2, 0, 3], [2, 3, 2, 5], [0, 2, 1, 5]], subtype = Matrix); -1
 

> GaussJordanEliminationTutor(M, output = steps);
 

(9.1)
 

 

Share your solution 

There's a connection to the new product Maple Learn as well.  These commands can output a link to a Maple Learn document containing the solution steps.  Maple Learn is a dynamic online environment for teaching and learning math, focused on high-school to second year university.  For more about Maple Learn, visit https://www.maplesoft.com/products/learn/ 

> with(Student:-Calculus1); -1
 

> cv := ShowSolution(Int(`*`(`^`(sin(x), 2)), x), output = canvas); -1
 

> DocumentTools:-Canvas:-ShareCanvas(cv);
 

https://learn.maplesoft.com/#/?d=COOROFHKHLBHPMHSIOFJCGHPPSARFJMSNQPFCRKKPSNQILITKLDMKNESLUCFNRDKFTELLNIKLMDREJDFFJKJDGMSJUOMPKHKIRJR 

> with(Student:-LinearAlgebra); -1
 

> M := rtable(1 .. 3, 1 .. 3, [[1, 2, 0], [2, 3, 2], [0, 2, 1]], subtype = Matrix); -1
 

> EigenvectorsTutor(M, output = link);
 

https://learn.maplesoft.com/#/?d=HTNRCGNJBSDQKOCNLFFPKFAGANHOHILKPSIOLTPPGPHSBROQBGNPLFDJFFPJEMCMMGKLOHHJGODRNIKUESCIOMIIJTEFOHNUFFNG 

 

Where did I go wrong? 

In Maple 2021, students can now solve an equation by entering the step-by-step solution to the problem themselves, and then asking Maple for feedback.  The responsive feedback lets the student know whether or not the solution is correct, and if not, where they went wrong. The SolvePractice command generates an interactive application where a student can type in the steps to solve a given problem. Then, the student clicks the button, and the application analyzes their steps and provides feedback.   

> with(Grading); -1
 

> SolvePractice(`+`(`*`(3, `*`(`^`(x, 3))), `*`(20, `*`(`^`(x, 2)))) = `*`(x, `*`(`+`(`-`(`*`(3, `*`(`^`(x, 2)))), `-`(`*`(9, `*`(x))), `-`(13)))), x);
 

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These practice-with-feedback sheets can be deployed to the web via Maple Learn: 

> SolvePractice(`+`(`*`(3, `*`(`^`(x, 3))), `*`(20, `*`(`^`(x, 2)))) = `*`(x, `*`(`+`(`-`(`*`(3, `*`(`^`(x, 2)))), `-`(`*`(9, `*`(x))), `-`(13)))), x, output = link);
 

https://learn.maplesoft.com/#/?d=BHPKHJMJLGDJJHFTPQKRMLDKAULUCTBPPRHFDOEIANLUCIBOGRATCOHNAQKGMGLULONLAPLKENFUBUFIBMGGHUIJDNJSGFDJBSFK