Stepwise Solutions in Maple

There are commands, assistants, tutors, and task templates that provide stepwise calculations in precalculus, calculus, linear algebra, and vector calculus. In addition, since Maple can implement nearly any mathematical operation, any stepwise calculation can be reproduced in Maple by assembling the appropriate intermediate steps, just as they would be assembled when working with pencil and paper.

In this note, we summarize the available stepwise tools. Full details and examples of each tool are available in the three articles listed in Table 1.

 Stepwise Solutions Precalculus and Calculus   Linear Algebra   Vector Calculus Table 1   Links to Tips & Techniques Reporter articles on stepwise solutions in Maple

For each applicable subject area, we list the calculation and the appropriate stepwise tools in the following sections.

Precalculus

Table 2 lists the two areas in basic algebra for which Maple provides stepwise solutions.

 Calculation Tool Category Tool Solving Equations Assistant Partial Fraction Decomposition Task Template Stepwise Partial Fraction Decomposition Table 2   Stepwise tools in algebra

Differential Calculus

Table 3 lists the areas in differential calculus for which Maple provides stepwise solutions.

Calculation

Tool Category

Tool

Limits

Tutor

Command

Context Menu

ShowSteps

Solve_Show Solution Steps

Derivatives

Tutor

Derivatives by Definition

Task Template

Command

Context Menu

Derivatives by Definition

ShowSteps

Solve_Show Solution Steps

Difference (Newton) Quotient

Task Template

Tutor

Difference (Newton) Quotient

Implicit Differentiation

Task Template

Implicit Differentiation

Tangent Line

Task Template

Tangent Line

Normal Line

Task Template

Normal Line

Mean Value Theorem

Task Template

Tutor

Mean Value Theorem

Rolle's Theorem

Task Template

Command

Rolle's Theorem

RollesTheorem

Curve Sketching:

 • Intercepts
 • Max/Min
 • Intervals of Increase/Decrease
 • Inflection Points
 • Concavity

Tutor

Command

Task Template

FunctionChart  (or FunctionPlot )

Find Special Points on a Function

Table 3   Stepwise tools in differential calculus

Integral Calculus

Table 4 lists the areas in integral calculus for which Maple provides stepwise solutions.

Calculation

Tool Category

Tool

Riemann Sums

Tutor

Task Templates

Riemann Sums

 • Left
 • Right
 • Lower
 • Upper
 • Midpoint
 • Random

Numeric Integration

Tutor

Surface Area of a Surface of Revolution

Tutor

Volume of a Solid of Revolution

Tutor

Table 4   Stepwise tools in integral calculus

Multivariate Calculus

Table 5 lists the areas in multivariate calculus for which Maple provides stepwise solutions.

Calculation

Tool Category

Tool

Iterated Multiple Integration

Command

MultiInt

Visualizing Regions of Integration

Task Templates

Cartesian Coordinates: 2D

Cartesian Coordinates: 3D

Polar Coordinates

Cylindrical Coordinates

Spherical Coordinates

Critical Points and the Second Derivative Test

Task Template

Critical Points and the Second Derivative Test

Center of Mass

Task Templates

Command

Center of Mass

 • Cartesian 2-D
 • Polar
 • Cartesian 3-D
 • Cylindrical
 • Spherical

CenterOfMass

Table 5   Stepwise tools in multivariate calculus

Linear Algebra

Table 6 lists the areas in linear algebra for which Maple provides stepwise solutions.

 Calculation Tool Category Tool Row-Reduction to Upper Triangular Form Tutor Row-reduction to Reduced Row-Echelon Form Tutor Solve a System of Linear Equations Tutor Matrix Inversion Tutor Determine Eigenvalues Tutor Determine Eigenvectors Tutor Geometric Interpretation of Matrix-Vector Multiplication Task Template Matrix Action 2-D Graphing a Plane and Its Normal Task Template Command Plane Plot PlanePlot Projection of a Vector onto and Orthogonal to another Vector Task Template Projection onto a 1-D Subspace Projection of a Vector onto and Orthogonal to a Plane Task Template Projection onto a 2-D Subspace Visualize the Geometry of Vector Addition Task Template Command Vector Sum Plot VectorSumPlot Table 6   Stepwise tools in linear algebra

Vector Calculus

Table 7 lists the areas in vector calculus for which Maple provides stepwise solutions.

Calculation

Tool Category

Tool

Integrate a Plane Vector Field

Task Template

Tutor

Integrate Planar Vector Field

Flux through a Plane Curve

Task Templates

Command

Flux Through:

 • Circle
 • Ellipse
 • Line Segment or Polygonal Line
 • General Plane Curve

Flux

Flux though a Surface

Task Templates

Command

Flux Through:

 • Box
 • Sphere
 • Parametric Surface
 • Surface Defined over a Disk
 • Surface Defined over an Ellipse
 • Surface Defined over a Triangle
 • Surface Defined over a General Planar Region

Flux

Surface Integrals

Task Templates

Command

Integrate over:

 • Box
 • Sphere
 • Parametric Surface
 • Surface Defined over a Rectangle
 • Surface Defined over a Disk
 • Surface Defined over an Ellipse
 • Surface Defined over a Triangle
 • Surface Defined over a General Planar Region

SurfaceInt

Iterated Double Integrals

Task Templates

Command

Maplet

Integrate over:

 • Rectangle
 • Disk
 • Ellipse
 • Triangle
 • General Planar Region

int

Multiple Integral Maplet

Iterated Triple Integrals

Task Templates

Command

Maplet

Integrate over:

 • Cube
 • Sphere
 • Tetrahedron
 • General 3-D Region

int

Multiple Integral Maplet

Visualize a Space Curve and Its Frenet-Serret Basis Vectors

Tutor

Table 7   Stepwise tools in vector calculus

In the VectorCalculus packages, the int command is modified to generate multiple integrals. The special geometric regions that the command then recognizes are then rectangle, disk, ellipse, triangle, cube sphere, tetrahedron, and general planar and three-dimensional regions.  The Multiple Integral Maplet is launched from a Task Template of the same name.

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