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.
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.
Differential Calculus
Table 3 lists the areas in differential calculus for which Maple provides stepwise solutions.
Integral Calculus
Table 4 lists the areas in integral calculus for which Maple provides stepwise solutions.
Calculation
|
Tool Category
|
Tool
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Riemann Sums
|
Tutor
Task Templates
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Riemann Sums
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Numeric Integration
|
Tutor
|
|
Surface Area of a Surface of Revolution
|
Tutor
|
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Volume of a Solid of Revolution
|
Tutor
|
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Table 4 Stepwise tools in integral calculus
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Multivariate Calculus
Table 5 lists the areas in multivariate calculus for which Maple provides stepwise solutions.
Linear Algebra
Table 6 lists the areas in linear algebra for which Maple provides stepwise solutions.
Calculation
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Tool Category
|
Tool
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Row-Reduction to Upper Triangular Form
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Tutor
|
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Row-reduction to Reduced Row-Echelon Form
|
Tutor
|
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Solve a System of Linear Equations
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Tutor
|
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Matrix Inversion
|
Tutor
|
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Determine Eigenvalues
|
Tutor
|
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Determine Eigenvectors
|
Tutor
|
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Geometric Interpretation of Matrix-Vector Multiplication
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Task Template
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Matrix Action 2-D
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Graphing a Plane and Its Normal
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Task Template
Command
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Plane Plot
PlanePlot
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Projection of a Vector onto and Orthogonal to another Vector
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Task Template
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Projection onto a 1-D Subspace
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Projection of a Vector onto and Orthogonal to a Plane
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Task Template
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Projection onto a 2-D Subspace
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Visualize the Geometry of Vector Addition
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Task Template
Command
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Vector Sum Plot
VectorSumPlot
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Table 6 Stepwise tools in linear algebra
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Vector Calculus
Table 7 lists the areas in vector calculus for which Maple provides stepwise solutions.
Calculation
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Tool Category
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Tool
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Integrate a Plane Vector Field
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Task Template
Tutor
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Integrate Planar Vector Field
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Flux through a Plane Curve
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Task Templates
Command
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Flux Through:
Flux
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Flux though a Surface
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Task Templates
Command
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Flux Through:
Flux
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Surface Integrals
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Task Templates
Command
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Integrate over:
SurfaceInt
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Iterated Double Integrals
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Task Templates
Command
Maplet
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Integrate over:
int
Multiple Integral Maplet
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Iterated Triple Integrals
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Task Templates
Command
Maplet
|
Integrate over:
int
Multiple Integral Maplet
|
Visualize a Space Curve and Its Frenet-Serret Basis Vectors
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Tutor
|
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Table 7 Stepwise tools in vector calculus
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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.