MaplePortal/Student/Details

はじめる前に
新機能一覧
Maple ワークシートの作成
Mapleワークシートを共有
Maple ウィンドウのカスタマイズ
Maple システムのカスタマイズ
コネクティビティ
Mathematics
数学
物理
プログラミング
グラフィックス
Student パッケージ
Science and Engineering
科学・エンジニアリング
アプリケーションと例題
リファレンス
システム
MapleSim
MapleSim ツールボックス
MapleSim ヘルプ
Tasks
Toolboxes
エラーメッセージガイド
マニュアル
数学アプリ

Find your task in the comprehensive list below and follow the instructions. For many tasks, the instructions will refer you to Task Templates. For more information on using task templates, see Student Resources.

Constructing algebraic objects

How do I...

enter a piecewise expression or function

•	Example 1.1: Use the piecewise template from the Expression palette

•	Task: Define a Piecewise Expression

•	Task: Define a Piecewise Function

enter an algebraic equation

•	See Example 1.2.

create a sequence

•	Context Menu: Sequence

•	Task: Sequences

•	Task: Build a Structured List

•	Task: Build a Structured List of Ordered Pairs

construct a loop

•	See Example 1.3.

write the exponential function

•	Example 1.4: Use the exponential template from the Expression palette or use Command Completion in Math mode

enter

•	In Math mode, the expression can be entered normally with the entered as a subscript. To enter the subscript level, press underscore [_]; after typing the subscript, press the right arrow key to leave the subscript. Finish the expression by entering

•	Example 1.5: Use the log template from the Expression palette

•	In Maple Input mode, log[a](x) can be used to represent

convert an expression to a function

•	Context Menu: See Example 1.6

•	Task: Convert an Expression to a Function

write a procedure

•	Task: Define a Procedure

Algebraic manipulations

How do I...

obtain the equation of a line

•	Task: Manipulate Form Equation of a Line

•	Task: Compute the Equation of a Line from a Point and the Slope

•	Task: Compute the Equation of a Line from the Slope and Intercept

•	Task: Compute the Equation of a Line Passing through Two Points

obtain the coordinates of the midpoint of a line segment

•	Task: Line Segment - Midpoint

obtain the slope of a line segment

•	Task: Line Segment - Slope

compute the distance between two points

•	Task: Distance between Two Points

complete the square

•	Context Menu: Complete Square

•	Task: Complete the Square

square both sides of an equation

•	Task: Square Both Sides of Equation

•	Context Menu: Manipulate Equation

substitute into an expression

•	Context Menu: Evaluate at a Point

•	Context Menu: Constructions → Evaluate At → [variable name] (yields unevaluated evaluation)

•	Use the template from the Expression palette; replace with the expression on which to perform the substitution, and overwrite with either the variable name equated to a value or a list of such equations

•	Task: Substitute into an Expression

•	Use the command eval to substitute a variable or value into an expression

substitute into an equation

•	Use any of the devices for substitution into an expression, except that the Context Menu for an equation does not provide the Constructions option

obtain the solution to RootOf

•	Context Menu: All Values

•	Context Menu: Conversions → To Radical

•	Use the allvalues command.

force an equation to be an identity

•	Task: Solve an Expression Using an Identity

•	Use the command solve(identity(eqn, x), vars); the expression (or equation) eqn is considered an identity in terms of the variable x, and solve attempts to find a solution in terms of vars that satisfies eqn for any value of x.

determine the inverse of a function

•	Task: Inverse Function

•	Function Inverse Tutor:

interpolate data

•	Context Menu: Curve Fitting → any of B-Spline, Interactive Curve Fitting, Least Squares, Polynomial Interpolation, Rational, Spline, Thiele

•	Curve Fitting Assistant: This assistant also allows you to import data into Maple from an external file to produce plots of various interpolating functions (Example 2.1)

•	Task: B-spline Curve Fitting

•	Task: Generate Bézier Curves

•	Task: Curve Fitting Assistant

•	Task: Interpolation with Equispaced Points

•	Task: Least Squares Approximation

•	Task: Polynomial Interpolation

•	Task: Rational Interpolation

•	Task: Spline

•	Task: Thiele Interpolation

obtain a partial fraction decomposition of a rational function

•	Context Menu: Conversions → Partial Fractions → [variable name]

•	Task: Partial Fraction Decomposition

•	Task: Stepwise Partial Fraction Decomposition

•	The command convert(f, parfrac, x) converts a function, f with main variable, x into partial fractions.

obtain real values of

•	Use the surd command.

Algebraic solvers

How do I...

solve algebraic equation(s)

•	Context Menu: Solve → any of Isolate Expression for, Numerically Solve, Numerically Solve from point, Obtain Solutions for, Solve, Solve (explicit), Solve (general solution), Solve for Variable

•	Task: Solve an Equation Symbolically

•	Task: Solve Analytically in Specified Interval

•	Task: Solve a Set of Equations Symbolically

•	Task: Solve an Equation Numerically

•	Task: Solve Numerically in Specified Interval

•	Task: Solve a Set of Equations Numerically

•	Task: Solve for Expression (Isolate)

solve an inequality

•	Context Menu: Solve

•	Task: Solve an Inequality

eliminate parameter in parametric equations

•	Context Menu: Solve → Eliminate a Variable → [parameter name]

eliminate selected variables in a set or list of equations

•	Context Menu: Solve → Eliminate Variables

•	Use the eliminate command

Polynomial arithmetic

How do I...

multiply out the factored form of a polynomial

•	Context Menu: Expand

factor a polynomial

•	Context Menu: Factor

find the zeros of a polynomial

•	Context Menu: Solve

obtain the quotient and remainder when dividing polynomials

•	Task: Polynomial Division - Quotient and Remainder

Plotting

How do I...

graph a curve or a surface

•	For an expression, Context Menu: Plots → Plot Builder

•	For a function, Context Menu: Plots → 2-D Plot or 3-D Plot

•	See the comprehensive Plotting Guide

create an animation

•	Context Menu: Plots → Plot Builder → Select Plot Type and Functions → Animation

•	Use the animate command in the plots package

animate the drawing of a plane curve

•	Use the animatecurve command in the plots package

trace coordinates along a plane curve

•	Context Menu (for graph): Probe Info → Nearest point on line

create a graph with one or more parameters controlled by sliders

•	Context Menu: Plots → Plot Builder → Select Plot Type and Functions → Interactive Plot with (n) parameter(s)

graph a rational function and its asymptotes

•	Task: Rational Function - Graph and Asymptotes

•	Rational Function Tutor:

graph linear inequalities

•	Task: Graph Linear Inequalities

•	Linear Inequalities tutor

•	Use the inequal command in the plots package

graph conic sections

•	Task: Conic - Analysis and Plot

•	Conic Sections tutor

graph the intersection of two surfaces

Use the intersectplot command from the plots package

Differential calculus in one variable

How do I...

construct a limit

•	Context Menu: Constructions → Limit → [variable name] and input the value

•	Limit Methods tutor: See Example 6.1

evaluate a limit

•	Context Menu: Limit

•	Limit Methods tutor

•	Task: Limit - Formal Rules

display an annotated stepwise evaluation of a limit

•	Load the Student[Calculus1] package (Tools → Load Package → Student Calculus 1) Expression palette: enter and complete , the limit template Context Menu: 2-D Math → Convert To → Inert Form Context Menu: Solve → Show Solution Steps

differentiate

•	Context Menu: Differentiate → [variable name]

•	Differentiation Methods tutor or See Example 6.2

•	Use the template from the Expression palette: See Example 6.3

exhibit annotated stepwise evaluation of a derivative

Load the Student[Calculus1] package (Tools → Load Package → Student Calculus 1)
Expression palette: enter and complete , the differentiation template
Context Menu: 2-D Math → Convert To → Inert Form
Context Menu: Solve → Show Solution Steps

differentiate implicitly

•	Context Menu: Implicit Differentiation

•	Task: Implicit Differentiation with Two Variables

•	Task: Implicit Differentiation with Three Variables

•	Task: Implicit Differentiation with Two Equations

•	Use the implicitdiff command

graph a function and its derivative(s)

•	Task: Graph f(x) and Its Derivatives

•	Derivatives tutor or See Example 6.4

obtain equations for tangent and normal lines along a curve

•	Task: Derivative Application - Tangent Line

•	Task: Derivative Application - Normal Line

analyze a plane curve

•	Curve Analysis tutor

•	Use the FunctionChart command from the Student Calculus 1 package

•	Task: Analyze a Continuous Function

•	Task: Find Special Points on a Function

•	Task: Minimum and Maximum of a Univariate Function

•	Task: Minimum and Maximum of a Univariate Function on an Interval

obtain Taylor series and polynomials

•	Context Menu: Series

•	Taylor Approximation tutor or See Example 6.5

•	Task: Taylor Approximation of a Univariate Function

•	Task: Taylor Expansion and Polynomials

implement Newton's Method

•	Task: Derivative Application - Newton's Method

•	Use the NewtonsMethod command from the Student Calculus1 package

Integral calculus in one variable

How do I...

obtain a Riemann sum for

•	Task: Calculate the Left Riemann Sum

•	Task: Calculate the Lower Riemann Sum

•	Task: Calculate the Midpoint Riemann Sum

•	Task: Calculate the Random Riemann Sum

•	Task: Calculate the Right Riemann Sum

•	Task: Calculate the Upper Riemann Sum

•	Riemann Sum tutor

obtain the indefinite integral of

•	Context Menu: Integrate

•	Task: Integration - Formal Rules

•	Integration Methods tutor or See Example 7.1

obtain the definite integral of

•	Context Menu: Constructions → Definite Integral

•	Task: Integration - Formal Rules

•	Integration Methods tutor or See Example 7.1

display annotated stepwise evaluation of an integral

•	Load the Student[Calculus1] package (Tools → Load Package → Student Calculus 1) Expression palette: enter and complete definite or indefinite integration templates: or Context Menu: 2-D Math → Convert To → Inert Form Context Menu: Solve → Show Solution Steps

enter and evaluate

•	Example 7.2: Use the template, , from the Expression palette

•	Example 7.3: Type and use Command Completion

enter and evaluate int(f(x), x = a .. b)

•	Example 7.2: Use the template, , from the Expression palette

•	Example 7.3: Type and use Command Completion

approximate a definite integral numerically

•	Context Menu: Approximate

•	Task: Approximate Definite Integral of a Function

•	Task: Numeric Integration

•	Approximate Integration tutor or See Example 7.4

integrate by parts

•	Task: Integration by Parts

•	Integration Methods tutor or See Example 7.1

integrate by trig substitution

•	Task: Integration by Substitution

•	Integration Methods tutor or See Example 7.1

compute the average value of a function

•	Function Average tutor or See Example 7.5

•	Task: Average Value of a Univariate Function

•	Use the FunctionAverage command from the Student Calculus1 package

calculate the length of a curve (arc length)

•	Arc Length tutor or See Example 7.6

•	Use the ArcLength command from the Student Calculus1 package

calculate the volume of a solid of revolution

•	Task: Volume of Revolution

•	Volume of Revolution tutor or See Example 7.7

•	Use the VolumeOfRevolution command from the Student Calculus1 package

calculate the surface area of a surface of revolution

•	Tasks: Surface of Revolution

•	Surface of Revolution tutor or See Example 7.8

•	Use the SurfaceOfRevolution command from the Student Calculus1 package

obtain the radius of convergence of a power series

•	Task: Radius of Convergence

apply the Ratio test for convergence of a series

•	Task: Ratio Test

Multivariate calculus

How do I...

obtain partial derivatives of a multivariate expression

•	Context Menu: Differentiate

•	Use the partial-differentiation template in the Expression palette

•	Use the diff command

•	Task: Partial Derivatives of a Multivariate Functional Expression

obtain partial derivatives of a multivariate function

•	Task: Partial Derivatives of a Multivariate Functional Operator

•	Use the D operator

find and test critical points of a multivariate function or expression

•	Task: Critical Points and the Second Derivative Test

•	Use the SecondDerivativeTest command in the Student Multivariate Calculus package

obtain the gradient vector for a multivariate function

•	Task: Compute the Gradient of a Function

•	Gradients tutor or See Example 8.1

•	Use the Gradient command from the Student MultivariateCalculus package

obtain the directional derivative of a multivariate scalar field

•	Task: Directional Derivative of a Multivariate Function

•	Use the DirectionalDerivative command from the Student MultivariateCalculus package

•	Directional Derivatives tutor or See Example 8.2

•	Use the DirectionalDiff command from the VectorCalculus package

•	Use the DirectionalDiff command from the Physics[Vectors] package

implement the Lagrange Multiplier method

•	Task: Lagrange Multiplier Method

•	Use the LagrangeMultipliers command from the Student MultivariateCalculus package

obtain a Taylor expansion of a multivariate expression

•	Context Menu: Series → Multivariate Taylor Polynomial

•	Task: Multivariate Taylor Series Expansion

•	Task: Taylor Approximation of a Multivariate Function

•	Taylor Approximation tutor or See Example 8.3

•	Use the TaylorApproximation command from the Student MultivariateCalculus package

•	Use the mtaylor command

obtain the Jacobian matrix and the Jacobian of a multivariate expression

•	Task: Jacobian Matrix and Jacobian

•	Use the Jacobian command from the Student MultivariateCalculus package

•	Use the Jacobian command from the VectorCalculus package

obtain the Hessian of a multivariate expression

•	Use the Hessian command from the VectorCalculus package

implement iterated integration

•	Example 8.4: Iterate an integral icon from Expression palette

•	Task: Iterated Double Integral in Cartesian Coordinates

•	Task: Iterated Triple Integral in Cartesian Coordinates

•	Task: Iterated Triple Integral in Cylindrical Coordinates

•	Task: Iterated Double Integral in Polar Coordinates

•	Task: Iterated Triple Integral in Spherical Coordinates

•	Task: Definite Integral of a Multivariate Function

evaluate iterated double integrals over pre-defined regions

•	Task: Over a Disk (or part thereof)

•	Task: Over a General 2-D Region

•	Task: Over a Rectangle

•	Task: Over a Triangle

•	Task: Over an Ellipse (or part thereof)

evaluate iterated triple integrals over pre-defined regions

•	Task: Over a Cube

•	Task: Over a General 3-D Region

•	Task: Over a Sphere

•	Task: Over a Tetrahedron

evaluate an iterated integral numerically

•	Context Menu: Approximate

•	Task: Approximate Definite Integral of a Multivariate Function

•	Multivariate Approximate Integration tutor or See Example 8.5

•	Use the ApproximateInt command from the Student MultivariateCalculus package

visualize the region of integration for an iterated integral

•	Task: Visualizing Regions of Integration: Cartesian 2-D

•	Task: Visualizing Regions of Integration: Cartesian 3-D

•	Task: Visualizing Regions of Integration: Polar

•	Task: Visualizing Regions of Integration: Cylindrical

•	Task: Visualizing Regions of Integration: Spherical

compute the average value of a multivariate expression

•	Task: Average Value of a Bivariate Function

•	Task: Average Value of a Trivariate Function

•	Task: Average Value of a Function in Cylindrical Coordinates

•	Task: Average Value of a Function in Polar Coordinates

•	Task: Average Value of a Function in Spherical Coordinates

determine the center of mass of a plane or spatial region

•	Task: Center of Mass for a Planar Region in Polar Coordinates

•	Task: Center of Mass for a Planar Region in Cartesian Coordinates

•	Task: Center of Mass for a 3-D Region in Cartesian Coordinates

•	Task: Center of Mass for a 3-D Region in Cylindrical Coordinates

•	Task: Center of Mass for a 3-D Region in Spherical Coordinates

calculate the surface area for a surface that is not a surface of revolution

•	Task: Surface Area

•	Task: Surface is a Box

•	Task: Surface is Parametrically Defined

•	Task: Surface is a Sphere

•	Task: Surface is Defined over a 2-D Region

•	Task: Surface is Defined over a Disk

•	Task: Surface is Defined over a Rectangle

•	Task: Surface is Defined over a Triangle

•	Task: Surface is Defined over an Ellipse

Vector calculus

How do I...

designate a coordinate system

•	Task: Set a Coordinate System

•	Use the SetCoordinates command from the VectorCalculus package

enter a free vector (the equivalent of a point)

•	Use the Matrix palette

•	Type , where inequality signs are used for angle brackets

•	Use the Vector command from the VectorCalculus package

attach a coordinate system to a free vector

•	Example 9.1: Use the Vector command from the VectorCalculus package

construct a vector field

•	Task: Vector Field Constructor

•	Use the VectorField command from the VectorCalculus package

evaluate a vector field at a point

•	Task: Evaluate a Vector Field at a Point

graph a vector field

•	Vector Fields tutor

•	Use the PlotVector command from the VectorCalculus package

obtain the dot product of two vectors

•	Use the period, or the dot () from the Common Symbols palette

•	Task: Dot Product of Two Vectors

•	Use the DotProduct command from the VectorCalculus package

calculate the magnitude of a vector

•	Context Menu: Norm

•	Task: Magnitude of a Vector

•	Use the Norm command from the VectorCalculus package

obtain the cross product of two vectors

•	In Math mode, use from the Common Symbols palette

•	In text mode, use &x as the cross-product operator

•	Task: Cross Product of Two Vectors

•	Use the CrossProduct command from the VectorCalculus package

visualize the cross-product vector

•	Task: Cross-Product Plot

obtain the gradient of a scalar field

•	Example 9.2: Gradient via the Nabla or Del operator

•	Task: Gradient

•	Task: Gradient of a Function

•	Use the Gradient command from the VectorCalculus package

obtain the divergence of a vector field

•	Example 9.3: Divergence via the Nabla or Del operator

•	Task: Divergence of a Vector Field

•	Use the Divergence command from the VectorCalculus package

obtain the curl of a vector field

•	Example 9.4: Curl via the Nabla or Del operator

•	Task: Curl of a Vector Field

•	Use the Curl command from the VectorCalculus package

obtain the Laplacian of a scalar field

•	Example 9.5: Laplacian via the Nabla or Del operator

•	Task: Laplacian of a Function

•	Use the Laplacian command from the VectorCalculus package

obtain the Laplacian of a vector field

•	Task: Laplacian of a Vector Field

evaluate iterated double integrals over pre-defined regions

•	Task: Over a Disk (or part thereof)

•	Task: Over a General 2-D Region

•	Task: Over a Rectangle

•	Task: Over a Triangle

•	Task: Over an Ellipse (or part thereof)

evaluate iterated triple integrals over pre-defined regions

•	Task: Over a Cube

•	Task: Over a General 3-D Region

•	Task: Over a Sphere

•	Task: Over a Tetrahedron

evaluate an iterated integral using the int command as modified by the VectorCalculus packages

•	Task: Double Integral over Circle

•	Task: Double Integral over Ellipse

•	Task: Double Integral over Rectangle

•	Task: Double Integral over Region

•	Task: Double Integral over Sector

•	Task: Double Integral over Triangle

•	Task: Triple Integral over Parallelepiped

•	Task: Triple Integral over Region

•	Task: Triple Integral over Sphere

•	Task: Triple Integral over Tetrahedron

compute a line integral along a plane curve

•	Task: Along a Circle

•	Task: Along a Curve

•	Task: Along a Line Segment

•	Task: Along a Polygonal Line

•	Task: Along an Ellipse

compute a line integral along a space curve

•	Task: Along a Circle

•	Task: Along a Curve

•	Task: Along a Line Segment

•	Task: Along a Polygonal Line

calculate a surface integral

•	Task: Surface Integral over a Box

•	Task: Surface Integral over a Parametrically Defined Surface

•	Task: Surface Integral over a Sphere

•	Task: Surface Integral on Surface Defined over a Disk

•	Task: Surface Integral on Surface Defined over a Rectangle

•	Task: Surface Integral on Surface Defined over a Triangle

•	Task: Surface Integral on Surface Defined over a Ellipse

compute the flux of a vector field through a plane curve

•	Task: Flux Through a Circle

•	Task: Flux Through a Plane Curve

•	Task: Flux Through a Polygonal Line

•	Task: Flux Through an Ellipse

compute the flux of a vector field through a surface

•	Task: Flux Through a Box

•	Task: Flux Through an Parametrically Defined Surface

•	Task: Flux Through a Sphere

•	Task: Flux Through a Surface Defined over a Disk

•	Task: Flux Through a Surface Defined over a Ellipse

•	Task: Flux Through a Surface Defined over a Planar Region

•	Task: Flux Through a Surface Defined over a Triangle

visualize the TNB (tangent-normal-binormal) frame for a space curve

•	Space Curve tutor

interactively implement the Frenet-Serret formalism for a space-curve

•	Example 9.6: Interactive Frenet-Serret formalism

programmatically implement the Frenet-Serret formalism for a space-curve

•	Use the TNBFrame command from the VectorCalculus package

•	Use the TangentVector command from the VectorCalculus package

•	Use the PrincipalNormal command from the VectorCalculus package

•	Use the Binormal command from the VectorCalculus package

•	Use the Curvature command from the VectorCalculus package

•	Use the Torsion command from the VectorCalculus package

•	Use the RadiusOfCurvature command from the VectorCalculus package

obtain the coordinates of a point in a different coordinate system

•	Use the MapToBasis command in the VectorCalculus package: See Example 9.7.

change coordinates in a vector field

•	Use the MapToBasis command in the VectorCalculus package: See Example 9.8.

Complex arithmetic

How do I...

enter a complex number

•	Example 10.1: Enter a complex number using , , or from the Common Symbols palette

obtain the real and imaginary parts of a complex number

•	Task: Real Part

•	Task: Imaginary Part

obtain the magnitude and argument of a complex number

•	Task: Modulus

•	Task: Argument

express a complex number in polar form

•	Task: Polar Form

convert a complex number to rectangular form

•	Task: Rectangular Form

•	Use the evalc command

ODEs

How do I...

enter an ordinary differential equation

•	Example 11.1: Enter a differential equation using dot notation, prime notation, or the command diff

obtain a direction field for

•	Task: Direction Field

obtain the Picard iterates for

•	Task: Picard Iterates

solve an ordinary differential equation

•	Context Menu: Solve ODE

•	Task: Solve an Ordinary Differential Equation

•	Use the dsolve command

solve an initial or boundary value problem

•	Context Menu: Solve DE Interactively

•	Task: Solve an Ordinary Differential Equation

classify the type of an ODE

•	Context Menu: Classify the ODE

•	Task: Identify the Type of an ODE

solve an ODE numerically

•	Context Menu: Solve DE Interactively, then choose Solve Numerically

•	Example 11.2: Use the dsolve command with the numeric option

obtain the Wronskian for a fundamental set of solutions

Use the Wronskian command from the VectorCalculus package

generate a phase portrait for an autonomous system of ODEs

•	Task: Phase Portrait of ODEs (Interactively, for planar system)

•	Use the DEplot command from the DEtools package

explore phase portraits for autonomous systems of ODEs

•	DE Plots tutor

Linear algebra

How do I...

for a given vector, find its coordinates with respect to a specific basis

•	Task: Coordinate Vector for a Vector

obtain the dot product of two vectors

•	Context Menu: Dot Product (apply to sequence of two vectors)

•	Task: Dot Product of Two Vectors

•	Example 12.1: Obtain the dot product of two vectors using the Common Symbols palette or using a period

determine the angle between two vectors

•	Task: Angle between Two Vectors

•	Use the VectorAngle command in the LinearAlgebra package

calculate a vector norm

•	Context Menu: Norm

•	Example 12.2: Calculate the norm of a vector using symbols or a command

project one vector onto another

•	Task: Projection onto 1-D

•	Task: Vector Projection onto Vector

project a vector onto a subspace spanned by two other vectors or onto a plane through the origin

•	Task: Projection onto 2-D

obtain , the cross-product of two vectors

•	Task: Cross Product and Its Visualization

•	Task: Cross Product of Two Vectors

•	Math mode: use from Common Symbols, or Operators palettes Text mode: use &x See Example 12.3

extract a maximal linearly independent subset from a set of vectors

•	Task: Basis for a Set of Vectors

•	Use the Basis command from the LinearAlgebra package

obtain the determinant of a matrix

•	Context Menu: Standard Operations → Determinant

•	Example 12.4: Use the absolute value template from the Layout palette

•	Task: Determinant of a Matrix

•	Use the Determinant command from the LinearAlgebra package

multiply a matrix by a scalar

•	In math mode, use a space as the multiplication operator

•	In text mode, use * as the multiplication operator

•	Task: Scalar Multiple of a Matrix

apply the function to each element of a vector or matrix

•	Use the elementwise operator:

•	Task: Map a Function onto Elements of a Vector

obtain the product of two matrices and

•	Use the period for noncommutative multiplication:

•	Task: Product of Two Matrices

raise a square matrix to a positive integer power such as 3

•	Use ordinary exponentiation:

•	Task: Nth Power of a Matrix

obtain the rank of a matrix

•	Context Menu: Queries → Rank

•	Task: Rank of a Matrix

•	Use the Rank command from the LinearAlgebra package

obtain the nullity of a matrix

•	Task: Nullity of a Matrix

obtain bases for row, column, and null spaces of a matrix

•	Task: Row Space of a Matrix

•	Task: Column Space of a Matrix

•	Task: Null Space of a Matrix (kernel)

•	See also the RowSpace, ColumnSpace, NullSpace commands in the LinearAlgebra package

obtain the transpose or Hermitian transpose of a matrix

•	Context Menu: Standard Operations → Transpose

•	Task: Transpose of a Matrix

•	Task: Hermitian Transpose of a Matrix

•	Example 12.5: In Math mode, for a matrix A, its transpose can be found by typing

construct a projection matrix

•	Task: Generate a Projection Matrix

perform augmentation or stacking operations on a matrix

•	Example 12.6: Stacking on top of , where and are vectors or matrices is done by typing ; Augmenting with is done by typing

solve the linear system

•	Task: Solve a System of Linear Equations

•	Augment by using and apply Context Menu: Solvers and Forms → Row-Echelon Form (see Example 12.6)

•	Use the LinearSolve command from the LinearAlgebra package

implement Gaussian elimination

•	Gaussian Elimination tutor: See Example 12.7

•	Task: Gaussian Elimination for an Augmented Matrix

•	Context Menu: Solvers and Forms → Row-Echelon Form

•	Use the GaussianElimination command from the LinearAlgebra package

obtain the inverse of a square matrix

•	In math mode, simply execute

•	In text mode, execute A^(-1)

•	Task: Inverse of a Matrix

•	Context Menu: Standard Operations → Inverse

•	Matrix Inverse tutor: See Example 12.8

•	Use the MatrixInverse command from the LinearAlgebra package

obtain the pseudoinverse of a singular or nonsquare matrix

•	Context Menu: Standard Operations → Pseudoinverse

•	Use the MatrixInverse command (LinearAlgebra package) with the "method = pseudo" option: See Example 12.9.

obtain eigenvalues and eigenvectors for a matrix

•	Context Menu: Eigenvalues, etc → Eigenvalues

•	Task: Eigenvalues and Eigenvectors of a Matrix

•	Use the Eigenvalues and Eigenvectors commands from the LinearAlgebra package

compute for a constant matrix

•	Task: Calculate the Exponential for a Constant Matrix

•	Use the MatrixExponential command from LinearAlgebra

apply the Gram-Schmidt process to the columns of a matrix, or a list or set vectors

•	Task: Gram-Schmidt Process

apply the Gram-Schmidt process to a list or set of vectors

•	Use the GramSchmidt command from LinearAlgebra

visualize the effect of multiplying a planar vector by a square matrix

•	Task: Matrix Action 2-D

Equate corresponding components in two vectors or matrices

•	Context Menu: Equate (applied to the sequence of objects)

•	Task: Equate Corresponding Components of Two Vectors

•	Use the Equate command

convert linear equations to matrix form

•	Context Menu: Generate Matrix (applied to sequence of equations)

•	Task: Convert a System of Linear Equations to Matrix Form

•	Use the GenerateMatrix command from the LinearAlgebra package

Numerical analysis

How do I...

approximate the roots of an expression to a given accuracy using Newton's method

•	Use the Newton command from the Student NumericalAnalysis package: See Example 13.1

approximate the roots of an expression using a specific method

•	Use the Roots command from the Student NumericalAnalysis package: See Example 13.2 Available methods: Newton, Modified Newton, Bisection, Secant, Fixed-Point Iteration, False-Position, and Steffensen

find the interpolating polynomial

•	Use the PolynomialInterpolation command from the Student NumericalAnalysis package and return the Interpolant: See Example 13.3 Available methods: Hermite, Lagrange, Neville, and Newton

find the error term for a polynomial interpolation problem

•	Example 13.4: Find the Polynomial Interpolation (see Example 13.3). Then use the command RemainderTerm to find the error term.

find the divided difference table

•	Example 13.5: Find the Polynomial Interpolation (see Example 13.3). Then use the command DividedDifferenceTable.

find the quadrature using a specific method

•	Use the Quadrature command from the Student NumericalAnalysis package: See Example 13.6 Available methods: Boole's rule, Simpson's rule, Simpson's 3/8 rule, trapezoid rule, Newton-Cotes rule, Gaussian rule, and Romberg integration. Adaptive quadrature can be applied to the first five methods.

solve an ODE initial value problem using Euler's method

•	Euler tutor

•	Use the Euler command from the Student NumericalAnalysis package: See Example 13.7

solve an ODE initial value problem using a specific method, or compare the numerical solutions found using various methods

•	IVP tutor Methods included: Euler, Taylor, Runge-Kutta, Adams-Bashforth, and Adams-Bashforth-Moulton

factor a square matrix using matrix decomposition

•	Matrix Decomposition tutor

use a numerical method to solve

•	Iterative Formula tutor

•	Use the LinearSolve command from the Student NumericalAnalysis package: See Example 13.8 Available methods: Jacobi, Gauss-Seidel, SOR, LU, LU[tridiagonal], PLU, and PLU[scaled]

Statistics

How do I...

define a random variable

•	Task: Define a Random Variable

evaluate the probability density function of a random variable

•	Task: Probability Density Function of a Continuous Random Variable

evaluate the probability function of a discrete random variable

•	Task: Probability Function of a Discrete Random Variable

evaluate the cumulative probability density function of a random variable

•	Task: Cumulative Distribution Function of a Random Variable

define a probability distribution

•	Task: Define a Custom Probability Distribution

sample a random variable with a given probability distribution

•	Task: Generate a Random Data Set

compute moments for a random variable

•	Task: Moments of a Random Variable

compute maximum likelihood estimates

•	Task: Maximum Likelihood Estimates

fit a regression model to data

•	Task: Fit a Linear Regression Model

•	Task: Fit a Nonlinear Regression Model

import data from a file

•	Import Data Assistant: Tools → Assistants → Import Data

•	Task: Import a Data Set from a File

create statistical process control charts

•	Task: Create Statistical Process Control Charts

Integer manipulations

How do I...

decompose an integer into the product of its prime factors

•	Task: Factor

obtain the greatest common divisor (GCD) of integers

•	Task: Greatest Common Divisor

obtain the lowest common multiple (LCM) of integers

•	Task: Least Common Multiple

obtain the value of an integer modulo

•	Task: Modulo n

solve an equation for integer values of the variables

•	Task: Solve an Equation for Integer Solutions

solve an equation for integers modulo

•	Task: Solve an Equation Modulo n

determine whether a specified integer is prime

•	Task: Test Primality

Units, errors, and tolerances

How do I...

apply a unit to a quantity

•	Example 16.1: Apply units to quantities by using either of the two Units palettes or by using the Context Menu: Units → Affix Unit.

convert units

•	Example 16.2: Convert a quantity with units to another unit using the Context Menus: Units → Convert → System → [desired system of units] and Units → Replace Units.

use tolerances

•	Example 16.3: Add tolerances to quantities by inserting from a palette or by using Command Completion, and then perform computations using tolerances.