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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
Algebraic manipulations
Algebraic solvers
Polynomial arithmetic
Plotting
Differential calculus in one variable
Integral calculus in one variable
Multivariate calculus
Vector calculus
Complex arithmetic
ODEs
Linear algebra
Numerical analysis
Statistics
Integer manipulations
Units, errors, and tolerances
Recurrence equations
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 Panel: 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 ⅇx
Example 1.4: Use the exponential template from the Expression palette or use Command Completion in Math mode
enter logax
In Math mode, the expression can be entered normally with the a entered as a subscript. To enter the subscript level, hold down [Ctrl] and press underscore [_]; after typing the subscript, press the right arrow key to leave the subscript. Finish the expression by entering x
Example 1.5: Use the log template from the Expression palette
In Maple Input mode, log[a](x) can be used to represent logax
convert an expression to a function
Context Panel: See Example 1.6
Task: Convert an Expression to a Function
write a procedure
Task: Define a Procedure
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 Panel: Complete Square
Task: Complete the Square
square both sides of an equation
Task: Square Both Sides of Equation
Context Panel: Manipulate Equation
substitute into an expression
Context Panel: Evaluate at a Point
Context Panel: Constructions → Evaluate At → [variable name] (yields unevaluated evaluation)
Use the template fxx=a|f(x)x=afrom the Expression palette; replace fx with the expression on which to perform the substitution, and overwrite x=a 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 Panel for an equation does not provide the Constructions option
obtain the solution to RootOf
Context Panel: All Values
Context Panel: 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 Panel: 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 Panel: 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 x1/3
Use the surd command.
solve algebraic equation(s)
Context Panel: 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 Panel: Solve
Task: Solve an Inequality
eliminate parameter in parametric equations
Context Panel: Solve → Eliminate a Variable → [parameter name]
eliminate selected variables in a set or list of equations
Context Panel: Solve → Eliminate Variables
Use the eliminate command
multiply out the factored form of a polynomial
Context Panel: Expand
factor a polynomial
Context Panel: Factor
find the zeros of a polynomial
obtain the quotient and remainder when dividing polynomials
Task: Polynomial Division - Quotient and Remainder
graph a curve or a surface
For an expression, Context Panel: Plots → Plot Builder
For a function, Context Panel: Plots → 2-D Plot or 3-D Plot
See the comprehensive Plotting Guide
create an animation
Context Panel: 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 Panel (for graph): Probe Info → Nearest point on line
create a graph with one or more parameters controlled by sliders
Context Panel: 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
construct a limit
Context Panel: Constructions → Limit → [variable name] and input the value
Limit Methods tutor: See Example 6.1
evaluate a limit
Context Panel: 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) Calculus palette: enter and complete limx→af, the limit template Context Panel: 2-D Math → Convert To → Inert Form Context Panel: Solve → Show Solution Steps
differentiate
Context Panel: Differentiate → [variable name]
Differentiation Methods tutor or See Example 6.2
Use the template ⅆⅆxf from the Calculus palette: See Example 6.3
exhibit annotated stepwise evaluation of a derivative
Load the Student[Calculus1] package (Tools → Load Package → Student Calculus 1) Calculus palette: enter and complete ⅆⅆxf, the differentiation template Context Panel: 2-D Math → Convert To → Inert Form Context Panel: Solve → Show Solution Steps
differentiate implicitly
Context Panel: Differentiate → Implicitly
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 Panel: 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
obtain a Riemann sum for fx
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 fx
Context Panel: Integrate
Task: Integration - Formal Rules
Integration Methods tutor or See Example 7.1
obtain the definite integral of fx
Context Panel: Constructions → Definite Integral
display annotated stepwise evaluation of an integral
Load the Student[Calculus1] package (Tools → Load Package → Student Calculus 1) Calculus palette: enter and complete definite or indefinite integration templates: ∫fⅆx or ∫abfⅆx Context Panel: 2-D Math → Convert To → Inert Form Context Panel: Solve → Show Solution Steps
enter and evaluate ∫fx ⅆx
Example 7.2: Use the template, ∫fⅆx, from the Calculus palette
Example 7.3: Type int and use Command Completion
enter and evaluate ∫abfx ⅆx
Example 7.2: Use the template, ∫abfⅆx, from the Calculus palette
approximate a definite integral numerically
Context Panel: 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
integrate by trig substitution
Task: Integration by Substitution
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
obtain partial derivatives of a multivariate expression
Context Panel: Differentiate
Use ∂∂xf, the partial-differentiation template in the Calculus 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 Panel: 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 Calculus 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
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
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 x1,…,xn, 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 Panel: 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 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
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.
enter a complex number
Example 10.1: Enter a complex number using ⅈ, ȷ, or I 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
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 y′=fx,y
Task: Direction Field
obtain the Picard iterates for y′=fx,y,yx0=y0
Task: Picard Iterates
solve an ordinary differential equation
Context Panel: Solve DE
Task: Solve an Ordinary Differential Equation
Use the dsolve command
solve an initial or boundary value problem
Context Panel: Solve DE Interactively
classify the type of an ODE
Context Panel: Classify the ODE
Task: Identify the Type of an ODE
solve an ODE numerically
Context Panel: 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
for a given vector, find its coordinates with respect to a specific basis
Task: Coordinate Vector for a Vector
Context Panel: Dot Product (apply to sequence 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 Student LinearAlgebra package
calculate a vector 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 A×B, the cross-product of two vectors
Task: Cross Product and Its Visualization
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 Student LinearAlgebra package
obtain the determinant of a matrix
Context Panel: 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 Student 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 f to each element of a vector or matrix A
Use the element-wise operator: f~A
Task: Map a Function onto Elements of a Vector
obtain the product of two matrices A and B
Use the period for noncommutative multiplication: A.B
Task: Product of Two Matrices
raise a square matrix A to a positive integer power such as 3
Use ordinary exponentiation: A3
Task: Nth Power of a Matrix
obtain the rank of a matrix
Context Panel: Queries → Rank
Task: Rank of a Matrix
Use the Rank command from the Student 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 Student LinearAlgebra package
obtain the transpose or Hermitian transpose of a matrix
Context Panel: 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 A%T
construct a projection matrix
Task: Generate a Projection Matrix
perform augmentation or stacking operations on a matrix
Example 12.6: Stacking A on top of B, where A and B are vectors or matrices is done by typing A,B; Augmenting A with B is done by typing A|B
solve the linear system Ax=b
Task: Solve a System of Linear Equations
Augment by using A|b and apply Context Panel: Solvers and Forms → Row-Echelon Form (see Example 12.6)
Use the LinearSolve command from the Student LinearAlgebra package
implement Gaussian elimination
Gaussian Elimination tutor: See Example 12.7
Task: Gaussian Elimination for an Augmented Matrix
Context Panel: Solvers and Forms → Row-Echelon Form
Use the GaussianElimination command from the Student LinearAlgebra package
obtain the inverse of a square matrix A
In math mode, simply execute A−1
In text mode, execute A^(-1)
Task: Inverse of a Matrix
Context Panel: Standard Operations → Inverse
Matrix Inverse tutor: See Example 12.8
Use the MatrixInverse command from the Student LinearAlgebra package
obtain the pseudoinverse of a singular or nonsquare matrix
Context Panel: Standard Operations → Pseudoinverse
Use the Pseudoinverse command from the Student LinearAlgebra package
obtain eigenvalues and eigenvectors for a matrix
Context Panel: Eigenvalues, etc → Eigenvalues
Task: Eigenvalues and Eigenvectors of a Matrix
Use the Eigenvalues and Eigenvectors commands from the Student LinearAlgebra package
compute eA t for a constant matrix A
Task: Calculate the Exponential for a Constant Matrix
Use the MatrixExponential command from Student LinearAlgebra package
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 the Student LinearAlgebra package
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 Panel: Equate (applied to the sequence of objects)
Task: Equate Corresponding Components of Two Vectors
Use the Equate command
convert linear equations to matrix form
Load Student[LinearAlgebra]
Context Panel: Student Linear Algebra → Constructions → Generate Matrix (applied to sequence of equations)
Task: Convert a System of Linear Equations to Matrix Form
Use the GenerateMatrix command from the Student LinearAlgebra package
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 Ax=b
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]
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
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 n
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 n
Task: Solve an Equation Modulo n
determine whether a specified integer is prime
Task: Test Primality
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 Panel: Units → Affix Unit.
convert units
Example 16.2: Convert a quantity with units to another unit using the Context Panel: 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.
change a default unit in a system of units
Task: Change Default Unit in a System
compute with quantities having units attached
Task: Compute Values with Units
compute with quantities having errors attached
Task: Compute with Quantities Containing Errors
access and use values of scientific constants
Task: Compute with Scientific Constants
change to equivalent units in a quantity carrying units
Task: Convert Expression with Units to Different Units
convert between Celsius and Fahrenheit
Task: Convert from Celsius to Fahrenheit
Task: Convert from Fahrenheit to Celsius
change the units associated with a quantity
Task: Convert Value from One Unit to Another
evaluate an expression at values having units
Task: Evaluate an Expression with Units
switch from one unit system to another
Task: Switch to a Different Unit System
compute with quantities carrying tolerance limits
Task: Tolerances
enter a recurrence equation
Example 17.1: Entering a recurrence equation in Maple
solve a recurrence equation
Task: Solve a Recurrence Relation
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