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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.
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Constructing algebraic objects
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How do I...
enter a piecewise expression or function
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Example 1.1: Use the piecewise template from the Expression palette
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enter an algebraic equation
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create a sequence
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Context Panel: Sequence
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construct a loop
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write the exponential function
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Example 1.4: Use the exponential template from the Expression palette or use Command Completion in Math mode
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enter
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In Math mode, the expression can be entered normally with the 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
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Example 1.5: Use the log template from the Expression palette
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In Maple Input mode, log[a](x) can be used to represent
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convert an expression to a function
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write a procedure
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Algebraic manipulations
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How do I...
obtain the equation of a line
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obtain the coordinates of the midpoint of a line segment
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obtain the slope of a line segment
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compute the distance between two points
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complete the square
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Context Panel: Complete Square
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square both sides of an equation
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Context Panel: Manipulate Equation
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substitute into an expression
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Context Panel: Evaluate at a Point
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Context Panel: Constructions → Evaluate At → [variable name] (yields unevaluated evaluation)
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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
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Use the command eval to substitute a variable or value into an expression
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substitute into an equation
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Use any of the devices for substitution into an expression, except that the Context Panel for an equation does not provide the Constructions option
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obtain the solution to RootOf
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Context Panel: All Values
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Context Panel: Conversions → To Radical
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force an equation to be an identity
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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.
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determine the inverse of a function
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Function Inverse Tutor:
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interpolate data
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Context Panel: Curve Fitting → any of
B-Spline, Interactive Curve Fitting, Least Squares,
Polynomial Interpolation, Rational, Spline, Thiele
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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)
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obtain a partial fraction decomposition of a rational function
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Context Panel: Conversions → Partial Fractions → [variable name]
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obtain real values of
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Algebraic solvers
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How do I...
solve algebraic equation(s)
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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
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solve an inequality
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eliminate parameter in parametric equations
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Context Panel: Solve → Eliminate a Variable → [parameter name]
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eliminate selected variables in a set or list of equations
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Context Panel: Solve → Eliminate Variables
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Polynomial arithmetic
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How do I...
multiply out the factored form of a polynomial
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factor a polynomial
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find the zeros of a polynomial
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obtain the quotient and remainder when dividing polynomials
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Plotting
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How do I...
graph a curve or a surface
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For an expression, Context Panel: Plots → Plot Builder
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For a function, Context Panel: Plots → 2-D Plot or 3-D Plot
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create an animation
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Context Panel: Plots → Plot Builder →
Select Plot Type and Functions → Animation
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Use the animate command in the plots package
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animate the drawing of a plane curve
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trace coordinates along a plane curve
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Context Panel (for graph): Probe Info → Nearest point on line
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create a graph with one or more parameters controlled by sliders
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Context Panel: Plots → Plot Builder →
Select Plot Type and Functions → Interactive Plot with (n) parameter(s)
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graph a rational function and its asymptotes
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Rational Function Tutor:
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graph linear inequalities
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Linear Inequalities tutor
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Use the inequal command in the plots package
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graph conic sections
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Conic Sections tutor
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graph the intersection of two surfaces
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Use the intersectplot command from the plots package
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Differential calculus in one variable
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How do I...
construct a limit
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Context Panel: Constructions → Limit → [variable name] and input the value
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evaluate a limit
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Limit Methods tutor
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display an annotated stepwise evaluation of a limit
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Load the Student[Calculus1] package (Tools → Load Package → Student Calculus 1)
Calculus palette: enter and complete , the limit template
Context Panel: 2-D Math → Convert To → Inert Form
Context Panel: Solve → Show Solution Steps
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differentiate
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Context Panel: Differentiate → [variable name]
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Use the template from the Calculus palette: See Example 6.3
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exhibit annotated stepwise evaluation of a derivative
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Load the Student[Calculus1] package (Tools → Load Package → Student Calculus 1)
Calculus palette: enter and complete , the differentiation template
Context Panel: 2-D Math → Convert To → Inert Form
Context Panel: Solve → Show Solution Steps
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differentiate implicitly
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Context Panel: Differentiate → Implicitly
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graph a function and its derivative(s)
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obtain equations for tangent and normal lines along a curve
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analyze a plane curve
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Curve Analysis tutor
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Use the FunctionChart command from the Student Calculus 1 package
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obtain Taylor series and polynomials
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implement Newton's Method
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Use the NewtonsMethod command from the Student Calculus1 package
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Integral calculus in one variable
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How do I...
obtain a Riemann sum for
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Riemann Sum tutor
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obtain the indefinite integral of
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Context Panel: Integrate
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obtain the definite integral of
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Context Panel: Constructions → Definite Integral
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display annotated stepwise evaluation of an integral
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Load the Student[Calculus1] package (Tools → Load Package → Student Calculus 1)
Calculus palette: enter and complete definite or indefinite integration templates: or
Context Panel: 2-D Math → Convert To → Inert Form
Context Panel: Solve → Show Solution Steps
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enter and evaluate
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Example 7.2: Use the template, , from the Calculus palette
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enter and evaluate
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Example 7.2: Use the template, , from the Calculus palette
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approximate a definite integral numerically
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Context Panel: Approximate
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integrate by parts
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integrate by trig substitution
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compute the average value of a function
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calculate the length of a curve (arc length)
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Use the ArcLength command from the Student Calculus1 package
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calculate the volume of a solid of revolution
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calculate the surface area of a surface of revolution
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obtain the radius of convergence of a power series
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apply the Ratio test for convergence of a series
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Multivariate calculus
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How do I...
obtain partial derivatives of a multivariate expression
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Context Panel: Differentiate
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Use the partial-differentiation template in the Calculus palette
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obtain partial derivatives of a multivariate function
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find and test critical points of a multivariate function or expression
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obtain the gradient vector for a multivariate function
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Use the Gradient command from the Student MultivariateCalculus package
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obtain the directional derivative of a multivariate scalar field
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implement the Lagrange Multiplier method
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obtain a Taylor expansion of a multivariate expression
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Context Panel: Series → Multivariate Taylor Polynomial
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obtain the Jacobian matrix and the Jacobian of a multivariate expression
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Use the Jacobian command from the Student MultivariateCalculus package
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Use the Jacobian command from the VectorCalculus package
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obtain the Hessian of a multivariate expression
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Use the Hessian command from the VectorCalculus package
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implement iterated integration
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Example 8.4: Iterate an integral icon from Calculus palette
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evaluate iterated double integrals over pre-defined regions
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evaluate iterated triple integrals over pre-defined regions
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evaluate an iterated integral numerically
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Context Panel: Approximate
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Multivariate Approximate Integration tutor
or See Example 8.5
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Use the ApproximateInt command from the Student MultivariateCalculus package
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visualize the region of integration for an iterated integral
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compute the average value of a multivariate expression
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determine the center of mass of a plane or spatial region
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calculate the surface area for a surface that is not a surface of revolution
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Vector calculus
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How do I...
designate a coordinate system
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enter a free vector (the equivalent of a point)
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Type , where inequality signs are used for angle brackets
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Use the Vector command from the VectorCalculus package
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attach a coordinate system to a free vector
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construct a vector field
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Use the VectorField command from the VectorCalculus package
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evaluate a vector field at a point
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graph a vector field
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Vector Fields tutor
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Use the PlotVector command from the VectorCalculus package
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obtain the dot product of two vectors
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Use the period, or the dot () from the Common Symbols palette
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Use the DotProduct command from the VectorCalculus package
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calculate the magnitude of a vector
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Use the Norm command from the VectorCalculus package
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obtain the cross product of two vectors
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In Math mode, use from the Common Symbols palette
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In text mode, use &x as the cross-product operator
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Use the CrossProduct command from the VectorCalculus package
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visualize the cross-product vector
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obtain the gradient of a scalar field
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Example 9.2: Gradient via the Nabla or Del operator
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Use the Gradient command from the VectorCalculus package
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obtain the divergence of a vector field
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Example 9.3: Divergence via the Nabla or Del operator
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Use the Divergence command from the VectorCalculus package
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obtain the curl of a vector field
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Use the Curl command from the VectorCalculus package
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obtain the Laplacian of a scalar field
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Example 9.5: Laplacian via the Nabla or Del operator
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Use the Laplacian command from the VectorCalculus package
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obtain the Laplacian of a vector field
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evaluate iterated double integrals over pre-defined regions
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evaluate iterated triple integrals over pre-defined regions
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evaluate an iterated integral using the int command as modified by the VectorCalculus packages
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compute a line integral along a plane curve
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compute a line integral along a space curve
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calculate a surface integral
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compute the flux of a vector field through a plane curve
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compute the flux of a vector field through a surface
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visualize the TNB (tangent-normal-binormal) frame for a space curve
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Space Curve tutor
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interactively implement the Frenet-Serret formalism for a space-curve
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programmatically implement the Frenet-Serret formalism for a space-curve
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Use the TNBFrame command from the VectorCalculus package
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Use the Binormal command from the VectorCalculus package
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Use the Curvature command from the VectorCalculus package
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Use the Torsion command from the VectorCalculus package
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obtain the coordinates of a point in a different coordinate system
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change coordinates in a vector field
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Complex arithmetic
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How do I...
enter a complex number
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Example 10.1: Enter a complex number using , , or from the Common Symbols palette
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obtain the real and imaginary parts of a complex number
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obtain the magnitude and argument of a complex number
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express a complex number in polar form
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convert a complex number to rectangular form
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ODEs
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How do I...
enter an ordinary differential equation
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Example 11.1: Enter a differential equation using dot notation, prime notation, or the command diff
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obtain a direction field for
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obtain the Picard iterates for
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solve an ordinary differential equation
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Context Panel: Solve DE
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solve an initial or boundary value problem
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Context Panel: Solve DE Interactively
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classify the type of an ODE
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Context Panel: Classify the ODE
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solve an ODE numerically
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Context Panel: Solve DE Interactively, then choose Solve Numerically
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obtain the Wronskian for a fundamental set of solutions
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Use the Wronskian command from the VectorCalculus package
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generate a phase portrait for an autonomous system of ODEs
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Use the DEplot command from the DEtools package
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explore phase portraits for autonomous systems of ODEs
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DE Plots tutor
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Linear algebra
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How do I...
for a given vector, find its coordinates with respect to a specific basis
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obtain the dot product of two vectors
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Context Panel: Dot Product (apply to sequence of two vectors)
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Example 12.1: Obtain the dot product of two vectors using the Common Symbols palette or using a period
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determine the angle between two vectors
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Use the VectorAngle command in the Student LinearAlgebra package
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calculate a vector norm
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Example 12.2: Calculate the norm of a vector using symbols or a command
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project one vector onto another
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project a vector onto a subspace spanned by two other vectors or onto a plane through the origin
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obtain , the cross-product of two vectors
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Math mode: use from Common Symbols, or Operators palettes
Text mode: use &x
See Example 12.3
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extract a maximal linearly independent subset from a set of vectors
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Use the Basis command from the Student LinearAlgebra package
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obtain the determinant of a matrix
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Context Panel: Standard Operations → Determinant
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Example 12.4: Use the absolute value template from the Layout palette
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Use the Determinant command from the Student LinearAlgebra package
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multiply a matrix by a scalar
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In math mode, use a space as the multiplication operator
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In text mode, use * as the multiplication operator
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apply the function to each element of a vector or matrix
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Use the element-wise operator:
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obtain the product of two matrices and
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Use the period for noncommutative multiplication:
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raise a square matrix to a positive integer power such as 3
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Use ordinary exponentiation:
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obtain the rank of a matrix
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Context Panel: Queries → Rank
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Use the Rank command from the Student LinearAlgebra package
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obtain the nullity of a matrix
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obtain bases for row, column, and null spaces of a matrix
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obtain the transpose or Hermitian transpose of a matrix
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Context Panel: Standard Operations → Transpose
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Example 12.5: In Math mode, for a matrix A, its transpose can be found by typing
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construct a projection matrix
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perform augmentation or stacking operations on a matrix
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Example 12.6: Stacking on top of , where and are vectors or matrices is done by typing ; Augmenting with is done by typing
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solve the linear system
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Augment by using and apply Context Panel: Solvers and Forms → Row-Echelon Form (see Example 12.6)
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Use the LinearSolve command from the Student LinearAlgebra package
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implement Gaussian elimination
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Context Panel: Solvers and Forms → Row-Echelon Form
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obtain the inverse of a square matrix
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In math mode, simply execute
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In text mode, execute A^(-1)
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Context Panel: Standard Operations → Inverse
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Use the MatrixInverse command from the Student LinearAlgebra package
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obtain the pseudoinverse of a singular or nonsquare matrix
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Context Panel: Standard Operations → Pseudoinverse
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Use the Pseudoinverse command from the Student LinearAlgebra package
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obtain eigenvalues and eigenvectors for a matrix
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Context Panel: Eigenvalues, etc → Eigenvalues
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compute for a constant matrix
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apply the Gram-Schmidt process to the columns of a matrix, or a list or set vectors
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apply the Gram-Schmidt process to a list or set of vectors
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Use the GramSchmidt command from the Student LinearAlgebra package
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visualize the effect of multiplying a planar vector by a square matrix
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Equate corresponding components in two vectors or matrices
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Context Panel: Equate (applied to the sequence of objects)
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convert linear equations to matrix form
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Load Student[LinearAlgebra]
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Context Panel: Student Linear Algebra → Constructions → Generate Matrix (applied to sequence of equations)
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Use the GenerateMatrix command from the Student LinearAlgebra package
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Numerical analysis
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How do I...
approximate the roots of an expression to a given accuracy using Newton's method
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approximate the roots of an expression using a specific method
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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
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find the interpolating polynomial
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find the error term for a polynomial interpolation problem
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find the divided difference table
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find the quadrature using a specific method
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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.
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solve an ODE initial value problem using Euler's method
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Euler tutor
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solve an ODE initial value problem using a specific method, or compare the numerical solutions found using various methods
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IVP tutor
Methods included: Euler, Taylor, Runge-Kutta, Adams-Bashforth, and Adams-Bashforth-Moulton
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factor a square matrix using matrix decomposition
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Matrix Decomposition tutor
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use a numerical method to solve
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Iterative Formula tutor
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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]
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Statistics
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How do I...
define a random variable
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evaluate the probability density function of a random variable
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evaluate the probability function of a discrete random variable
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evaluate the cumulative probability density function of a random variable
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define a probability distribution
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sample a random variable with a given probability distribution
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compute moments for a random variable
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compute maximum likelihood estimates
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fit a regression model to data
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import data from a file
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Import Data Assistant: Tools → Assistants → Import Data
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create statistical process control charts
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Integer manipulations
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How do I...
decompose an integer into the product of its prime factors
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obtain the greatest common divisor (GCD) of integers
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obtain the lowest common multiple (LCM) of integers
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obtain the value of an integer modulo
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solve an equation for integer values of the variables
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solve an equation for integers modulo
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determine whether a specified integer is prime
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Units, errors, and tolerances
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How do I...
apply a unit to a quantity
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Example 16.1: Apply units to quantities by using either of the two Units palettes or by using the Context Panel: Units → Affix Unit.
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convert units
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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.
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use tolerances
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Example 16.3: Add tolerances to quantities by inserting from a palette or by using Command Completion, and then perform computations using tolerances.
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change a default unit in a system of units
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compute with quantities having units attached
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compute with quantities having errors attached
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access and use values of scientific constants
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change to equivalent units in a quantity carrying units
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convert between Celsius and Fahrenheit
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change the units associated with a quantity
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evaluate an expression at values having units
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switch from one unit system to another
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compute with quantities carrying tolerance limits
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Recurrence equations
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How do I...
enter a recurrence equation
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solve a recurrence equation
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