return the Taylor series for a multivariate function - Maple Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Education : Student Package : Multivariate Calculus : Visualization : Student/MultivariateCalculus/TaylorApproximation

Student[MultivariateCalculus][TaylorApproximation] - return the Taylor series for a multivariate function

Calling Sequence

TaylorApproximation(f(x,y,...), [x,y,...]=[a,b,...], order, x=xmin..xmax, y=ymin..ymax, ..., opts)

Parameters

f(x, y, ...)

-

algebraic expression

x, y, ...

-

name; specify the independent variables

a, b, ...

-

name or real constants; point around which the function is expanded

order

-

(optional) positive integer; order of taylor polynomial

xmin, xmax, ymin, ymax, ...

-

(optional) real constants specifying range over which to plot function

opts

-

(optional) equation(s) of the form option=value where option is one of centeroptions, functionoptions, output, showcenter, showfunction, tayloroptions; specify output options

Description

• 

The TaylorApproximation command returns the Taylor approximation of f of a specified order around a specified point. By using options, you can specify that the command returns a plot or animation.  This feature is only available if one or two variables are specified.

• 

The opts argument can contain any of the following equations that set output options.  Plotting is only available for univariate or bivariate functions.

• 

The TaylorApproximationTutor routine offers equivalent capabilities to TaylorApproximation in a tutor interface.  See Student[MultivariateCalculus][TaylorApproximationTutor] help page.

  

 

  

centeroptions = list

  

Specifies the plot options for plotting the point x,fx or x,y,fx,y.  For more information on plotting options, see plot3d/options.

  

 

  

functionoptions = list

  

Specifies the plot options for plotting the function f. For more information on plotting options, see plot3d/options.

  

 

  

output = value, plot, or animation

  

This option controls the return value of the function.

  

* output = value specifies that the value of the approximation is returned. Plot options are ignored if output = value.  The default is output = value.

  

* output = plot specifies that a plot displays, which shows the expression and the Taylor approximation to the function.

  

* output = animation specifies that an animation displays, which shows the Taylor approximation approaching the function as the order of the Taylor series increases with each frame.

  

 

  

showcenter = true or false

  

Determines whether the point around which the series is expanded is plotted. The default is true.

  

 

  

showfunction = true or false

  

Determines whether the function f is plotted. The default is true.

  

 

  

tayloroptions = list

  

Specifies the plot options for plotting the Taylor approximation to f. The default is 'color'='red','transparency'=0.5. For more information on plotting options, see plot3d/options.

  

 

  

caption = anything

  

A caption for the plot.

  

The default caption is constructed from the parameters and the command options. caption = "" disables the default caption. For more information about specifying a caption, see plot/typesetting.

  

 

  

title = anything

  

A title for the plot.

  

The default title is constructed from the parameters and the command options. title = "" disables the default title. For more information about specifying a title, see plot/typesetting.

  

 

• 

For information on how to change the default colors, see the Student[SetColors] help page.

Examples

withStudent[MultivariateCalculus]:

TaylorApproximationsinx+y,x,y=1,0,5

1120cos1y5+124sin1y4+124cos1x1y416cos1y3+16sin1x1y3+112cos1x12y312sin1y212cos1x1y2+14sin1x12y2+112cos1x13y2+cos1ysin1x1y12cos1x12y+16sin1x13y+124cos1x14y+sin1+cos1x112sin1x1216cos1x13+124sin1x14+1120cos1x15

(1)

To play the following animation in this help page, right-click (Control-click, on Macintosh) the plot to display the context menu.  Select Animation > Play.

TaylorApproximationsinx+y,x,y=1,0,5,output=animation

The command to create the plot in the Plotting Guide is

TaylorApproximationsinx,x,y=0,0,5,x=3..3,y=3..3,output=plot

See Also

plot3d/options, Student, Student[MultivariateCalculus], Student[MultivariateCalculus][TaylorApproximationTutor]


Download Help Document

Was this information helpful?



Please add your Comment (Optional)
E-mail Address (Optional)
What is ? This question helps us to combat spam