NA_WorkSheet Help Contents Manual

Copyright © 2005-2006 Dana M. Proctor

December 2006


Table of Contents
  1. ToolBar
  2. Polynomial Roots
  3. Differentiation
  4. Integration
  5. Interpolation
  6. Matrix Operations
  7. Linear Systems
  8. Non-Linear Systems
  9. EigenValues
  10. Expression Functions

1. Toolbar

    The NA_WorkSheet ToolBar provides several features that allow either special operations to be executed or setting of parameters. The ToolBar menu is made up of the File, Edit, Evaluate, Graph, and Help menu items. The File menu allows the worksheet to be closed by the exit option, or to print a basic page that contains the GraphPanel, MainInputPanel, MethodPanel, and the current data in the OutputPanel data area.

    The Edit menu allows the copy, cutting, and pasting of data in the worksheet. The operations can be performed via the toolbar, mouse, or keyboard. The mouse operation is executed by a right click in the focused textfield or textarea. This holds for all the panels except the MethodPanel where a right click anywhere in the panel besides those fields will activate the popup. The keyboard copy cut, and paste are actuated by the ctl-c, ctl-x, and ctl-v sequences respectively.

    The Data menu has three options Format, Import, and Export. The Format option provides a means to control the formatting of the output data in the worksheet. An input dialog allows the setting of the number of decimal places to be used and the spacing in columns of data. Generally the formatting works with most algorithms except those that have a tolerance input. A tolerance specification will replace the decimal places setting for data in the output. The final result(s) on most algorithms will normally not apply this formatting. The Import data operation will allow the importing of data into some selected algorithms, ie matrix operations. If the import is active for an algorithm a file input dialog will appear. If the NA_WorkSheet is run as an Applet then this will not be available for security reasons. The data in the input file should be arrange in the same manner as expected in the input panel and be space delimited. The Export data takes all the current information in the output panel data area and places it in the specified file. Of course The worksheet run in a web page as an Applet will not allow this option.

    The Evaluate menu allows the setting of the worksheet's ability to output complex number formats. Anytime a complex number is output as data by an evaluation or algorithm it will use this setting to determine either the rectangular or polar format.

    The Graph Menu allows the setting of colors that will be used in the GraphPanel. The axis, grid, background, and plot can be changed to the user's preferences. The default colors, scaling, and translation can also be returned to their original state as when the worksheet was first started.

    The Help menu allows access to an NA_WorkSheet Introduction document and this Help information. The Na_WorkSheet's web page information is also available along with acknowledgment/credit build date in the About section.


2. Polynomial Roots

    The polynomial roots approximations in the NA_WorkSheet provide a procedure to determine the value(s) of an input function where f(x)=0. The approximations generally require an input guess to the value of the root. In addition a tolerance and iteration limit is required. In the case of the Bisection method two values need be input that are on either bound of the estimated root location. Each of the approximations except the Newton/Horner find the localized root near the approximated root input. Newton/Horner will try to find all the real roots. The Newton/Horner approximation though needs the coefficients and polynomial degree input and does not use the Equation for Analysis. The Muller approximation can find the complex roots of the input Equation for Analysis.


3. Differentiation

    The differentiation approximations in the NA_WorkSheet provide the means to determine the slope or derivative of an input given a set of points or the Equation for Analysis. If a set of points are input then they need to have a fixed incremental delta between them. The derivative by evaluation allows this delta to be specified. Generally the smaller the delta the more accurate the result. The second derivative algorithm only performs the calculation on the Equation for Analysis.


4. Integration

    The integration approximations in the NA_WorkSheet give an estimate of the area or volume given an input Equation for Analysis. The single integrals require the boundary, input points, where the area is to be calculated. The double and triple integral approximations allow not only just points for the limits, but also equations in terms of the first, and second integral if a triple. The approximations are generally divided into composite and adaptive. The composite apply the algorithm directly while the adaptive techniques use the same composite, but on subintervals in a recursive manner. The Gaussian approximation is somewhat different then the others because it uses a table of Legendre roots and weights to calculate the integral directly. The Legendre table will only provide data to accurately calculate an integral in the Gaussian approximation for a polynomial of degree forty-seven. The adaptive Gaussian is not limited by the Legendre table because only the first six roots and weights are used. The subinterval inputs in the algorithms for the direct methods determine incremental subdivision. Generally the smaller the interval the more accurate and time consuming the approximation.


5. Interpolation

    The interpolation approximations in the NA_WorkSheet generate an equation for a set of input points. Depending on the method the equation is either a single equation or a series of equations or segments. Each of
the algorithms has the ability to either set or plot the equation(s)
generated. The Lagrange, Newton Divided Difference, and Hermite have a
checkbox to Set the Equation for Analysis when the algorithm is executed.
The MainInput Panel's Graph button then can be used to view a plot of the
polynomial in the Graph Panel. The Cubic Spline and Bezier interpolations
generate a polynomial for each segment given by the endpoints. The checkbox
Plot Polynomial Segments will automatically graph the segment equations
when those approximations are executed. The Beizer approximation is
different than the others because besides the x, y points there are guide-
points associated with the endpoints. The first and last endpoints have
one guidepoint each, but points having segments on either side will have
two. The quidepoints can be fixed, input with the points, or selectable.
The best way to work with select guide points is input the points and execute
the algorithm with fixed guide points. Once the algorithm is executed then
switch to selected then use the mouse to grab, hold down the active
button, near one of the guide points and move to the desired position. The
equations in the Output Panel Data textarea will automatically update along
with the graph. Each of the interpolation algorithms can either have
points input manually or through the worksheet's Data Import mechanism.
All the algorithms can be evaluated at points other then the specified
ones with the Output Panel Evaluate pane. The Evaluate pane has the ability
to evaluate complex numbers in any equation in the worksheet.

    Tip: If you would like to do polar to rectangular conversions put "x" in the Equation for Analysis textfield and use the Evaluate pane, and the Evaluate toolbar setting for the desired conversion.


6. Matrix Operations

    The Matrix Operations section of the NA_WorkSheet is a new addition from the alpha release. The Matrix Operations provide the ability to perform basic computations on two matrixes. The matrixes can be input manually or through the Data Import. The format for imported files should be the same has if manually entering with space delimited. If the resultant operation is desired to be substituted back into the worksheet has the next operand select the Output Results to => Matrix A checkbox. Some of the operations on matrixes will require specify types of Matrix A and B inputs. The worksheet generally will try to check these requirements. The operations available in the worksheet are addition, subtraction, multiplication, constant multiplication, inverse, transpose, determinant, and two of the standard norms.


7. Linear Systems

    The linear systems approximations in the NA_WorkSheet provides the ability to solves a system of input equations in terms of single variables. There are several algorithms in this category and each can be used to to solve a system. The LU, LDL, and LL Decomposition have an additional checkbox that can be used to store the reduction in the system then used for solving the same system again more efficiently with a new set of constants in the right hand side. The Cramer approximation is unique in this set of systems solvers because it will handle a system of equation with complex coefficients. The algorithm might be of use to students that would like quickly check/solve some engineering problems.


8. Non-Linear Systems

Not yet implemented.


9. EigenValues

Not yet implemented.


10. Expression Functions

    The expression evaluation in the NA_WorkSheet allow the use of common math functions in the equation for analysis. All the functions will handle real and complex numbers. Note: Not all algorithms support complex input. Complex input in the equations also will not graph, but will evaluate, try x^2 then evaluate i. Follows are the NA_WorkSheet support functions. Unless noted all functions are single argument.

abs() - Absolute
acos() - ArcCosine
actan() - ArcTangent
add() - Add
asin() - ArcSine
atan() - CoTangent
box() - Box
ceil() - Ceiling
cos() - Cosine
ctan() - CoTangent
div() - Divsion Two Argument
exp10() - Exponential Power 10
exp() - Natural Exponent
floor() - Floor
ln() - Natural Logorithm
log(0 - Base 10 Logorithm
mult() - Mulitplication Two Argument
one() - One Real and Complex
pow() - Power Two Argument
round() - Round
sinc() - Better Look At This One
sin() - Sine
sqr() - Square
sqrt() - Square Root
sub() - Subtraction Two Argument
tan() - Tangent
twoArg() - Better Look At This Before Use