Current Summary of Contents of the Package math191
created by Daniel F. Symancyk
(for R4, R5, and R5.1 under Windows)
(as of 10/23/00)
Note: You must type with(math191): at a command prompt in Maple and then press enter in order to access the commands listed in this table.
Command in the package math191 |
Description |
Part of MenuMaple |
| BoxIterates | shows steps in simple iteration x = g(x) | |
| Cirsum | integral estimate with circumscribed rectangles | Yes |
| Inssum | integral estimate with inscribed rectangles | Yes |
| LPanimate | produces animation of linear programming (specify number of slides or points through which the objective function passes) | Yes |
| LPgraph | sketch feasible region and objective function for linear programming problem (specify value of objective function or a point through which it passes) | Yes |
| Lsum | integral estimate with left endpoint rectangles (will work with a variable number of rectangles) | Yes |
| Lsum3d | estimate double integral using left endpoints | Yes |
| Msum | integral estimate with midpoint rectangles (will work with a variable number of rectangles) | Yes |
| Msum3d | estimate double integral using midpoints | Yes |
| PlotBoxIterates | produces web diagram for iteration x = g(x) | Yes |
| PlotIterates | graphs x = g(x) | Yes |
| Randsum | integral estimate with random point rectangles | Yes |
| Riemann | evaluate a general Riemann sum | Yes |
| Rsum | integral estimate with right endpoint rectangles (will work with a variable number of rectangles) | Yes |
| Rsum3d | estimate double integral using right endpoints | Yes |
| Simp | Simpson's Rule | Yes |
| Trap | Trapezoidal Rule (will work with a variable number of subdivisions) | Yes |
| addto | add same amount to both sides of an equation | Yes |
| addvectoranimate | produces an animation of vector addition (see the parallelogram law) | |
| areaBetween | find area between two values for a normal distribution with specified mean and standard deviation | Yes |
| areaToLeftOf | find area to the left of a value for a normal distribution with specified mean and standard deviation | Yes |
| areaToRightOf | find area to the right of a value for a normal distribution with specified mean and standard deviation | Yes |
| basicstats | compute basic statistics for one or two lists of data | Yes |
| bestfit | find the equation of best fit | Yes |
| binomhistogram | create binomial histogram with option of superimposing a normal curve | Yes |
| binomialdist | computes probabilities for binomial distribution (also shows computation of mean and standard deviation the long way) | Yes |
| chisq | chi square distribution | Yes |
| confidenceint | creates a confidence interval given data or given the mean, std dev, and sample size | Yes |
| crossprodanimate | produces an animation of the cross product | |
| cumlfreqdist | produces a cumulative frequency table | Yes |
| cumulchisq | cumulative chi square distribution | Yes |
| cumulexpdist | cumulative exponential distribution | Yes |
| cumulnormaldist | cumulative normal distribution | Yes |
| cumultdist | cumulative t distribution | Yes |
| cumuluniformdist | cumulative uniform distribution | Yes |
| dataAddAmnt | add same amount to list of data | Yes |
| dataMultAmnt | multiply values in data list by same amount | Yes |
| diffsolve | solve differential equations and systems of differential equations | Yes |
| discreteLsum | produces left endpoint estimate of integral given paired data with equally spaced independent values | Yes |
| discreteRsum | produces right endpoint estimate of integral given paired data with equally spaced independent values | Yes |
| discreteTrap | produces trapezoidal estimate of integral given paired data with equally spaced independent values | Yes |
| discreteprobdist | computes mean, variance, and standard deviation for user defined probability distribution | Yes |
| diskdemo | shows n disks as expression in x is revolved about a line y = c | Yes |
| distribute | breaks down steps in distributive property | Yes |
| epdeltanimate | produces an animation related to the definition of limit (shows epsilon and delta regions) | |
| epdeltplot | graphs function along with epsilon and delta regions for specified f, a, epsilon, and delta | Yes |
| epdelttab | shows table of the epsilons and deltas relating to epdeltanimate | |
| expdist | exponential distribution | Yes |
| factorDenoms | allows you to factor only the denominator | Yes |
| findMeanStd | shows calculation of mean, variance and standard deviation for a data list | Yes |
| freqdist | create a frequency distribution table | Yes |
| freqhistogram | create a frequency histogram | Yes |
| gCirsum | essentially Cirsum with a graph | Yes |
| gCirsumanimate | animation involving circumscribed rectangles | Yes |
| gInssum | essentially Inssum with a graph | Yes |
| gInssumanimate | animation involving inscribed rectangles | Yes |
| gLsum | essentially Lsum with a graph | Yes |
| gLsum3d | essentially Lsum3d with a graph | Yes |
| gLsumanimate | animation involving left endpoint rectangles | Yes |
| gMsum | essentially Msum with a graph | Yes |
| gMsum3d | essentially Msum3d with a graph | Yes |
| gMsumanimate | animation involving midpoint rectangles | Yes |
| gRandsum | essentially Randsum with a graph | Yes |
| gRandsumanimate | animation involving random point rectangles | Yes |
| gRiemann | essentially Riemann with a graph | Yes |
| gRsum | essentially Rsum with a graph | Yes |
| gRsum3d | essentially Rsum3d with a graph | Yes |
| gRsumanimate | animation involving right endpoint rectangles | Yes |
| gSimp | Simp with a graph (parabolas are shown) | Yes |
| gTrap | Trap with a graph (line segments shown) | Yes |
| gTrapanimate | animation of trapezoidal rule | Yes |
| gareaBetween | areaBetween with a graph | Yes |
| gareaToLeftOf | areaToLeftOf with a graph | Yes |
| gareaToRightOf | areaToRightOf with a graph | Yes |
| gdiscreteLsum | discreteLsum with a graph | Yes |
| gdiscreteRsum | discreteRsum with a graph | Yes |
| gdiscreteTrap | discretTrap with a graph | Yes |
| glinsys | graph the system of equations corresponding to a matrix with 3 or 4 columns | Yes |
| gnPercentile | creates graph showing where the nth percentile is on a normal distribution | Yes |
| gpplot | produces a graph on graph paper | Yes |
| gseclines | produces an animation of secant lines at a point on a graph (approach from left, right, or both sides) | Yes |
| hypergeohistogram | creates histogram for hypergeometric distribution | Yes |
| hypergeometricdist | computes probabilities, mean and standard deviation for hypergeometric distribution | Yes |
| impdiff | performs implicit differentiation | |
| intByParts | returns steps involved in integration by parts (user specifies u) | Yes |
| intBySubs | returns steps involved in u substitution (user specifies u) | Yes |
| invcumulchisq | inverse cumulative chi square | Yes |
| invcumulnormaldist | inverse cumulative normal distribution | Yes |
| invcumultdist | inverse cumulative t distribution | Yes |
| invcumuluniformdist | inverse cumulative uniform distribution | Yes |
| invplot | graphs a given function and along with its inverse relation | Yes |
| limtab | make a "limit table" (as x approaches finite value from left, right, or both sides or as x approaches plus or minus infinity) | Yes |
| limtab3d | make a "limit table in 3d" (as (x,y) approaches (a,b) along a curve) | Yes |
| mseclines | table of slopes of secants | Yes |
| mult | multiply both sides of an equation by the same amount | Yes |
| newtonraphson | animation of newton raphson method (each slide shows tangent line, location of its x-intercept, and location of point where next tangent will be drawn) | |
| normalTable | creates standard normal z table | Yes |
| normaldist | normal distribution | Yes |
| ogive | create ogive or cumulative frequency graph | Yes |
| pccumlfreqdist | cumulative frequency table with user specified class boundaries | Yes |
| pcfreqdist | frequency distribution table with user specified class boundaries | Yes |
| pcfreqhistogram | frequency histogram with user specified class boundaries | Yes |
| pcogive | ogive or cumulative frequency graph with user specified class boundaries | Yes |
| pcrelfreqdist | relative frequency table with user specified class boundaries | Yes |
| pcrelfreqhistogram | relative frequency histogram with user specified class boundaries | Yes |
| plotvalutable | plot points on a graph (specify step size for independent variable or number of independent values) | Yes |
| poissondist | poisson distribution | Yes |
| poissonhistogram | histogram for poisson distribution | Yes |
| ptsplot2d | plot data points | Yes |
| regplot2d | plot data points and curve of best fit (which you should get using bestfit) | Yes |
| relfreqdist | create a relative frequency table | Yes |
| relfreqhistogram | create a relative frequency histogram | Yes |
| rotate | create final graph or a movie of the rotation of an expression in x about y = c or x = d | Yes |
| samplefromExponential | get a sample from the exponential distribution | Yes |
| samplefromNormal | get a sample from normal distribution | Yes |
| samplefromUniform | get a sample from uniform distribution | Yes |
| samplemeansExponential | extract sample means using the exponential distribution | Yes |
| samplemeansNormal | extract sample means using the normal distribution | Yes |
| samplemeansUniform | extract sample means using the uniform distribution | Yes |
| seclines | get a table of equations of secant lines | Yes |
| showslopes | animation that displays rise and run | Yes |
| sortstat | sort a data set | Yes |
| squareBothSides | square both sides of an equations | Yes |
| squareRootBothSides | take square root of both sides of an equation | Yes |
| stdscores | convert list of data to standard scores | Yes |
| subtvectoranimate | animations of vector subtraction | |
| tTable | create a table of critical t values | Yes |
| tayloranimate | animation of Taylor polynomials for a function | Yes |
| tdist | t distribution | Yes |
| testhypothesis | test hypothesis given data or given mean, standard deviation, and sample size | Yes |
| uniformdist | uniform distribution | Yes |
| valutable | create a table of values for one or two expressions (specify step size for independent variable or number of points) | Yes |
| zoomepdeltplot | a zoomed epdeltplot | Yes |
| `&X` | allows infix notation for cross product | Yes |
| `&d` | allows infix notation for dot product | Yes |
Note that many of these commands are included with the program, MenuMaple, which
works in conjunction with Maple V for Windows.
Send your questions or comments to Daniel F. Symancyk at dfsymancyk@aacc.edu
Description of Some Commands in the Package math191
To use the commands first execute the Maple command
> with(math191):
FUNCTION: valutable
- generates a table of values for one or two real-valued functions or algebraic
expressions of one variable
CALLING SEQUENCES:
valutable(expr,x=a..b,numbpts);
valutable([expr1,expr2],x=a..b,numbpts);
valutable(f,a..b,numbpts);
valutable([f1,f2],a..b,numbpts);
valutable(expr,x=a..b,step=amnt);
valutable([expr1,expr2],x=a..b,step=amnt);
valutable(f,a..b,step=amnt); or
valutable([f1,f2],a..b,step=amnt);
PARAMETERS:
expr - an algebraic expression in one variable
x - the name of the variable in expr
a,b - starting and ending values of the independent variable
numbpts - postive integer greater than one giving the number of points in the table
f - a function of one variable
amnt - size of increase between successive x values in table
(return)
FUNCTION: plotvalutable
- generates a graph of real ordered pairs for a
real-valued function or algebraic expression of
one variable
CALLING SEQUENCES:
plotvalutable(expr,x=a..b,numbpts);
plotvalutable(f,a..b,numbpts);
plotvalutable(expr,x=a..b,step=amnt);
plotvalutable(f,a..b,step=amnt);
PARAMETERS:
expr - an algebraic expression in one variable
x - the name of the variable in expr
a,b - starting and ending values of the independent variable
numbpts - positive integer greater than one giving the number of points to be used
f - a function of one variable
amnt - size of increase between successive x values used
(return)
FUNCTION: limtab
- generates a table of values for a real-valued expression of one variable as the variable
"approaches" a specified value.
CALLING SEQUENCES:
limtab(expr,x=a); or
limtab(expr,x=a,dir);
PARAMETERS:
expr - an expression in one variable
x - the name of the variable in expr
a - value the independent variable "approaches"
may be finite, infinity, or -infinity
dir - optional direction, left or right
(return)
FUNCTION: invplot
- returns a graph showing the function, its inverse relation, and y=x
CALLING SEQUENCES:
invplot(expr,x=a..b); or
invplot(f,a..b);
PARAMETERS:
expr - an algebraic expression in one variable
x - the name of the variable in expr
a,b - limits for the independent variable
f - a function of one variable
(return)
FUNCTION: gseclines
- generates an animation showing a sequence of secant lines as x "approaches" a
specified value.
CALLING SEQUENCES:
gseclines(expr,x=a); or
gseclines(expr,x=a,dir);
PARAMETERS:
expr - an expression in one variable
x - the name of the variable in expr
a - the finite value the independent variable "approaches"
dir - optional direction, left or right
(return)
FUNCTION: epdeltplot
- generates a graph featuring an expression, two horizontal lines within epsilon of L, and
two vertical lines within delta of a.
CALLING SEQUENCES:
epdeltplot(expr,x=a,L,ep,delt); or
epdeltplot(expr,x=a,L,ep,delt,yrange);
PARAMETERS:
expr - an expression in one variable
x - the name of the variable in expr
a - finite value the independent variable "approaches"
L - finite value you think dependent variable "approaches"
ep - positve value of epsilon
delt - positive value of delta
yrange - optional range for dependent variable
NOTE: Using this routine you get to see whether your choice of delta works.
(return)
FUNCTION: Lsum
- estimates a definite integral by using left endpoints of uniform partition of [a,b]
CALLING SEQUENCES:
Lsum(expr,x=a..b,numrects); or
Lsum(f,a..b,numrects);
PARAMETERS:
expr - an algebraic expression in one variable
x - the name of the variable in expr
a,b - limits of integration for the independent variable
numrects - the number of rectangles which must be a positive
integer or in some cases may be a variable.
f - a function of one variable
RELATED COMMANDS: Rsum, Msum
(return)
FUNCTION: Riemann
- estimates a definite integral using a Riemann sum
CALLING SEQUENCES:
Riemann(f,part,evalpts);
Riemann(expr,varname=part,evalpts);
PARAMETERS:
f - a function of one variable
part - list of points (in order) forming partition of [a,b]
evalpts - list of points (in order) at which f is to be evaluated
expr - an expression of one variable
varname - the name of the variable in expr
(return)
FUNCTION: Trap
- estimates a definite integral by the trapezoidal rule
CALLING SEQUENCES:
Trap(expr,x=a..b,numrects); or
Trap(f,a..b,numrects);
PARAMETERS:
expr - an algebraic expression in one variable
x - the name of the variable in expr
a,b - limits of integration for the independent variable
numrects - the number of trapezoids which must be a positive
integer or in some cases may be a variable.
f - a function of one variable
(return)
FUNCTION: Simp
- returns the approximation of a definite integral on [a,b] using Simpson's Rule
CALLING SEQUENCES:
Simp(expr,x=a..b,numbrparabolas); or
Simp(f,a..b,numbrparabolas);
PARAMETERS:
expr - an algebraic expression in one variable
x - the name of the variable in expr
a,b - limits of integration for the independent variable
numbrparabolas - the number of parabolas which must be a
positive integer or in some cases a variable
f - a function of one variable
(return)
FUNCTION: Inssum
- estimates a definite integral by using inscribed rectangles
CALLING SEQUENCES:
Inssum(expr,x=a..b,numrects); or
Inssum(f,a..b,numrects);
PARAMETERS:
expr - an algebraic expression in one variable
x - the name of the variable in expr
a,b - limits of integration for the independent variable
numrects - the number of rectangles which must be a positive integer
f - a function of one variable
RELATED COMMAND: Cirsum
(return)
FUNCTION: Randsum
- estimates a definite integral by using random points of uniform partition of [a,b]
CALLING SEQUENCES:
Randsum(expr,x=a..b,numrects); or
Randsum(f,a..b,numrects);
PARAMETERS:
expr - an algebraic expression in one variable
x - the name of the variable in expr
a,b - limits of integration for the independent variable
numrects - the number of rectangles which must be a positive integer
f - a function of one variable
(return)
FUNCTION: gLsum
- returns a graph showing the approximation of a definite integral using left endpoint
rectangles of a uniform partition of [a,b]
CALLING SEQUENCES:
gLsum(expr,x=a..b,numrects); or
gLsum(f,a..b,numrects);
PARAMETERS:
expr - an algebraic expression in one variable
x - the name of the variable in expr
a,b - limits of integration for the independent variable
numrects - the number of rectangles which must be a positive integer
f - a function of one variable
RELATED COMMANDS: gRsum, gMsum, gTrap, gSimp, gInssum, gCirsum, gRandsum
(return)
FUNCTION: gRiemann
- estimates a definite integral using a Riemann sum and displays the rectangles and the
function
CALLING SEQUENCES:
gRiemann(f,part,evalpts);
gRiemann(expr,varname=part,evalpts);
PARAMETERS:
f - a function or expression in one variable
part - list of points (in order) forming partition of [a,b]
evalpts - list of points (in order) at which f is to be evaluated
expr - an expression of one variable
varname - the name of the variable in expr
(return)
FUNCTION: gLsumanimate
CALLING SEQUENCES:
gLsumanimate(expr,x=a..b, k); or
gLsumanimate(f,a..b, k);
PARAMETERS:
expr - an algebraic expression in one variable
x - the name of the variable in expr
a,b - limits of integration for the independent variable
k is the number of slides. Slide i uses 2^(i-1) subdivisions.
f - a function of one variable
RELATED COMMANDS: gRsumanimate, gMsumanimate, gTrapanimate, gSimpanimate,
gRandsumanimate
(return)
FUNCTION: PlotBoxIterates
- produces a graph of y=x, y=g(x), and iterates of x=g(x)
CALLING SEQUENCE: PlotBoxIterates(expr,x=a,numits );
PARAMETERS:
expr - an expression in one variable
x - the name of the variable in expr
a - initial value of x in the iteration
numits - positive integer giving the desired number of iterations
SYNOPSIS:
A call to this procedure returns a graph of y=x, y=g(x), and iterates of x=g(x) where g(x)
is the expression given by the first parameter. Since the iterates are connected by line
segments, the graph helps one to see the convergence or divergence of the simple iteration
x=g(x).
(return)
FUNCTION: PlotIterates
- produces a graph of g(x) from the iteration x=g(x) versus the iteration number
CALLING SEQUENCE: PlotIterates(expr,x=a,numits );
PARAMETERS:
expr - an expression in one variable
x - the name of the variable in expr
a - initial value of x in the iteration
numits - positive integer giving the desired number of iterations
SYNOPSIS:
A call to this procedure returns a graph of g(x) from the iteration x=g(x) versus the
iteration number. Here g(x) is the expression given by the first parameter. The procedure
uses plot with style set to points.
(return)
FUNCTION: newtonraphson
- generates an animation showing the Newton-Raphson iterative method
CALLING SEQUENCE:
newtonraphson(expr,x=a,k); or
newtonraphson(expr,x=a);
PARAMETERS:
expr - an expression in one variable
x - the name of the variable in expr
a - starting value for the iteration
k - number of iterations (frames)
If k is not provided, the routine produces 5 slides by default.
(return)
FUNCTION: bestfit
- returns expression using least squares approx.
CALLING SEQUENCE: bestfit(varlist, eqtn, ListOfdatalists);
PARAMETERS:
varlist - list of variables such as [x,y]
eqtn - the desired equation such as y=m*x+b or y=a*x^2+b*x+c
ListOfdatalists - list of data lists for each variable such as [xdata,ydata] where xdata
is list of x values and ydata is list of corresponding y values
(return)
FUNCTION: regplot2d
- returns a graph of the given data points and the best fitting curve
CALLING SEQUENCE: regplot2d(ListOfdatalists,expr);
PARAMETERS:
ListOfdatalists - list of two data lists such as [xdata,ydata] where xdata is list of x
values and ydata is list of corresponding y values
expr - the expression in x to be graphed along with the data points (usually you use the
result of bestfit)
(return)
FUNCTION: tayloranimate
- returns an animation featuring taylor approximations to an expression
CALLING SEQUENCES:
tayloranimate(expr, x=a, x=c..d, degree); or
tayloranimate(expr, x=a, c..d, degree);
PARAMETERS:
expr - an expression in one variable
x - the name of the variable in expr
a - the value about which the taylor series is expanded
c - the left end point of the desired domain
d - the right end point of the desired domain.
degree - the degree of the last taylor polynomial to be used
(return)
Note that many of these commands are included with the program, MenuMaple, which works in conjunction with Maple V for Windows.
Send your questions or comments to Daniel F. Symancyk at dfsymancyk@aacc.edu