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Current Summary of Contents of the Package math191 (for R4 and R5 under Windows)
(as of 3/31/99)

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 See example
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 See example
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 See example
PlotIterates	graphs x = g(x)	Yes See example
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
areaToLeftOf	find area to the left of a value for a normal distribution with specified mean and standard deviation
areaToRightOf	find area to the right of a value for a normal distribution with specified mean and standard deviation
basicstats	compute basic statistics for one or two lists of data	Yes See example
bestfit	find the equation of best fit	Yes
binomhistogram	create binomial histogram with option of superimposing a normal curve	Yes See example
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 See example
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 See example
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
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 See example
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 See example
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 See example
gTrapanimate	animation of trapezoidal rule	Yes
gareaBetween	areaBetween with a graph
gareaToLeftOf	areaToLeftOf with a graph
gareaToRightOf	areaToRightOf with a graph
gdiscreteLsum	discreteLsum with a graph	Yes See example
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 See example
gnPercentile	creates graph showing where the nth percentile is on a normal distribution
gpplot	produces a graph on graph paper	Yes See example
gseclines	produces an animation of secant lines at a point on a graph (approach from left, right, or both sides)	Yes See example
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)
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 See example
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 See example
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)	Yes
normalTable	creates standard normal z table
normaldist	normal distribution	Yes See example
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 See example
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
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 See example
seclines	get a table of equations of secant lines	Yes
showslopes	animation that displays rise and run
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
tayloranimate	animation of Taylor polynomials for a function
tdist	t distribution	Yes See example
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 See example
zoomepdeltplot	a zoomed epdeltplot
`&X`	allows infix notation for cross product	Yes
`&d`	allows infix notation for dot product	Yes

Note that several of these commands are demonstrated on the portion of this site devoted to MenuMaple 1.5. Click here if you want to see what you can do with MenuMaple.

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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);

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);

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);

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
- returns an animation of k slides showing the approximations of a definite integral using left endpoint rectangles

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)

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