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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);

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
- 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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