Maple 18 Training for Educators and Researchers

To learn about our newest release, Maple 2015, visit: http://www.maplesoft.com/products/map...

This webinar offers educators a quick and easy way to learn some of the fundamental concepts of Maple. Learn a few simple techniques that will allow you to use Clickable Math™ features to compose, visualize, and solve a wide variety of mathematical problems without commands. This webinar will also provide an introduction to some of the technical documentation features in Maple, including the use of interactive components such as buttons and sliders.

We'll also explore some of the new features in our latest release, Maple 18, including new and improved authoring tools for creating interactive apps, new Clickable Math tools, and the extensive updates made to visualizations.

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Closed Caption:

hello everyone this is the maple
training for educators and researchers
webinar today I'm going to be walking
you through some of the fundamental
concepts of working with maple this is
gonna include things like working with
maple is clickable map interface to
visualize and solve mathematical
problems as well i'm going to show you
some of the tools the design for
education things like our students our
student packages and math apps which
were created to interactively explore
mathematical concepts i'm also going to
show you some examples of how you can
easily create your own interactive
demonstrations inside of maple so let's
begin by talking about maples interface
so as you can see here this is the main
maple interface and when we load maple
you'll see things like pallets over here
on the left and I'll use these pallets
quite a bit today and pallets include
things like expression pallets for
things like commonly use expressions and
terms from calculus as well we have a
common symbols palette palette for
loading data plots creating data plots
we have a matrix construction palette
and several more if you want to see all
the different palettes we can just right
click over here on the palate bar and we
can now browse through and add various
pallets myself I usually like to use the
second palette area so we should open
this up by in the right area the right
arrow here I usually like to use the
right a pallet doc to display
information so here I've moved over the
variables palette as well as the maple
cloud and moving pallets from one doctor
to another is a simple as just grabbing
one and dragging it over so I like
having these two over here because I
basically let me take stock and see
what's going on inside of maple session
so here I can be the variables palette
which will let me see any existing
variables in my session as well the
maple cloud which shows many examples
that have been submitted to the cloud
itself so here I can open up maps that
have been submitted by us here at maple
offshore by users all around the world
so for now I'm just gonna minimize the
stock using the down arrow here and
let's talk a little bit more about
maples toolbars so here on the top
you'll see maples main toolbar and the
toolbar feature is a quick help search
and this is very useful if you're
looking to explore any of the concepts
or any of the terms i'm going to be
using today so say we did a search here
for something like Archimedes i can now
pull up several key terms several terms
that are more pages to help pages that
we find we search for that term our
communities so here for example i can
pull up one of the new start pages or
maybe a help page for the g m3 is
Archimedean command here i can be the
calling sequence as well as copying it
directly from the pop-up I can also see
say the definition for Archimedes the
greek mathematician i can also at the
bottom here
view existing math app so here we have a
math lab for the Archimedes
approximation of pie and as well here we
have several maps taken from the Mobius
clouds so here we can see the similar
Archimedes approximation of my mouth as
well as a polar plot math up taken from
the cloud the second row here of
toolbars our context toolbars and here
we'll see toolbars that give specific
functionality when we're working within
say our texts or math modes so here we
can see we're just have a text prompt so
we're obviously in text mode so we can
apply formatting and so on but if we
press f5 on your keyboard we can switch
over to math mode which gives us
different options for math the same way
that we would have different options see
if we were no go over and use the
drawing or the plot or the animation
toolbars whenever we go over a relevant
floor animation within the maple session
but for now let's probably enough about
the maple interface lets talk instead
about performing some calculations
entering math and so on into maple and
we're going to do instead of just doing
these in line here i'm gonna open up a
new document because this is more than
likely what many users will see when I
first opened make for the first time so
as I mentioned before switching between
text and math is very simple
we can just press f5 on our keyboard so
if you want to do a combination of text
and that can do something like the
answer of press f5 7-2 and hit alt enter
on my keyboard and artists return that
value in the same line so usually maples
output is given on the next line so if i
do something like 3 squared minus 9 get
return it's given on that next line if
we hit alt enter instead he gives us the
result in the same line and this is
really handy for working in this hybrid
text and math mode where were using kind
of an introduction text and we want to
have some live math in the middle of a
sentence now this is the second example
here and the third of which i'm typing
right now they bring up important points
so here we can see that might have been
3 squared squared actually jumped up to
the superscript the same way that when
we typed in 3 / 7 plus four or five this
actually looks like an addition of two
fractions and this is what we like to
refer to as our natural math notation
that the math really looks like math it
doesn't we don't try to obscure behind a
lot of command or codes so say if we
have sine of a again this is just going
to look like math itself and this makes
it very easy for students to understand
what we're working with
so here i have just entered in sign i
just entered and pie for my first
argument i had escaped to put to perform
a command completion and now you can see
that I've just got signed pie which we
can quickly easily return a value for so
we talked a little bit more about enter
against more natural-looking math and
i'm going to show you a couple more
examples from the pallets so let's start
by building a quick example here so
build an example of a sum so grab this
from the expression palette and will do
from k i'm just going to press tab order
to move through this from k is equal to
0 to n minus one of each the power of K
hitting return return this on the next
line we can also do one from calculus so
here let's open up the calculus palette
and let's grab a partial derivative with
respect to X I'm going to use two
pallets of one's here so we'll grab
square root from here and type in x
squared minus y squared so again return
returns a result of next line or if we
wanted to we could press alt enter in
order to return that on the same line so
I'm sure you know a couple more examples
using this idea of clickable math and
able so see if i were to build an
integral and again I can do this from
the expression palette so i'll just grab
an integral here of x squared minus 1 DX
evaluate the results painting enter any
math to enter into maple get input or
output is clickable i can click on this
and apply operations using our context
menus so say if we had something like
this one third X cubed minus x
I right click on this i can now start to
apply operations i can say integrated
using context menu I can differentiate
it i can also quickly and easily just
generate a 2d blood using the context
menu so there's a two-deep lot of that
of that expression we can also use our
smart pop-ups which are extension of our
context menu system to solve problems
and to work through questions so say if
we were to ask a student to prove the
left hand side of this equation is in
fact equal to the right-hand side we can
give them this problem and ask them to
do this using the smart pop-ups and
maple and see if i was to just highlight
a sub expression hear this but the smart
pop-ups actually let us operate on
sub-expressions rather than just a whole
fully-formed expression so that this
would be ideal for stepping through a
problem of this sort so now i can save
grab sign of 3a and view the trig
identities and we'll move down and we'll
apply the angle reduction and identity
so here when we pause we can see any of
them
for of the names about any number of
these trig identities and just by
clicking we can apply them so here we
have now applied the ankle reduction
identity and of course it's showing us
the step-by-step breakdown as we're
walking through this problem let's do so
let's go all the way for this one let's
grab now sign of to a hover over this
apply a trig identity in this case we're
going to scroll down and we're going to
find the double angle identity
alright and now we're gonna start to use
technology called drag to solve so I'm
going to grab something like this minus
sign of a since we have a common sight
my sine of a over here just drag it over
when we do this we get a preview of what
this operation would look like and then
we can just apply that we can also grab
something like sign of a divide both
sides by sign of a just by dragging it
across the equal sign
now we can grab this whole right side
and will apply normal to this and now
we're getting very close obviously so i
move the four over now we've got coast
of a squared is equal to 1 minus sign of
a squared + 2 last step we will apply
the Pythagorean identity in order to
prove in fact the left-hand side is
equal to the right hand side so this is
a this is expected an example of this
this clickable math too smart pup
technology that really lets us step
through a problem from question to
answer as well keep all of the steps for
further use
so here we can actually see where we've
come from in this problem we can
actually get the full step-by-step
breakdown and beyond i screen and in in
our tools for education section which
i'll be talking about in just a few
minutes also mention a few other
technologies that we have built up for
this type of step-by-step breakdown of
problems but for now let me move over
and show you a couple of more examples
and let's talk some more about the
context menus so here I can enter in
something like a differential equation
got the differential equation i can
right click on this and we can solve
this differential equation using the
context menu so i'll go solve
differential equation for yfx
and there's our general solution there
let's do a couple more and this is
another example here of calculation of
an integral and in this example i'm also
going to make some assumptions on our
variables so here we're just assuming
the case between 0 and 1 when we get
this result it should return this to its
hopefully and a an elementary form of
possible couple other more examples here
so let's do some symbolic minimization
so minimize sine of X or minimize sine
of X between x is equal to 0 and 4 as
well looks let's do another one here so
another larger minimization and here is
the result of this minimize command and
of course if we wanted to we see this
this is the symbolic result if we wanted
to approximate this numerically we can
right-click choose approximate to say a
hundred digits and there's a result now
another handy command to know is the
value F command this lets us evaluate an
expression to a set number of digits so
here i can say use of LF to two hundred
digits of our expression or if we want
to see this even more digits let's take
this up to 2,000 so maybe we can really
take this as far as you'd like to take
it will you run a screen real estate
before maples going to run out of digits
to to show you let's show a couple more
examples using the context menu so here
we have 1x squared is equal to x and
solve this for X using the context menu
saw shoes solve solve for a variable X
there's a result will do one more using
the solve command itself so important it
an important note when we're using these
context menu operations is that these
contexts many operations often
correspond to an underlying maple
command in the maple programming
language so for this business for this
specific example we used the solve
command and here we can more explicitly
use the solve command to solve a an
expression with an inequality for the
variable X and there's a result
so i'll be showing more examples of the
context menu throughout this talk but
let's let's go on now and talk about
entering some matrices and work with
matrices in maple and for that i'm going
to open up our matrix palette so too for
these first example i'm just gonna build
you a four-by-four matrix you should
click Choose here and drag this out the
four-by-four and make an identity matrix
insert that all right let's make this a
little bigger so just increase this by
five by five and make a upper diagonal
matrix with one's on and directly above
the main diagonal we can insert this
matrix clicking the insert matrix button
and one last example we'll do a three
element column vector so here we'll have
three rows one column and let's fill
this with random values and we'll insert
that column vector and matrix palette is
a great tool if you're looking to build
some smaller matrices are some commonly
known matrices that like the identity
matrix and so on but another important
command to know is the matrix command so
the matrix command lets you very quickly
easily generate large matrices and it's
structured such as you just type in
matrix then the number of rows in the
number of columns you want to build so
here's our matrix and what maple does by
default it returns the matrix to you in
a summary format so anything over them
anything larger than a ten-by-ten matrix
is returned in this format because we
really just don't want to print all
those lines to the screen there are
interface options if you look under the
interface command for printing off more
lines this is the our table size option
but for referred for basically just just
in the interest of keeping this clear
and not printing out too many lines
anything over them anything greater than
a ten-by-ten matrix is automatically put
into a data summary format it's very
easy to of course explore that summary
format so we can just double click here
on the blue text her to browse all the
entries of this matrix for now this is
just filled with zeros because we didn't
give a third argument but if we were to
give us a third argument say one then
one is used as a generating function for
this matrix now we can browse through we
can see it
this is all just filled with one's
what's more interesting is say if we
were to use a maple command something
like Rand and give ran values random
values between 1 and 10 we can now use
this command as a generating function to
fill this large matrix with random
values and just to prove you to that
this is entirely random i can also
browse the image for this matrix here we
can now see that there's no period
there's no function we could easily
apply to this data this just looks like
static deflection we can also use the
metrics browser to export and therefore
click export we can automatically export
this to an XL xls file so if you were
using maple to do operations are large
matrix is a very quick and easy way for
you to then take that data for maple and
export it to an xls file for use in
Excel let's move on now and talk a
little bit more about visualization and
to begin with I'd shown you a couple
examples before of generating some plots
very quickly with the context menu but
let me show you a couple examples here
of generating a sequence of plots on the
same plot interface where my type in two
expressions so sine of x squared + sine
of x over 2 as we said before we can
quickly generate a 2d plug just by right
clicking on an expression choosing plots
and then to the plot now what we can
also do is we can add an existing
expression to an existing plot just by
grabbing it and dragging it down so here
if I have something like this expression
sine of x squared i can highlight this
drag this down and drop it right on top
of our plot in order to put that second
expression into that first plot that we
generated so again just I'll just click
on this delete it and do that one more
time so just select this drag it down
with your mouse and that way we have got
both plots are both curves on the same
plot of course if you wanted to change
properties you can also right-click on a
plot and then start to work with that
plot directly then context menu
operations on that plots here we can now
change the line style for the second
line to be a dotted line for example
and of course once we're happy with our
plot we can do things like export so if
we right-click on the plot we can now
choose to export it to a couple
different file formats directly so
similar to what we saw with the solve
command the underlying plot Derek
underlying command for the operations we
just do it for 2d plots is the plot
command itself and the plot command is
pretty straightforward
we want to generate a plot we can just
type in something like plot of X and it
will return a plot of X the line of y is
equal to x if we use the plot command we
can also get things like a sequence of
plots and when i get a sequence of plots
I have to enclose the sequence in a list
or put this into a list and here you can
see there's our square bracket notation
for a list so in this plot in this
example I'm going to show is a sequence
of this LJ curves over a range so x is
equal to 0 to 10 and lastly the last
option giving it is filled option and
what Phil does it fills the area between
the curve and the x-axis here we can see
your example of this is for mrs. LJ
curves here each one has been filled
alright so couple more examples let's
talk about three dimensions so i'll grab
some more maps from here just copy down
so something like sine of X plus coats
of white let's generate a quick 3d plot
of that we can right-click on the input
the same we could right-click on the
output quickly generate 3d plot of X&Y
and as a result by default we can scroll
around on a three plot we can also do
things like pan and pan around on the
plot using our plot toolbar up here so
here we can zoom in zoom out and pan
around a similar to 2d plots we can of
course also right click on this and
apply different different style set to
apply different coloring and so on
directly to the plot but more
importantly potentially we can also
export directly from the right-click
context menu and now you can see we have
a couple different file formats for 3d
files
we can export 243 plots the
corresponding command is called plot 3d
and he'll give you a couple quick
examples of some different coordinate
systems we can plot so here is just a
simple pretty plot of the height from
minus 5 25 of the court a cylindrical
coordinate system and as well here's
another fun one using a spherical
coordinate system and here specified the
style to wireframe just we can get a
little bit more of an understanding of
how this looks
and it produces some pretty fantastic
plots now another way to actually build
both block code as well as plots is by
using the interactive plot building
assistant to see if we've got an
expression something like x squared plus
x squared we can right click on this and
as we saw before we can quickly generate
a 3d plot using this plots menu but if
we go to the bottom put up plot builder
we can now step through and generate 3d
plots so here if we wanted to we can
change axis values for X&Y if we're
happy we can just plot this and have
this return a plot to us or we can also
go in and further customize it using
this plot builder looking going to go to
the options menu in order to do things
like add a title change the caption
change line Styles coordinate systems
color schemes and so on
before we return this plot we can of
course preview it and what happened we
can click plot here or if we want to we
can also use this plot builder in order
to build command code for us so let's
use the command button here at the
bottom and what this will return is the
actual command code for generating this
plot so that way if we go on in our
maple session here and we were to enter
this again we can reproduce the spot
over and over again and this is great if
you say looking to prototype say if i
want to go back now and I want to change
the X values from minus fifty 250 i can
now see the surface changes
this is an important consideration and
this is why the popular often gets used
for things like generating animations so
see if we have the same expression we
multiply this by a parameter terms of
sine of a so if we wanted to see how r
surface changes as we vary a parameter
we can do this using that slot building
a system so again we're plots flop
builder rather than choosing a plot
where choose an animation and with the
animation we can preview this and we can
play this back in order to see how the
surface changes for various values of a
if we're happy we can return plot in
order direction animation or we can do
some different options under our plot
type so if we wanted to return an
interactive animation with one parameter
or maybe an interactive plot with one
parameter we can do so using this menu
this is pretty exciting so see if we
wanted to have a an interactive Joe an
interactive demonstration created we can
choose interactive plot with one
parameter I choose 3d plot and had the
slidable parameter b four values of a
between 0 & 2 for 2 pi but let's not
likely this at ten for now let's return
that plot insert these rows and you can
see we've actually built an interactive
component let's very values of a and see
how this changes is the surface itself
I've got one more example for you when
we talk about animations and this is
going to use a couple of the commands
shown you so far but to use them in
slightly different ways so first we use
the matrix camp command in order to
generate a coordinate matrix this is
going to have coordinates in XY and set
the second command i'm going to use is
to make the plant 3d command just to
generate a plot of a sphere so this is
just a sphere of radius 1 now that the
special option i'm using here is called
viewpoint and what viewpoint lets me do
is it lets me specify a path to view
this 3d plot using so now if I've given
a plot of x y&z coordinates i can
basically give the illusion of
flying by or flying through a a
three-dimensional plot so here you can
see we're actually using the coordinates
we're starting at 600 600 600 more
slowly moving in until we land on that
surface at 111 so again these are two
very simple command just matrix and
flawed 3d but used together can generate
these really really neat animations and
examples so again similar to what we saw
with food for 2d and 3d plots if you
right-click on an animation you could of
course export that to a couple different
file formats and of all these the jet
file format here with would be the one
that will actually give you that
animation feel so the rest of these
would be just essentially a static image
but if you export it to a jiff file
you'll get an animated gif image that
would then be used easily within any
type of dynamic application or
presentation you might be generating so
before we leave visualization I wanted
to make one more mention and that's two
are plotting guide and english if you're
working in Maple you want to get to our
help system there's a couple of easy
ways to do that one is through the help
search like we saw before help search
box and otherwise just by typing in ?
than your keyword into a maple session
so now if i type in ? plotting guide
just bring me to the maple plotting
guide the plotting guide show is all the
different visualization types that we
have available to you inside of maple so
if you're interested in and say looking
at what we have available for explaining
mathematical concepts you could view you
can browse them plotting guide and find
this section here where we have
different visualization options for
doing things like plotting secant lines
are planning a Taylor approximation flow
lines and various other commands and
visualizations that have been built
through all of our different packages
and in particular there's a lot of
really excellent plots and realizations
and animations that have been created
within the student packages which i'll
be talking about in just a moment that
are featured prominently in this
planning guide so i highly recommend
going through having look through the
plotting guides again that's just a
search for plotting guide and you'll be
able to go in and search through all the
different visualizations that we have
been
LT in Maple let's move on now and talk
more about tools for education research
so given our kind of a foundation for
maple I've shown you a lot of our clip
of math options are showing you some of
our tools for visualization and working
with mathematical expressions and so on
but I want to focus in now on some of
our are features in Maple they are
really designed for yourself it as
educators and researchers and as well
for students for students to use maple
as an interactive environment to to
understand mathematical concepts to use
it for kind of learning tool and so on
so let's let's start by talking about
content design for students and within
maple we have several student packages
and the student packages were they were
written with the student in mind they're
written with a negative with the
educator in mind as well in kind of
hoping that we are going to give you a
solid basis of content that you can use
within any course say within Polly
precalculus calculus 1 multivariate or
vector calculus and linear algebra
numerical analysis it or statistics but
each one of these features a lot of
interactive tools these ones are real
interested students and open up for
example our students statistics package
and just show you one of the interactive
tools from that today so if we were to
load students 26 package first we just
do this by using the with command can
also do this by going up to the Tools
menu and loading the package directly
from the load package menu you can see
are all of our student packages will now
run the Explorer RV command and explore
rvs it stands for explore random
variable and we can use it to explore
properties of of statistical
distributions so say we wanted to
explore the properties of a normal
random variable with mean mu and
standard deviation Sigma we can give
that to explore be and now explorer
we'll ask us for parameter ranges from
you and Sigma so we can just fly from
zero to hundred safer are mean and from
125 will say for our standard deviation
we can now choose to explore
and explore will return a collection of
embedded components and just zoom out
here for a second
so now we can see is basically a
collection of interactive components we
can slide out values for R mean we can
see how this changes the statistical
properties obviously when we change the
value of the mean 21 we can now see that
the mean is 21
well you can also change things like our
standard deviation to see how that
effects things like our moment
generating function and as well the
proper low probability distribution
function and CDF of this specific
distribution more interesting perhaps is
also to be able to skip these two and
just view this symbolically so now we
can look at the symbolic meaning in the
mode as well the support various the
moment generating function as well the
bottom here we see the PDF and CDF
return to symbolically so this is just
one of these interactive tools that
students can use in order to to do
things like like browse random variable
distributions in order to look through
hypothesis test in order to step through
problems in multivariate calculus or
linear algebra so ones and and speaking
little bit more about this idea of being
able to step through a problem let me
show you some examples from the student
basics package so the student basic
package has a command called linear
solve steps what linear solve steps
lets us do is show a full step-by-step
breakdown for things like expanding and
simplifying of mathematical expressions
and includes things like simplifying
fractions expanding products and
polynomials solving linear equations and
more so we can see is our full
step-by-step step-by-step breakdown as
well as details on what was done during
each one of these steps so this one is
great for pre calculus but we've also
got some tools that are great for
students in calculus 1 or linear algebra
you'll find a lot of these are tools
tutors menu so also you couple of
examples today so let's go to calculus
single variable and this is certainly
one of the handiest ones will go to
differentiation methods and this
differentiation methods tutor
asks us for a function and then what we
can do is interactively step through
this derivative so let's get a hand just
to begin here so notice the
multiplication expression so this might
lead us to apply something like the
product rule so now we apply the product
rule we can see the result of that will
get a hint
what is the differentiation variable
let's say for instance that we just
don't know what the next step is we can
have maple just do that next step for us
by clicking next step
ok so now we apply the identity rule get
hint notice assign the expression
ok again if we're not sure which way to
go we can place next step and have the
sine rule applied now for happy we can
also just press all steps and this will
basically just returned a full
step-by-step derivation for us if we
click close here this will return this
to our maple session and we can see all
the steps along the way that were
applied for doing this derivative so we
have this for differentiation we also
have a tutor for integration methods
that's another really handy one that
certainly when i was a student I would
have loved to have had but let's let's
instead show
let's show another tutor let's show one
from linear algebra and was shown it's
really handy for checking your
arithmetic so we'll check the
gauss-jordan elimination tutor and here
you can enter a matrix and have maple
step through all the steps of rodeo Roy
reducing this matrix for us this is
great again if you want to have maple
check all the arithmetic for you you can
basically just use maple as this tool to
step through a problem and show you all
the different steps show you all the
numbers of the arithmetic just make sure
you're correct all along the way so we
have a lot of different to theirs is
over 50 different tutors for various
subjects we have several tutors for each
and every single student package that we
have included inside of maple and even a
couple more here we see there's even a
couple for a differential equations and
and complex variables and so on but this
so these are a couple of resources that
really are fantastic for students to get
a full understanding full step-by-step
breakdown of walking through problem
johnson and this is kind of talking
about this idea of using maple as as an
excellent training devices as a way to
learn more about mathematics but let's
turn the table of it let's talk now
instead about you as an instructor you
as a researcher using maple to create
this type of content to create some
interactive documentation that students
can interact with or your peers can
interact with so one of the ways we can
make this very easy for you inside of
maple is by using the Explorer command
the Explorer command makes it possible
to create an interactive application
with just a click your mouse so here say
we have a term we wanted to explore so
something like some over from x is equal
to one to n of X to the parameter case
we want to see how this varies as we
vary values for K so x squared X cubed
and so on so just right click on this
and choose to explore now this gives us
the Explorer pop-up and within the
Explorer pop-up we can choose to very
values for certain parameters in this
case we're going to look at the
parameter K so i'm going to skip and
just focus on values of K we're gonna
leave everything else the same for now
but also an example of it later on how
we can animate parameters as well so for
now I'm just going to explore insert the
rose now we can see were given a simple
interface just a slider that a student
can slide out in order to see how
different values of K changes the result
the resulting value for this some this
is this is really handy for math is also
even better for something like a a plot
where we can explore how plot changes
over two parameters so in this case
parameters a and B so again let's excuse
to right-click and explore this plot in
this case we're gonna explore for both
prem parameters a and B and I'm actually
to choose by default to animate be we
can choose to animate both we'd like to
but I think for now we're just going to
leave the choice to animate the
parameter for B and we can change any
default settings we'd like to as well
but for now I'm just going to press
explore
insert the rose and now let's play this
back so here we can playback how this
changes I'll just pause your first
second just to make an important note so
when we use these sliders we can
obviously see how this surface changes
over various values of a and B but if we
use an animation we can have maple do is
we have maple run a parameter sweep for
values of B all the while weekend
ourselves control values for a so this
is really handy if we basically kind of
want to have the program doing the work
for us of running to anime animation all
the while we want to see how valid
values of a influence the overall
feeling of where the the shape of this
of the surface we can do so
interactively using a combination of
these two sliders as might become even
more apparent this next example this
next example is going to use our new
escape time fractals package and we're
going to generate and animation of a
Mandelbrot fractal and we're going to do
so using to animation parameters one is
going to be the zoom and it was going to
be iteration limit so if you just play
this back we can just see how this
changes for values of a and the zoom at
the sighted at this exact same time but
if we turn off say a we can now view
this for various values of Ages by
ourselves dragging out the a slider so
this is a really easy way for you to
basically use maple to zoom in to take
care of that animation type feel for you
while you can change it yourself to view
how it is effective for specific
parameters so this is great if you're
kind of looking to do a multiple
parameter sweep at once you want to
actually have maple sweeping through
parameters such as a or b and have East
see how values of a are influenced by
the sweep of parameter B
alright i'll show you one more example
and this one is gonna be taken from
signal processing and not going to focus
too much on the example itself today but
i will talk about is what we can do with
explore so in this example we're talking
about signal processing so we're just
showing here this is a single plot of
some data and very simply over doing is
we're looking to clean up this signal
here so we see that there might be some
underlying trend here but we're not
really sure so what we want to do is we
want to apply some clams from signal
processing first we're just going to do
a frequency domain representation of
this data and view the power spectrum so
you can see the power spectrum you can
see within this power spectrum there's
two dominant frequency is here and here
as well as a lot of high-frequency he
could be noise or could just be a lot of
high frequency data what we can do is we
can now take a couple of commands from
signal processing something like an F IR
filter or generator and if I of filter
in order to go through and filter out
some of the noise from our data and when
we do so we can wrap this into a
procedure in Maple this is just a little
bit of elementary programming and maple
we can understand that procedure over to
explore in order to explore how if we
subtract certain frequencies from our
data how this impacts that filtered
signal and putting this into explore we
can now have this return his collection
of three plots as well as an interactive
slider when I slide this out i'm going
to see in the bottom plot here that high
frequencies are disappearing and
simultaneous heels will see that this
middle plot here is slowly getting
cleaned up any trend in the signal is
becoming more and more apparent as i
mentioned i'm not going to cover the
idea behind the signal processing app in
detail today but what I'm going to talk
about is is this idea of of of creating
these interactive demonstrations and
it's very very very simple using the
Explorer command to do so that all you
need to do is give it a plot given
mathematical expression even give it a
procedure or function call and we can
explore
for those procedures we can explore
these things over a parameter range and
it gives us this very in cheesy
interactive interface to do so and once
once you've created this interactive
interface it's really easy for somebody
else to come in and just interact with
it you know if you share this if you
share this maple content in some way
they can interact with the the idea
itself they don't have to worry about
going into learning code or anything
like that you can have your peers or
students just directly interact with an
interface that shows a concept and
that's basically the thinking that we've
put into building a lot of our math apps
and maple
so inside of maple we have overthrown
and 70 different math apps and this is
in a bunch of different subject areas
we've got math apps that cover things
like biochemistry as well as all the
naturals that physics and Natural
Sciences we've got math apps for finance
and statistics we've got maps for
calculus algebra and a couple other
subjects after that as well
here you can see is our math appt guide
and here we can browse through different
subject areas of math apps so for today
I'm going to show you a couple from from
calculus will say so look up the
calculus section and let's open up a
mission it can use the arrows here to
see this little bit larger
let's open up the surface of revolution
map formats are built in such a way that
we usually outline the main concept or
the main idea behind the map so the
reason essentially we're building it and
what we're trying to show with it then
we usually give a interactive section so
here are a couple of interactive
components that student can come in and
interact with in some way say here we
can draw a curve and then we can have
the math up to things like have revolved
that curve around an axis so here we're
evolving the curve around an axis and
we're showing that three-dimensional
plot so that's one example let's go back
and let's see some other examples
let's say open up this but approximate
volume of a sphere using cylinders mass
out here again very simple proof any
underlying math we want discusses is
outlined here the man concept section
and then we have an interactive section
where you can do things like drag the
slider rode hard to see how when we
increase the number of cylinders the
total volume of those cylinders will get
closer and closer to the volume of a
similar-sized sphere so we have a lot of
different maps as i mentioned this
around so many different maps available
within maple and it's certainly worth
exploring twenties maps to see if a
there's any content that can be used
within the classroom setting and or B
there's any content that can be done
used by yourself and expanded on in
order to create your own interactive
demonstrations before I talk more about
building your own interactive
demonstrations let me show you have more
tools we have available to you for
things like grading so I'm gonna start
by opening up the draw a line math app
and this is a really really simple math
that but it was built to to talk more
about some of our grading functionality
so within this math app we ask a student
to come in and simply click out two
points in order to graph the line of 2 X
1 is 5 so here I'm going to click out
two points what I know is correct one is
false
now click great now when we grade this
we're going to receive the correct line
shown here as well grade so in this case
we just received a great 0 that's the
way that the grating algorithm works in
this particular math that of course this
is completely customizable by you when
you're building your own math apps so
let's reset this again we'll try this
one more time will now use known values
grade this again and now our value is
one we got perfect score on this so
that's one example of a grayble math
have something we can grade student
interaction interactively we can also
use commands like the quiz command from
the grating package to generate
interactive demonstration so here I'm
gonna give you a couple very quick easy
examples so the quiz command structure
such as we give it a question and answer
questions start
so here we're going to ask a simple
question is 1 plus 1 equal to true
we're going to say true check the answer
we see this correct
so this here this is a collection of
components that you can use for an
interactive demonstration so if you just
copies over to move maple worksheet you
have a question you actually have an
interactive map that will do a couple
more here so here's a more procedural
question or an algorithmic question is a
number is chosen at random here a prime
so we can try another and this okay
seven prime will say false in this case
just for fun just to show this and back
checked as being incorrect
you can also change your answer back and
make this correct so these are these are
just these are fairly simple examples
but of course we built into more complex
examples that are then they can be
incorporated into say a maple ta
framework or or some type of other
interactive training framework
hi here's our last question so we're in
which of the following could be portion
of the plot of sine of X and this is a
multiple select questions this allows us
actually select multiple parts because
both of these are actually part of the
curve sign of any sign of X so now we
can select both choose check answer and
have that deemed correct so explore and
the the quiz command these great ideas
are these are always for you to use our
tools to it quickly easily create
interactive content in maple and what
all this is built upon is this idea of
working with interactive components and
I've opened up the component palette
here on the left side side of maple and
the component palette collects all of
the different interactive interfaces
that we have for you to use in order to
interact with maple worksheets directly
so for example in this example i can
drag the slider out in order to change
the amplitude of the line
so we can simply just drag this slider
here for amplitude and make this line
grow up and down and moreover we can
also do things like affect the phase
shift so here we can drag out this dial
in order to move this line back and
forth and we're moving this weekend of
course see the function the derivative
of the function and the plot changed all
at one time so this case is an
interactive way of exploring math
concepts and whoever is interacting with
this of course doesn't have to really
know how to code themselves they'd have
to know how to turn the style or
interact with it in some way and i'll
just show you a quick example of
generating one of these demonstrations
very quickly i'll just do one here of
say like the plot of X or X to a power
so let's go in here let's change some of
the attributes of this wheel here let's
just do X from one to five powers of X 1
X 2 power water next to the squared X
cubed and so on
alright and just grab the name of this
was this was plot three so we just need
to know that in order to know where to
send some data to so now let's do let's
do a lot 3 is equal to plot of x to the
power of this is dial one can see that
right up here so this is all we're doing
here is just telling plot three
we're just sending out some information
we're setting a plot of x to the power
of the dial value and now we simply drag
this out you can see x cubed x to the
4th X to the fifth and so on so this is
a very very simple and naive example but
of course this can be built out and
turned into much more complex examples
such as what we have for our map
collection and we even feature
functionality for doing things like
inserting a video into your maple
worksheet so using the video component
we can insert live streaming video into
maple and with this live video you can
use this playback to to start other
events instead of the maple session
using the action markers and so on so
it's another great way of having an
all-inclusive interactive training
environment built entirely within the
maple document mode so moving on let's
talk a little bit about the idea of
sharing this content so say you've gone
through you built a map and you know
want to share with your students so one
of the ways you can do that is through
the maple cloud so if i open up the
maple cloud over here i can now see
collection of content it
we've been uploading ourselves here at
math math work at maplesoft as well as
content that's been updated by users and
users all around the world so for
example i can open up this solo growth
math up just by double-clicking it from
the obvious cloud and now interact with
this map so here we have various styles
and gauges that we can interact with in
order to explore this map so this is
great if you've got a copy of maple but
see if you don't have a copy of maple if
one of your students doesn't have a copy
of maple and you do have some different
options for sharing this content with
him too so we put we've started this
project called The Mobius project here
maplesoft and with the Mobius project
you can share maple content live through
the maple cloud over our website at
mobius top microsoft.com sonia petrova
stomach dot-com i can now view all the
content from that mobius cloud Rider
shoulder inside of maple on the web so
say if i was to go here and we'll load
up one of the maps the monte carlo
approximation of time at that i'm going
to reload this very quickly
this opens up and it looks the exact
same way that it would if you opened up
inside of maple so here we have the
concept section as well we have a plot
an interactive dialogue down here so now
we can slide this out in order to view
this demonstration so this one is just
showing us that we can get a an
approximation of pie taking the ratio of
the number of dots inside this circle to
the number of
dots outside the circle and then just
multiplying this by four obviously this
gives us a description for pi over 4 we
want it forward by four to get a Monte
Carlo approximation of pie but there are
lots of different other maps that we've
now shared to this mobile movies project
so it and for you inside of maple it is
as simple as just going down and just
checking send document to cloud over
here on the Mobius cloud in order to
submit any Content that you'd like
now as well as an important
consideration for the maple cloud is the
fact that you can use the maple cloud to
store your own documents or to open up
your own classes so if you create your
own private groups will see these listed
here under the different section
headings what you can do is say create a
private group will call calc 101 or you
can end and enter in your own maple
documents you can assign homework you
can have the students interacting with
one another through that private cloud
so this is a great technology for you to
share that content now another way for
you to share your content directly with
students is using the maple player and
the maple player it's it's a free
download from our website you'll find it
on www.hsn.com and it's it's it's
basically a have a version of maple that
lets you open any maple content so this
maple worksheet that we hope when
working on today I can just open this up
if it has interactive sections if it has
dials or sliders I can interact with
those the same way I could have that
mobius cloud but i can't author so that
that's the one drawback of the maple
player but it's basically just there for
for you to share content for students to
use for interactive means so here I can
say again i can open up i'll show you
another example here the periodic table
of the elements taken from the Mobius
cloud so soon as you have any type of
interactive content you can just grab
this from the cloud you can also share
directly just by email he sent him a
maple worksheet and you can open this up
inside of the maple player in order to
interact with it so here for example
with the periodic table of the elements
math that we can do things like show
halogen or noble gas and it's love date
down here in our plot of all the
periodic table of the elements
so the movie player is is certainly a
great way to share your content with
anybody who doesn't have a couple of
copies of maple it installed but let's
talk a little bit more also about
options for exporting from maple so say
you're using the plaza as a technical
documentation environment and you wanted
to then share your ear your maple
worksheet with a publisher or something
like this we can use things like our
ebook publishing system so if we go up
here tools assistance a publisher in
order to generate an e-book so here we
can save maple worksheets our collection
of maple worksheets with a construction
a glossary a table of contents and
appendix and so on using this public
book publisher and publish this to epub
HTML PDF remember our maple MW file
formats we can also use the export as
minus funder file to export maple
worksheets directly to things like latex
HTML and PDF so here if I just click
export items you'll see HTML PDF latex
as well as several other proprietary
maple formats here too and into clothes
talking about some of the tools for for
educators and researchers I quickly want
to mention our code generation assistant
so this is lastly if you're using maple
as a prototyping environment and safe
using able to prototype some some code
and then take that coat and put it out
to a production environment you can use
our code generation facilities to take
maple code and translate that to things
like c c sharp fortran java matlab perl
python or even visual basic so here this
is basically just out of interface and
easy-to-use interface for cogeneration
but with something like the cogeneration
system makes it very quick and easy for
you to take maple code and to then
generate a target language versions of
your code they can use in your any type
of production level
so that you might be using someplace
else
so a couple more resources to mention
before we close this webinar first is
the help and menu in the help search box
so i mentioned this i'm going to use it
a couple times today but anytime you can
search inside of maple it's really
quickly and easily done just using the
search box up here on maples main
toolbar you can also use things like the
? keyword command so here I would just
happen ? plot in order to pull up the
plot help page from are able help system
also within our help menus you'll find
things like our user manual so if you
have manuals resources and more you'll
find our user manual and programming
guide both of which are excellent
resources for even the the the most
hardened maple user as well as beginning
maple users so the user manual is great
if you're just starting off if you want
to learn about using some of the so the
fundamentals of working with maple you
can progress on start using the advanced
programming guide to learn a little more
about the maple programming language
also within our within ourself help
system is the maple portal in particular
is the maple portal for educators
so here I've opened up a new worksheet
is called the maple portal here you can
see is is tutorial so if you're just
getting started with maple i would
recommend going through any one of these
then if you are coming in as a student
you can you can direct any one of your
students to go and look at the maple
portal for students as well if you have
students in engineering you can look at
the maple portal for engineers for
yourselves as math educators you may be
interested in seeing the math portal for
math educators which fit would build up
some of our content we've created for
using maple the classroom and as well
building on this point we have within
our website we have our teacher resource
center if you go to resources but you
teacher resource center you can view all
the different content we've been
building over the years for using maple
in a classroom
this includes things like our teaching
concepts with maple section we can view
short two to three minute videos on how
you can you can demonstrate mathematical
concepts using maple the classroom
environment so here for example be a
three-minute video on how you can show
or demonstrate riemann sums in a
classroom using maple so there's a lot
of videos here
calculus linear algebra differential
equations there's a lot of different
content and i would highly recommend
going through and looking through the
teaching concepts with maple section in
the website again that was featured on
our maple homepage under the resources
tab so there's a lot of other resources
I can definitely talk about today
including things like our application
center which has a white paper is math
apps full maple libraries and much more
but I think at this point that closes
off this this webinar for today and
thank you very much for joining us