>	# this is a comment line. if you read this, then you have successfully started your session, congratulations!!!

>	# I recommend you use ctrl-3 to adjust the font size. Better? yeah!

>

1+1;

>	# hey, we can compute 1+1, great.

>

%+1;

>	# the % stands for the latest result, so you don't have to type it again, that's nice

>

%+1;

>	# note that = is test for equality, not assignment

>

x = 3;

>	# the := is used to assign something to something # in this case, we assign the value 3 to x.

>

x := 3;

>	# now x has the value 3;

>

x;

>	# test for equality:

>

x = 3;

>	# how can we get rid of the assignment? # well we need to unassign it, here is how this is done:

>

x := 'x';

>

x;

>	# that's right, now x is a symbol without a value.

>

x := 4;

>	# there's another way to get rid of all assigned variables, # it is a complete memory clear:

>

restart;

>

x;

>	# OK, now everything is fresh again. # let's move on.

>	#guess what, we are going to do some fractions, yeah!

>

1/3;

>

0.333333;

>	# 1/3 and 0.333333 is not the same thing, so get used to it!

>	# however, if you want to treat 1/3 as floating point number, # you can give evalf on it.

>	evalf(1/3);

>	# you can have more digits if you like:

>	evalf(1/3,100);

>	# Maple treats mathematical quantities exact, i.e. the way mathematicians # would treat them. For applications, you may want to switch to # floating points. As we have seen, you can do that.

>	# another example is that of factorials. # n! (read n factorial) is defined as the product of all # numbers from 1 to n. For example 5! = 5 * 4 * 3 * 2 * 1 = 120:

>

5!;

>	# Let's do 6!= 6*5*4*3*2*1 = 6 * 5! = 6 * 120 = 720

>

6!;

>	# now let's do double factorials

>

6!!;

>

# wow, what was that? # That was 6!! = 720! = 720 * 719 * 718 * ... * 2 * 1, # which of course is a very large number. Notice that Maple gives you # the exact answer, even though you might not have expected such a large output. # This is typical for Maple. # Now if you like, you can turn that number into a floating point. # Here, the % notation comes in handy.

>

evalf(%);

>	# Let's give it a name using the assignment operator. # Notice that it is now already the next to last result, so we # use the double percent notation:

>	a := %%:  # no output this time

>

evalf(a);

>	evalf(a,100);

>	# this was a floating point number with 100 decimal digits precision.

>	# Do you know what Pi is?

>

Pi;

>	# hmmm, maybe you were expecting 3.14... # here we go:

>	evalf(Pi);

>	#want more digits? Here we go:

>	evalf(Pi,100);

>	# OK, I hope you see the difference between a symbolic system and a numeric system. # Maple is symbolic, Matlab is numeric, for example.

>	# let's move on.

>

>

>

>

>	#uhh adding fractions, let Maple do it:

>

1/3+1/5;

>	# that was correct! 1/3 + 1/5 = 5/15 + 3/15 = 8/15.

>

1/%;

>	# now we want powers, this is how we do it:

>

2^2;

>	#more powers:

>

2^3;

>

2^4;

>	# want more? why not have a little loop? guess what, Maple starts counting from 1 (I repeat: one)

>	for i to 10 do 2^i; end;

>	# you can do whatever you want inside the loop.

>	# lets say you want to compute 2^i - 1

>	for i to 10 do 2^i - 1; end;

>	# now we want to start the loop from i=2. # this is how we do it.

>	for i from 2 to 10 do 2^i; end;

>	# notice that the output starts with 2^2 = 4 rather that 2^1 = 2.

>	# I want a sequence. Notice the assign operator :=

>	seq1 := 1,2,3;

>	#another one:

>	seq2 := 4,5,6;

>	#let's concatenate the sequences:

>	seq3 := seq1,seq2;

>	#let's access elements of the sequence, for example the third:

>

seq3[3];

>	# uhh, don't access the zeroth element, this is Maple and not C, OK!?

>

seq3[0];

Error, invalid subscript selector

>	#let's make the sequence longer:

>	seq3 := seq3,7,8,9;

>	#how long is it?

>	length(seq3);

>	# well, that can't be right. In fact you must use nops and square brackets, don't ask why at this point

>	nops([seq3]);

>	# OK let's add more stuff:

>	seq3 := seq3,a,b,c;

>	nops([seq3]);

>	# you have noticed that we always have a semicolon at the end of a command.

>	# we can also have a colon. That would then suppress output, as follows:

>	seq3:=seq3,d,e,f:

>	# want to see seq3 ?, here you go:

>

seq3;

>	# lets make a sequence of the first few powers of 2:

>	S := seq( 2^i, i=1..10);

>	# we could also do it this way:

>	S := seq( 2^i, i={1,2,3,4,5,6,7,8,9,10});

>	# let's do something crazy

>	S := seq(i^2, i={x,y,z});

>	# these are just symbolic terms, we cannot do much with them now.

>	# notice that we have overwritten S each time

>	# in the last few examples. That is OK, as long as we don't need the old content any more.

>

%[2];

>	# BTW, that was the second element of S.

>	# now we want to have a set:

>	{1,2,3,4,5};

>	#let's give it a name:

>

S := %;

>	# another set:

>	T := {2,4,6,8};

>	#union, minus, intersect:

>	S union T;

>	S minus T;

>	S intersect T;

>	#is 2 a member of S?

>	member(2, S);

>	# OK, and at which position?

>	member(2, S, 'position');

>

position;

>	#OK, second position of S.

>

S[2];

>	for i to 10 do  2^i; end;

>

>

>	for i from 0 to 10 do  2^i; end;

>

>	for i from 0 to 10 do  printf("%d ", 2^i); end;

>

1 2 4 8 16 32 64 128 256 512 1024

>	A := Matrix(7,7);

>

A[1,1];

>

A[7,7];

>

A[8,8];

Error, Matrix index out of range

>	for i from 1 to 7 do  for j from 1 to 7 do    A[i,j] := 1/(i+j);  end; end;

>

A;

>

A[7,7];

>	# let's learn how to use lists!

>	# a list is just a sequence put into square brackets

>	L := [1,2,3,4,5];

>	# access goes from 1 to 5:

>

L[1];

>

L[2];

>

L[3];

>

L[4];

>

L[5];

>	# we can change an entry in the list using the assignment operator :=

>	L[1] := 2;

>

L;

>	# how can we append? # Our first guess is this

>	L := [L,6];

>	# hmm, that was't what we wanted.

>	# here is the solution. Let's first restore L:

>	L := [1,2,3,4,5];

>	# its a bit tricky, we need to get the contents # of the list first, and then add one more entry and # make it a list, such as

>	op(L); #the content of the list, as a sequence:

>	[op(L),6]; #now we add an element and make another list:

>	# we can have a loop create a list as long as we wish:

>	L := [];  # start with an empty list

>	for i from 1 to 10 do  L := [ op(L), i ]: end;

>	# uhh, what was that. # That was one line of output for each execution of the # loop body.

>	# Maybe that is too much output for you. # turning the ";" to a ":" after the end prohibits output:

>	L := []: for i from 1 to 10 do  L := [ op(L), i ]: end:

>

L;

>	# there is a quick way to generate repeated elements in lists # for example 0$10 would generate 10 entries 0

>	L := [3$7]; # seven 3's

>

>	HOMEWORK PROBLEMS:

>	# My big advice is that you open up a word file next to the # maple window and that you copy past stuff into a word document # once you are done with it. # Otherwise, you may loose data if the Maple session # happens to crash

>

# hw 1

>	the Fibonacci sequence  1, 1, 2, 3, 5, 8, 13, 21, ...  is defined as follows:  f[1] = 1, f[2] = 1, f[i] = f[i-2] + f[i-1] for i >= 3.  Create a list with the first 30 Fibonacci numbers.  Use a for loop to create the list.

>	# hw 2 # the Chebyshev Polynomial T[i] is defined as # T[0] = 1, T[1] = x and T[i] = 2*x*T[i-1] - T[i-2] for i >= 2 # create a list holding the first 10 Chebychev polynomials. # Attention, you cannot access the zero's element of lists, # hence you need to store T[i] in T[i+1].

>

# hw 3:

>	# Pascal's Triangle is the following array of numbers:

>	# 1 # 1  1 # 1  2  1 # 1  3  3  1 # 1  4  6  4  1 # 1  5 10 10  5  1 # 1  6 15 20 15  6  1 # etc.

>	# Figure out what is going on.

>	# After that, have a little Maple program

>	# compute Pascal's Triangle of 15 rows

>	# use a Matrix to store the numbers.

>	# The unused spots in the matrix shall be zero.

>

# Remark: to copy the matrix into a word document, # you may want to "right click" on the Maple matrix and # export it to a "Tab Delimited" file. # In word you go file .. insert... and insert that same file. # Notice: If you cannot find your file the reason might # be that Word is looking for "doc" files, # whereas your file is only a simple text file. # you may want to change the search option to "all files" # in word. You should then see your exported file. OK?

>

>

# hw 3

>	# Read Kraft's notes, Worksheet #1

>