@Carl Love 

Thanks

A clear example, but not al my questions are answered.

Another question came up : can i see in a procedure what are the return values? ( automatically)
The last statement in the procedure is the return value, so if there is plot return value, before the last  statement.
Then i must use then add a return statement after the plot statement in order to see the plot in the procedure i think.
 

@janhardo 

Also this in another procedure: the use of p, L ?

p,L:=approxL( f, a, b, N):
#
# Display function and "piecewsie approximation
# to function
#
  p;
  L;
 

@Carl Love 

Thanks

You can outcomment this and then the procedure get a error.

return A[1..n+1,..], P; in NewtM ac.mw has to do with of (R1,P1):=NewtonM(g,-1,1,1,100,1e-6):?

A is a matrix and P is plot , so this ( ?  ):=procedure ( )  ?  

@janhardo 

The use of return statement is not clear : when to use?

• return x0;  in exc set task 6 ac .mw 
• return A[1..n+1,..], P; in NewtM ac.mw

Use of (R1,P1):=NewtonM(g,-1,1,1,100,1e-6): in NewtM ac.mw 

R1; 

P1; 

Seems to split the output of the procedure? 

@mmcdara 

Thanks

This programming of NewtonsMethod is more complicated then programmed on the forum :
showstat(NewtonsMethod);

NewtonsMethod can be used for a idea how its as plot presented to users in the forum programmed version

@acer 

Thanks

That's really programming you did with NewM compared with the book
It shows exactly about the iterations and values and gives insight .

"You wrote "I am leaving most of the rest as it was, and not addressing the inefficiency of augmenting a set with each new plot, or cleaning up the role of A, and so on.

Well that's probably too complicated for me .

Why is there a print command used, while it always with display was? ( was in a earlier code example)

Note: this last NewM is different programmed then the book example   
And there is solve ! (tough)..i tried 3 x times and go then to fsolve

Context sensitive command for solve : selecting the function and Maple shows the solve ( this is possible in the interactive worksheet )..no solution

Ah ,yes of course fsolve ...via contextmenu possible sin(x) - x*cos(x) ?..no
A shortcoming ? 

@acer 

Thanks

Did some more with it

@acer 

Thanks

Looks great and you corrected a lot.
That's is the pittfall when i took over the static code for a procedure  : must analyze better it for the all involving variables.
 The search interval start with a initial value: xinit 

Following the book example for : NewtonM(x->x^2-1,0,2,2,100,1e-4); (parabola )

@Carl Love 

Thanks

Maplemint has not detected a variable T a function of x, T:= x->x-f(x)/D(f)(x):

Its corrected, and it was indeed Newton's iteration function as you mentioned.
It was defined at the top of the example worksheet and i did not a solid check for all local variables ( not aware )    

Now i can answer the questions

CDExercises
(1)  Figure 3.9 shows the convergence of Newton's method to a root  r of  the equation sin x - xcos x = 0. This was for
                          "x[0] = 5.5"

 and
                       "epsilon = 0.0001"

, and gives  r =
                         "4.503123428"

, approximately. Obtain a better approximation, as suggested in the book, by using
                           "epsilon"

 = .000001. and altering the above code appropriately. Compare your answer with the approximation to r that you get by using Maple's  fsolve command. How close to zero is  E =| f (r)|  for each of these values of r ?

(2) Alter the above code for Newton's method and use it to draw the picture shown in Figure 3.10 in the book.

The procedure is correct working

exc_set_3_task_6.mw

@Carl Love 

About the formula defintion for the chord section : 

 "The final result for the area must include arc-functions" 

For me it is not direct clear why is that arcsin appears in calculation : it is a angle in radians
If the final reslut has used earlier arcsin result , yes then it goes further in the calculation: make this sense ?  

@tomleslie 

Thanks

I will study examples of this in my worksheets tasks again and using help ( elementwise).
I reread post from you too ( its not possible to link this post here? : a handy feature of a forum)

Ah yes it can be linked of course https://www.mapleprimes.com/questions/229763-Righthand-And-Midpont-Rule-For-Riemann-Sums-#comment269722

Another useful comment about he likewise ~operator

@janhardo 

Some things are left:

- return display  : when using this ?

- role of [ ] in 2 examples ?

yv:=unapply( f, indets(f, 'name') [ ] )~(xv);   

plot
                            ( f,
                              indets(f, 'name') [ ] =a..b,
                              color=red
                            ),
- p,L:=approxL( f, a, b, N):    p, L  ?  

@tomleslie 

Looking again to the code.

I aspected that yv  -values of f  should be stored in a array, but that happened here.

yv:=unapply( f, indets(f, 'name')[])~(xv);

But there is not Array made for this at forehand , well perhaps it has to do with the  ~ (xv) operator
It depend then from what datacontainer type( source container)  is used by ~(xv) ?

In this case it was a Array ,but was it a list then you get probabably a target datacontainer  list?   

Its s strange symbol [ ], it can also used as a range ? [ ]= a..b

plot
                            ( f,
                              indets(f, 'name')[]=a..b,
                              color=red
                            );

Than there is also return display   why is this ?

The procedure is p, L: = approxL( f, a, b, N):  were stands p, L for ?

So i am unsure about the [ ] used to free a variable from a set  and used a range [ ]=a..b

And unsure about the ~ operator about source datatcontainer to target datacontainer

@tomleslie 
Thanks

Very helpful.

Seems that [ ] is used for {x} to get into x  for the right function definition
Its a good idea/approach  to strip elements of the commando and to see what it actually does with the outcome.  

 

@Carl Love 

This basic derivation for a chordal segment there is used arcsin why not  sin ? 
Makes it difference in a calculation.

Its is more userfriendler to use in calculation degrees , and the central angle is measured in degrees in the basic derivation.