8 years, 46 days

## MaplePrimes Activity

### These are replies submitted by janhardo

While ago is also deleted the answering of my post

Isn't one of the moderators the culprit here , who removes post just like that?

## To get idea how to doing a proof by indu...

To get idea how to doing a proof by induction

Its here solved with Mathematica

In this case its a sum ,so you need a another solutionstrategy

## I don't see my thread here anymore ?...

I don't see my thread here anymore ?

What is happened?

Is it removed or something malfunctioning on the website ?

## @janhardo The presentation of this ...

The presentation of this format of a complex function, here in this example is not accepted by the procedure :

What is representation of f(z)  = with variable z ?

## @acer ThanksI wrote:  I must d...

Thanks

I wrote:  I must differentiate z = e^i.phi   in order to get the differential dz

In normal math format i was thinking for the expression here above notated
Indeed it must be  z(phi) = exp(i.phi) for maple and the procedure can differentiate this rightside of the equation!

dz= z(phi)'. d(phi)     (dz is differential of z )

## @janhardo The complex function must...

The complex function must be "analytic" in order to possible differentiate it
note: i must look at information for complex functions classes who are proven analytic

 >

 > restart;

3.2  The Cauchy-Riemann Equations

content

 a complex analytical function

## @acer Thanks"I really hope tha...

Thanks

"I really hope that you understand that it is impossible for anyone to create a procedure that will produce your as-yet-unstated, desired form of output for all future examples which are not yet known. That is not a Maple thing; it is a logical consequence."

That would be Maplemagical , but i don't believe in fairy tales ( although some people say: it was a fairy tale what they have experienced)

## @acer Thanks You are right ,gu...

@acer
Thanks

You are right ,guessing a intended scope is not workable.

Instead of working all this out in Maple, i show you a  link
Nieuwe pagina 1 (hhofstede.nl) ( in Dutch)
You do see a circle and left of it some math written and above the intergral is written  z= e^i .phi  so,  dz= i.e^i.phi
dz is differential (already  calculated here) and in general  dy = f '(x) . dx

I must differentiate z = e^i.phi   in order to get the differential dz
Can the "differentiate procedure" handle complex differentiating maybe?

Hopefully its clear now i hope, or not and do you want it worked out in Maple the problem description ?

## @janhardo Don't know how the pr...

Don't know how the procedure is behaving for complex differentiating ?

Example : would calculate a differential  for  z= e^i. phi   => dz=  ...d(elta)phi

## @acer  Thanks That is a powerful ...

Thanks

That is a powerful procedure that differentiates all kinds of functions !
For intergration, such a procedure would also be useful and call the indefinite integral: the primitive ( F(x) ).
The suppression of notation is useful for memorizing certain differentiation rules.

combine(diff(eq, x), power) seems to be also useful for differentation ( what is the advantage here ?)

## @acer ThanksGoal was to derive the ...

Thanks

Goal was to derive the powerrule in  textbook form and its easy to type in that form in Maple

 > restart;
 > interface(typesetting=extended):
 > Typesetting:-Settings(typesetprime=true): #Typesetting:-Settings(prime=s):
 > Typesetting:-Settings(typesetprime=true);
 (1)
 > f(s)^n=-((1/2)*I)*factorial(n)*(int(f(z)*(z-s)^(-1-n), z))/Pi;
 (2)

My first goal was to find a general expression for a derivative of a function ( real or complex).

I have succeeded with a intergral formula from Cauchy

Now for a function  of type

 > restart;
 >
 > y(x)=x^n;
 (3)
 > map(diff,%,x);# the power rule
 (4)
 >

In math textbook form it is  for (2) for manual calculating to memorize.
=============================================================

That was my goal: the power rule finding , but it can be typed in as a textbook form

=============================================================

 >

I have now done two examples of functions to find a general expression for the derivative.
To do this in Maple differs for both functions and it is impossible for me to have a general approach to do this in Maple for all kinds of functions.

Coincidentally, I see this here , but can't recognise here the power rule from a  textbook

 > diff(f(x)^n,x);# the power rule , compared with (3) ?
 (5)
 >

The product rule : (f.g)' =f 'g +g'f  (memorize)

 > h(x)=f(x)*g(x);
 (6)
 > map(diff,%,x);
 (7)
 > restart;
 >
 (8)
 >
 (9)
 >

## @acer ThanksI needed the other way ...

Thanks

I needed the other way around as teached in math books for differentiating

in textbook form it is

Its impossible to get a general approach to learn for me to get  a general formula for differentiating a (complex) functions

That was the start for this thread, a intergral formula from Caughy in Complex analysis

## @acer ThanksIt's amazing how yo...

Thanks
It's amazing how you can bend Maple to your will
This is about getting a particular expression into a desired form but is not really important for the math I am trying to do with Maple, as it is easy to get it into the right form by hand as well
Probably some advanced users needed this typesetting conversion.

## @janhardo Ok, i made a mistake by p...

Ok, i made a mistake by posting a separate question again , about the topic here: a general derative formula and could do it in this thread.

The post is removed and why is it not placed hereunder ( if possible ) ?

Note: i don't care anymore about the answer Maple produces if it is not a textbook form, because some manual elementair math can be performed to get the wanted notebook form.

-------------------------------------------

The additional question was : the general derative for y= x^n   =>  y'= n. x^n-1

How to get this general formula ?

## @acer Thanks for the effortSome man...

Thanks for the effort

Some manual math...gives the desired formula form!

 > restart;
 > -((1/2)*I)*factorial(n)*(int(f(z)*(z-s)^(-1-n), z))/Pi;
 (1)

manual

 >
 >

first thinking on a mistake made maybe by the author of source of the integral ?, but  the number i is a special number to handle in complex numbers

There is a :  in the formula derived by Maple  it has different forms

This  formula by Maple derived can be written as

=

So maple gives not always the textbook answer , but doing manual further you get the wanted answer