are there books/sources for some types of classifications of functions/sequences or functional sequences?

[ahmet]

Dear maths lovers

I need sources that classify functions/sequences or functional sequences (in broad view (wide count of examples)) ,such as;

*** convergent functions / sequences

*** divergent functions / sequences 

*** differentiable functions (>1 variables)

*** differentiable functions (>2 variables)

*** regular continous functions

*** continuous functions

*** integrable functions

*** lipschitz criterion satisfied functions

*** cantor theorem satisfied functions

*** regular convergence (functional sequences)

(note: thesis and/or books are preferred ,because the soruce(s) I look for should provide broad view)

Thanks in advance

 

 

 

Edited August 7, 2020 by ahmet
additional information

[ahmet]

that examplify with broad view of:

** simple functions (exponential, trygonometric, hyperbolic, logaritmic, inversed trygonometric and hyperbolic)

** riemann surfaces

**  differentiable functions

** Laurent series (all types)

**C-R equations

** conform transformations 

 

Note: preferred language is English but  (if it is not againts the rules of this website) sources in russian ,arabic and turkish and are also welcome.

(theoretical explanations such as lemmas,theorems,corollaries are not needed (should not be emphasized or concentrated on.))

 

Thanks

 

 

 

 

Edited August 7, 2020 by ahmet
explanation of the information given in the parahthesis

[studiot]

Not sure what you are trying to achieve here, seems like a very tall order to me.

Have you looked in standard texts such as Titchmarsh "theory of functions" or Knopp "Infinite series and Sequences"  ?

Edited August 7, 2020 by studiot

[studiot]

Again not sure what you seek here.

The best book I know for understanding is Ahlfors "Complex  Analysis"

A wide ranging use of complex analysis is Churchill's "Complex Variables and Applications"

Also lots of detailed worked examples in Alan Jeffrey's "Complex Analysis and Applications"

[Strange]

!

Moderator Note

Similar threads merged.

I would recommend a library or bookshop (online or physical)

 

[ahmet]

17 hours ago, studiot said:

Not sure what you are trying to achieve here, seems like a very tall order to me.

Have you looked in standard texts such as Titchmarsh "theory of functions" or Knopp "Infinite series and Sequences"  ?

 

16 hours ago, studiot said:

Again not sure what you seek here.

The best book I know for understanding is Ahlfors "Complex  Analysis"

A wide ranging use of complex analysis is Churchill's "Complex Variables and Applications"

Also lots of detailed worked examples in Alan Jeffrey's "Complex Analysis and Applications"

thank you very much for your suggestions. I do not deal with theoretical explanations anymore or they are not so much important to me.

generally books in mathematics are following these scheme:

theorem 

proof

lemma 

proof

corollary

but here examples are very important to me. I try to analyze them. mmm, some samples of books would be very good if those books include graphs of such functions. (e.g. a differentiable function f(x,y)= x.y , this is just one example for differentiable function 

or [math] g(x,y)=\frac {e^{x^2-y^2}}{1+sin^4(x^2+3xy+y^2)} [/math] is continuous at everywhere. but I need many many examples. Graphs would be very nice (if exists))

16 hours ago, Strange said:

!

Moderator Note

Similar threads merged.

I would recommend a library or bookshop (online or physical)

 

sorry for the occasion if I am doing a mistake but I just thought that complex analysis and basic analysis would be very different branches of maths.

(normally these examples (if we divide into two categories) will never appear in same book or any else literature imo. )

but you might be right because the expression of wishes seem similar. 

   

Edited August 8, 2020 by ahmet
scripting latex

[studiot]

4 hours ago, ahmet said:

but here examples are very important to me. I try to analyze them. mmm, some samples of books would be very good if those books include graphs of such functions. (e.g. a differentiable function f(x,y)= x.y , this is just one example for differentiable function 

or g(x,y)=ex2−y21+sin4(x2+3xy+y2) is continuous at everywhere. but I need many many examples. Graphs would be very nice (if exists))

You can often get examples from google by selecting the  'images tab for example

Fourier series

https://www.google.co.uk/search?q=Fourier+series&source=lnms&tbm=isch&sa=X&ved=2ahUKEwjQ-IDVo4zrAhVWiFwKHSePAjIQ_AUoAnoECBIQBA&biw=1366&bih=646

 

This should keep you busy.

Edited August 8, 2020 by studiot

[ahmet]

15 hours ago, studiot said:

You can often get examples from google by selecting the  'images tab for example

Fourier series

https://www.google.co.uk/search?q=Fourier+series&source=lnms&tbm=isch&sa=X&ved=2ahUKEwjQ-IDVo4zrAhVWiFwKHSePAjIQ_AUoAnoECBIQBA&biw=1366&bih=646

 

This should keep you busy.

thnak you for suggestion,I had better read the books you provided here and similar books. Because I hope I shall see the proofs of claims (e.g. if this is regular continuous then ...(it will show me)) 

Edited August 9, 2020 by ahmet