Prof, related to what you spoke about in the beginning about R2 and complex plane and the difference in Calculus in R2 and complex plane reminds me of the time when I was having sleepless nights thinking about this issue. Then a friend who had taken complex analysis told me, that the difference is of Field Structure on R^2 that gives complex analysis as opposed to usual multivariable calculus where no field structure in imposed on R^2 .. It was a casual conversation which I can still never forget, the clarity and contentment was incredible ..
Very good discussion on the subtleties of complex analysis to kindle the mathematical flame. However I would add some humble suggestion on books that I found particular interesting: 1. Tristan Needham-Visual Complex Analysis-Oxford University Press, USA (1997) (simply amazing) 2. complex analysis with Mathematica - Willam T. Shaw (CUP) (fascinating visuals with applications to physics) 3. Elias Wegert (auth.)-Visual Complex Functions_ An Introduction with Phase Portraits-Birkhäuser Basel (2012) These are very pedagogical books.
@@rinkubharali4688 Some books that immediately come to my mind: 1. John H. Hubbard - Vector Calculus, Linear Algebra and Differential Forms_ A Unified Approach-Prentice Hall (1998) 2. Steven H. Weintraub - Differential Forms_ A Complement to Vector Calculus-Academic Press (1997) 3 Serge Lang - [Addison-Wesley series in mathematics] Calculus of Several Variables - AW 4. Advanced Calculus of Several Variables - C.H. Edwards - - Academic Press Inc Enjoy !! P.S. These are for analysis on R^n
Great channel! Let's not forget about the classic book on Complex Variables by Lars Alfors....and also Complex Variables with Applications by Churchill.
@@kamrupexpress Also I would highly recommend a Schaum's Outline on Complex Variables by Murray Spiegel. Great source of wonderful problems with solutions.
@@martinhawrylkiewicz2025 Fully agree I had used that to teach. I will find these books out from my collection and definitely make a program. Many thanks Martin.
Sir ,I ask some information about our college,sir i intrested engineering field but not allotted engineering branch,i allotted degree course in NIT Rourkela Life sciences integrated MSc (2021),(i intrested math subject)is there branch good or not and future scope these branch.sir now i don't intrest but can I get some other engineering college 2year direct admission.sir please reply me i wait for u reply.
@@kamrupexpress i m sorry to disturb you sir, But if there's time please tell me the way i should prepare for the exam And the books that are required? If you can take out some of your precious time!
Dear Sir, your recommendations on Differential Equations and some tips to learn it will be beneficial. Also, sir it's been a while since you spoke anything about "Life of an average mathematician."
@@kamrupexpress Dear sir, I'm not sure if you know about this book called "Vector Calculus, Linear Algebra, And Differential Forms A Unified Approach" by John Hamal Hubbard and Barbara Burke Hubbard, if in case you don't then I think you will absolutely love it. If in case you know about it can you review it since I'm considering to read it in near future.
@@kamrupexpress then sir I highly recommend that you have a look at it beacuse I'm sure that you will simply love it and please keep up the great work.
@@kamrupexpress For you, it is ok, but I am telling you that it is too low, even at max volume here, and I am using an apple monitor, which on other channels would be so loud that I would have to turn it down.
![FNAF vs TF2 - Episode 2 [SFM]](http://i.ytimg.com/vi/z5b3V2-VLb0/mqdefault.jpg)
I fully agree ... I own all five of the KNOPP books and have for decades. ... beautifully written and easy to understand!!
Prof, related to what you spoke about in the beginning about R2 and complex plane and the difference in Calculus in R2 and complex plane reminds me of the time when I was having sleepless nights thinking about this issue. Then a friend who had taken complex analysis told me, that the difference is of Field Structure on R^2 that gives complex analysis as opposed to usual multivariable calculus where no field structure in imposed on R^2 .. It was a casual conversation which I can still never forget, the clarity and contentment was incredible ..
I believe the key is complex multiplication. This is not inner product of vectors. Cross product needs three dimensions.
Very good discussion on the subtleties of complex analysis to kindle the mathematical flame. However I would add some humble suggestion on books that I found particular interesting:
1. Tristan Needham-Visual Complex Analysis-Oxford University Press, USA (1997) (simply amazing)
2. complex analysis with Mathematica - Willam T. Shaw (CUP) (fascinating visuals with applications to physics)
3. Elias Wegert (auth.)-Visual Complex Functions_ An Introduction with Phase Portraits-Birkhäuser Basel (2012)
These are very pedagogical books.
Thanks a lot. Tristan Needham is wonderful. I will make a review of it. The others I have not seen and thanks a ton I will look into them
@@kamrupexpress the first and the second books are actually praised by Sir Roger Penrose.
Dear Soumyadeep, can you recommend me some good books of *Real Analysis* & *Analysis in R^n* as you did for Complex Analysis.
@@rinkubharali4688 Some books that immediately come to my mind:
1. John H. Hubbard - Vector Calculus, Linear Algebra and Differential Forms_ A Unified Approach-Prentice Hall (1998)
2. Steven H. Weintraub - Differential Forms_ A Complement to Vector Calculus-Academic Press (1997)
3 Serge Lang - [Addison-Wesley series in mathematics] Calculus of Several Variables - AW
4. Advanced Calculus of Several Variables - C.H. Edwards - - Academic Press Inc
Enjoy !!
P.S. These are for analysis on R^n
Glad to see you back
We really appreciate that you take time out of your busy schedule to make amazing videos for us
Thanks a lot. You all keep me going.
I wish this channel gets to millions other subscribers. Thanks for spending your valuable time for enlightening mathematics lovers.
It's nice to see you again sirji. we're missing you and yours valueables thought sirji
Great channel! Let's not forget about the classic book on Complex Variables by Lars Alfors....and also Complex Variables with Applications by Churchill.
Sure I agree...may be I should review those books
@@kamrupexpress Also I would highly recommend a Schaum's Outline on Complex Variables by Murray Spiegel. Great source of wonderful problems with solutions.
@@martinhawrylkiewicz2025 Fully agree I had used that to teach. I will find these books out from my collection and definitely make a program. Many thanks Martin.
Sir with due respect, before Complex Analysis part-2, Please make a part-2 of Real Analysis.
Sure I will...
There are 2 other books by amol sasane.both are supposed to be good!
Sir, can we hope for videos on complex analysis?
Will try surely...
Thank you sir
Even i am back here after a lot of time
Do you have any thoughts on Complex Analysis by Stein and Shakarchi?
I will discuss this in the next video.
Love this one
That's why cosx can be equal to 2 when you put x = 2-√3 in Euler complex and domain of cos is not real number it is imaginary ♥️♥️
Sir ,I ask some information about our college,sir i intrested engineering field but not allotted engineering branch,i allotted degree course in NIT Rourkela Life sciences integrated MSc (2021),(i intrested math subject)is there branch good or not and future scope these branch.sir now i don't intrest but can I get some other engineering college 2year direct admission.sir please reply me i wait for u reply.
Sir, how many books do u read on an average in a year?
A do see a lot of books. You don't read mathbooks like a novel. We pick a book up when you need them.
Good day Sir , I m in class 12......should i try for prmo or rmo examination ?
Why not you definitely should
@@kamrupexpress i m sorry to disturb you sir,
But if there's time please tell me the way i should prepare for the exam
And the books that are required?
If you can take out some of your precious time!
@@aiseop31415 I will surely check
Sir what will the best book for fourier transform
I will look into it.
Dear Sir, your recommendations on Differential Equations and some tips to learn it will be beneficial.
Also, sir it's been a while since you spoke anything about "Life of an average mathematician."
Will do....
@@kamrupexpress Dear sir,
I'm not sure if you know about this book called "Vector Calculus, Linear Algebra, And Differential Forms A Unified Approach" by John Hamal Hubbard and Barbara Burke Hubbard, if in case you don't then I think you will absolutely love it. If in case you know about it can you review it since I'm considering to read it in near future.
@@saiprasadmohanty8339 Unfortunately I do not know about this book.
@@kamrupexpress then sir I highly recommend that you have a look at it beacuse I'm sure that you will simply love it and please keep up the great work.
I am at max volume and can't hear you clearly.
I checked on my mobile. It seems to be OK.
@@kamrupexpress For you, it is ok, but I am telling you that it is too low, even at max volume here, and I am using an apple monitor, which on other channels would be so loud that I would have to turn it down.
@@takforalt I will try to use an external Mike next time.
@@kamrupexpress much appreciated.