Complex Analysis material question

[jimmypoopins]

I'm an undergraduate studying mathematics. I did really well in differential equations and abstract algebra, but struggled with our course "Analysis I."

I'm taking complex analysis next spring (here's a description of the course, but I'm sure it's not much different than any other complex analysis course http://www.reg.msu.edu/Courses/Request.asp?SubjectCode=MTH&CourseNumber=425&Source=SB&Term=1086").

I want to get a head start on the material so that i don't struggle with it as badly as i did with my first analysis course. I'm absolutely fascinated by complex numbers so hopefully this run will be better.

Can anyone suggest a text for me to pick up so that i can get a good head start? Thanks

 

[dx]

Try Tristan Needham's "Visual Complex Analysis".

 

[BryanP]

Try Tristan Needham's "Visual Complex Analysis".

Agreed.

I own this book and it's a very "involved" way of learning stuff in Complex Analysis.

The way it is presented as well as the diagrams give the reader a much better understanding of what's being talked about.

I also recommend picking this book up.

 

[jimmypoopins]

thanks i'll check it out :)

 

[ehrenfest]

Try "Basic Complex Analysis" by Marsden and Hoffman. Their exposition is exceptionally clear and suitable for someone in self-study since they make extra effort to write out all the steps in their proofs so you don't have to do much "filling in the blanks" like you do in Rudin for example.

 

[Pseudo Statistic]

A nice concise book is Introduction to Advanced Complex Calculus by Kenneth S. Miller (though I'm not sure how much of "harmonic functions" would be covered in this book).

 

[malawi_glenn]

We used Complex analysis by Saff & Snider, very good.

 

[ehrenfest]

Wow, it seems like everyone is suggested a different "good" Complex Analysis book. I had no idea there were so many. How is the OP going to decide? Does anyone know of a complex analysis book that they don't like?

 

[SCV]

Wow, it seems like everyone is suggested a different "good" Complex Analysis book. I had no idea there were so many. How is the OP going to decide? Does anyone know of a complex analysis book that they don't like?

Complex Analysis is one of the most developed areas of mathematics. It is also one of the ones with the most applications to other areas. There a lots and lots of books. I myself have used at least 25 different complex analysis books (my research area is complex analysis in several variables otherwise known as "Several Complex Variables"). Because many different groups within mathematics and outside of mathematics need to learn complex analysis pickup up just any complex analysis book might not be the best option. Also books vary in the amount of knowledge they assume and who the audience is.

I have seen some books that I myself don't like (Saff & Snider is one), even some of the most widely recommended books I don't like and its not the authors fault. For example, I did not like Ahlfors' treatment because there was certain knowledge that he did not assume and I already had. I'm sure those chapter were useful for some people, but not for me, and I could just find another book that was apropriatie (which is the good thing of there being lots of books on complex analysis.

At my school many people don;t like the book used for undergrad compelx analysis (one by Ted Gamelin), the problem with that class and book combination is that the class is called "Complex Analysis for Applications" and the book has essentially nothing about the (non-math) applications in it. Also although the book is theoretical it is not the most complete (you have to fill in many steps). I for one loved this book but like I said I know many other people don't.

What I suggest, if it is possible, is to go to the section of your math (or science) where the complex analysis books are and check out a lot of them. You never know what book you might find that you like but no one ever talks about or recommends. This is also, in my opinion, the best way to pick a book when there are so many to choose from.

Edit: Let me add that Needham's book is pretty good for getting intuition but you would need to supplement it with a book that focuses on theory.

 

[Howers]

Try Tristan Needham's "Visual Complex Analysis".

I second that, good book for a preview of complex analysis. Another good one is Fisher's Complex Variables.

 

[kts123]

I was recommended the "Fundamentals of Complex Analysis: With applications to engineering and science (third edition)" by E.B. Saff / A.D. Snider. It has plenty of exercises, many of which lead you -- the reader -- to make conclusions for yourself. I'm very pleased with my purchase, though to be honest it's the only book I own on the subject, so I can't really be a good judge.

 

[jimmypoopins]

Wow, it seems like everyone is suggested a different "good" Complex Analysis book. I had no idea there were so many. How is the OP going to decide? Does anyone know of a complex analysis book that they don't like?

my main intention after reading a few replies was to buy "Visual Complex Analysis" because it was recommend by three people.. unfortunately it seems to be roughly $50ish no matter where i search so it'll take a week or so until i can afford it.

thanks for the replies. hopefully this'll help :)

 

[vijigeeths]

can anyone of you explain how to post a new quesion to the forum.i am new to this.

 

[ehrenfest]

Go to the subforum that best describes your question (you can find the list at https://www.physicsforums.com/) and click on the "New Topic" button near the upper left corner of the screen.

 

[vijigeeths]

pardon me..i couldn't find out the option "new topic".