Complex analysis prerequisites

manpreet Best Answer 2 years ago

I really wanna learn complex analysis but I don't know where to start.

Basically I can do olympiad problems, but I don't know calculus that well, so I would appreciate it if someone can post a list of topics (preferably in chronological der">order, if that makes sense) for me to learn before I am absolutely 100% d">ready to start learning the complex analysis, which I've d">read about and think is A-M-A-Z-I-N-G.

Thx for your time everyone! :D

manpreet 2 years ago

• Sequences and series of numbers and of vectors
• Derivative in one variable
• Integration in one variable
• Integration with parameters (i.e. of the form f(x)=∫Dϕ(x,t)dtf(x)=∫Dϕ(x,t)dt)
• Sequences and series of functions
• Uniform vs. pointwise convergence
• Derivative in several variables
• Line integrals
• Topology of metric spaces

I'm told that the Stewart text is good for learning calculus for the first time.

If you're looking for a challenge, Buck's Advanced Calculus is rigorous. He even introduces complex variables at the end.

If you want a fun introduction without too much rigor, there are some popular books on complex variables, such as An Imaginary Tale: The Story of −1−−−√−1.