I am a graduate student of Mathematics.I am planning to study complex analysis.I am a beginner,so I want a book to help me understand each idea.I have referred to J B Conway-Complex analysis book but it is not good for beginners like me.I am mainly interested in studying contour integration and Cauchy's theorem and analytic functions.Can somebody help me find a suitable book?
Complex Analysis text for beginners.
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Best Answer
Some properties of holomorphic functions comes the fact that the function has a derivative, like the Cauchy-Riemann equations. Other properties such the discreteness of roots or the maximum modulus principle, comes from the fact that the function is analytic. I think Serge Lang's Complex Analysis does a good job in splitting analyticity and holomorphism up and making sure we know what comes from what before telling us that all holomorphic functions are analytic. Tao's notes for 246A is also a very good place to start if you put in the time to solve all the exercises.