This is a pletely revised edition, with more thafifty pages of new material scattered throughout. Ikeeping with the conventional meaning of chapters and sections, I have reorgaruzed the book into twenty-nine sections isevechapters. The maiadditions are Sectio20 0the Lie derivative and interior multiplication, two intrinsic operations oa manifold too important to leave out, new criteria iSectio21 for the boundary orientation, and a new appendix oquaternions and the symplectic group. Apart from correcting errors and misprints, I have thought through every proof again, clarified many passages, and added new examples, exercises, hints, and solutions. Ithe process, every sectiohas beerewritten, sometimes quite drastically. The revisions are so extensive that it is not possible to enumerate them all here. Each chapter now es with aintroductory essay giving aoverview of what is to e. To provide a timeline for the development ofideas, I have indicated whenever possi- ble the historical origiof the conce

This book is intended as a textbook for a first course in the theory offunctions of one plex variable for students who are mathematicallymature enough to understand and execute arguments. The actual pre-requisites for reading this book are quite minimal; not much more than astiff course in basic calculus and a few facts about partial derivatives. Thetopics from advanced calculus that are used (e.g., Leibniz's rule for differ-entiating under the integral sign) are proved in detail.

This is a pletely revised edition, with more thafifty pages of new material scattered throughout. Ikeeping with the conventional meaning of chapters and sections, I have reorgaruzed the book into twenty-nine sections isevechapters. The maiadditions are Sectio20 0the Lie derivative and interior multiplication, two intrinsic operations oa manifold too important to leave out, new criteria iSectio21 for the boundary orientation, and a new appendix oquaternions and the symplectic group. Apart from correcting errors and misprints, I have thought through every proof again, clarified many passages, and added new examples, exercises, hints, and solutions. Ithe process, every sectiohas beerewritten, sometimes quite drastically. The revisions are so extensive that it is not possible to enumerate them all here. Each chapter now es with aintroductory essay giving aoverview of what is to e. To provide a timeline for the development ofideas, I have indicated whenever possi- ble the historical origiof the concepts, and hav

This book is intended as a textbook for a first course in the theory offunctions of one plex variable for students who are mathematicallymature enough to understand and execute arguments. The actual pre-requisites for reading this book are quite minimal; not much more than astiff course in basic calculus and a few facts about partial derivatives. Thetopics from advanced calculus that are used (e.g., Leibniz's rule for differ-entiating under the integral sign) are proved in detail.

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