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# A first course in complex analysis with applications by Dennis G. Zill and Patrick Shanahan Pdf

Here we are providing A first course in complex analysis with applications by Dennis G. Zill and Patrick Shanahan Pdf Free Download. This Book was published by Johns and Bartlett Publishers. This book is useful for Electrical and Electronic Engineering Students. The author Dennis G. Zill and Patrick Shanahan Clearly explained about A first course in complex analysis with applications Pdf Book by using simple language. This book will also useful to most of the students who are preparing for Competitive Exams.

## About A first course in complex analysis with applications by Dennis G. Zill and Patrick Shanahan Pdf

We have purposely limited the number of chapters in this text to seven. This was done for two “reasons”: to provide an appropriate quantity of material so that most of it can reasonably be covered in a one-term course, and at the same time to keep the cost of the text within reason. Here is a brief description of the topics covered in the seven chapters.

### Contents of the Book

Chapter 1: The complex number system and the complex plane are examined in detail.
Chapter 2: Functions of a complex variable, limits, continuity, and mappings are introduced.
Chapter 3: The all-important concepts of the derivative of a complex function and analyticity of a function are presented.
Chapter 4: The trigonometric, exponential, hyperbolic, and logarithmic functions are covered. The subtle notions of multiple-valued functions and branches are also discussed.
Chapter 5: The chapter begins with a review of real integrals (including line integrals). The definitions of real line integrals are used to motivate the definition of the complex integral. The famous Cauchy Goursat theorem and the Cauchy integral formulas are introduced in this chapter. Although we use Green’s theorem to prove Cauchy’s theorem, a sketch of the proof of Goursat’s version of this same theorem is given in an appendix.
Chapter 6: This chapter introduces the concepts of complex sequences and infinite series. The focus of the chapter is on Laurent series, residues, and the residue theorem. Evaluation of complex as well as real integrals, summation of infinite series, and calculation of inverse Laplace and inverse Fourier transforms are some of the applications of residue theory that are covered.
Chapter 7: Complex mappings that are con formal are defined and used to solve certain problems involving Laplace’s partial differential equation. 