**AMS/MAA Textbooks**

Volume: 71;
2022;
433 pp;
Softcover

MSC: Primary 30;
Secondary 47

**Print ISBN: 978-1-4704-6565-0
Product Code: TEXT/71**

List Price: $85.00

AMS Member Price: $63.75

MAA Member Price: $63.75

**Electronic ISBN: 978-1-4704-6901-6
Product Code: TEXT/71.E**

List Price: $85.00

AMS Member Price: $63.75

MAA Member Price: $63.75

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#### Supplemental Materials

# The Calculus of Complex Functions

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*William Johnston*

MAA Press: An Imprint of the American Mathematical Society

The book introduces complex analysis as a
natural extension of the calculus of real-valued functions. The
mechanism for doing so is the extension theorem, which states
that any real analytic function extends to an analytic function
defined in a region of the complex plane. The connection to real
functions and calculus is then natural. The introduction to analytic
functions feels intuitive and their fundamental properties are covered
quickly. As a result, the book allows a surprisingly large coverage of
the classical analysis topics of analytic and meromorphic functions,
harmonic functions, contour integrals and series representations,
conformal maps, and the Dirichlet problem. It also introduces several
more advanced notions, including the Riemann hypothesis and operator
theory, in a manner accessible to undergraduates. The last chapter
describes bounded linear operators on Hilbert and Banach spaces,
including the spectral theory of compact operators, in a way that also
provides an excellent review of important topics in linear algebra and
provides a pathway to undergraduate research topics in analysis.

The book allows flexible use in a single semester, full-year, or
capstone course in complex analysis. Prerequisites can range from only
multivariate calculus to a transition course or to linear algebra or
real analysis. There are over one thousand exercises of a variety of
types and levels. Every chapter contains an essay describing a part
of the history of the subject and at least one connected collection of
exercises that together comprise a project-level
exploration.

Both a solutions manual and instructor's manual are available
electronically to those instructors who have already adopted the
textbook for classroom use. Please send email to textbooks@ams.org for more
information.

#### Readership

Undergraduate students interested in analysis.

#### Table of Contents

# Table of Contents

## The Calculus of Complex Functions

- Cover Cover11
- Title page iii7
- Copyright iv8
- Contents vii11
- Preface ix13
- Chapter 1. Analytic Functions and the Derivative 119
- Chapter 2. Complex Integration 93111
- Chapter 3. Non-Entire Functions 155173
- Chapter 4. Solving the Dirichlet Problem 215233
- Chapter 5. Further Topics and Famous Discoveries 269287
- Chapter 6. Linear Algebra and Operator Theory 327345
- Acknowledgments and Credits 395413
- Solutions to Odd Exercises 399417
- Bibliography 423441
- Index 431449
- Back Cover Back Cover3456