Item Successfully Added to Cart
An error was encountered while trying to add the item to the cart. Please try again.
OK
Please make all selections above before adding to cart
OK
Share this page via the icons above, or by copying the link below:
Copy To Clipboard
Successfully Copied!
Introduction to Complex Analysis
 
Rolf Nevanlinna
Veikko Paatero
Introduction to Complex Analysis
AMS Chelsea Publishing: An Imprint of the American Mathematical Society
Hardcover ISBN:  978-0-8218-4399-4
Product Code:  CHEL/310.H
List Price: $69.00
MAA Member Price: $62.10
AMS Member Price: $62.10
eBook ISBN:  978-1-4704-1132-9
Product Code:  CHEL/310.E
List Price: $65.00
MAA Member Price: $58.50
AMS Member Price: $58.50
Hardcover ISBN:  978-0-8218-4399-4
eBook: ISBN:  978-1-4704-1132-9
Product Code:  CHEL/310.H.B
List Price: $134.00 $101.50
MAA Member Price: $120.60 $91.35
AMS Member Price: $120.60 $91.35
Add to cart
Introduction to Complex Analysis
Click above image for expanded view
Introduction to Complex Analysis
Rolf Nevanlinna
Veikko Paatero
AMS Chelsea Publishing: An Imprint of the American Mathematical Society
Hardcover ISBN:  978-0-8218-4399-4
Product Code:  CHEL/310.H
List Price: $69.00
MAA Member Price: $62.10
AMS Member Price: $62.10
eBook ISBN:  978-1-4704-1132-9
Product Code:  CHEL/310.E
List Price: $65.00
MAA Member Price: $58.50
AMS Member Price: $58.50
Hardcover ISBN:  978-0-8218-4399-4
eBook ISBN:  978-1-4704-1132-9
Product Code:  CHEL/310.H.B
List Price: $134.00 $101.50
MAA Member Price: $120.60 $91.35
AMS Member Price: $120.60 $91.35
Add to cart
  • Book Details
     
     
    AMS Chelsea Publishing
    Volume: 310; 1969

    It really is a gem, both in terms of its table of contents and the level of discussion. The exercises also look very good.

    —Clifford Earle, Cornell University

    This book has a soul and has passion.

    —William Abikoff, University of Connecticut

    This classic book gives an excellent presentation of topics usually treated in a complex analysis course, starting with basic notions (rational functions, linear transformations, analytic function), and culminating in the discussion of conformal mappings, including the Riemann mapping theorem and the Picard theorem. The two quotes above confirm that the book can be successfully used as a text for a class or for self-study.
    Readership

    Undergraduate and graduate students interested in complex analysis.
  • Table of Contents
     
     
    • Front Cover
    • FOREWORD
    • CONTENTS
    • CHAPTER 1: THE CONCEPT OF AN ANALYTIC FUNCTION
    • §1. THE COMPLEX NUMBERS
    • §2. POINT SETS IN THE COMPLEX PLANE
    • §3. FUNCTIONS OF A COMPLEX VARIABLE
    • CHAPTER 2: GENERAL PROPERTIES OF RATIONAL FUNCTIONS
    • §1. THE n-TH POWER
    • §2. POLYNOMIALS
    • §3. RATIONAL FUNCTIONS
    • CHAPTER 3: LINEAR TRANSFORMATIONS
    • §1. BASIC PROPERTIES OF LINEAR TRANSFORMATIONS
    • §2. MAPPING PROBLEMS
    • §3. STEREOGRAPHlC PROJECTION
    • CHAPTER 4: MAPPING BY RATIONAL FUNCTIONS OF SECOND ORDER
    • CHAPTER 5: THE EXPONENTIAL FUNCTION AND ITS INVERSE. THE GENERAL POWER
    • §1. DEFINITION AND BASIC PROPERTIES OF THE EXPONENTIAL FUNCTION
    • §2. MAPPING BY MEANS OF THE EXPONENTIAL FUNCTION. THE LOGARITHM
    • §3. THE GENERAL POWER
    • CHAPTER 6: THE TRIGONOMETRIC FUNCTIONS
    • §1. THE SINE AND COSINE
    • §2. THE TANGENT AND THE COTANGENT
    • §3. THE MAPPINGS GIVEN BY THE FUNCTIONS tan z AND cot z. THEIR INVERSE FUNCTIONS
    • §4. THE MAPPINGS GIVEN BY THE FUNCTIONS sin z AND cos z. THE FUNCTIONS arc sin z AND arc cos z
    • §5. SURVEY OF THE RIEMANN SURFACES OF THE ELEMENTARY FUNCTIONS
    • CHAPTER 7: INFINITE SERIES WITH COMPLEX TERMS
    • §1. GENERAL THEOREMS
    • §2. POWER SERIES
    • CHAPTER 8: INTEGRATION IN THE COMPLEX DOMAIN. CAUCHY'S THEOREM
    • §1. COMPLEX LINE INTEGRALS
    • §2. THE PRIMITIVE FUNCTION
    • §3. CAUCHY'S THEOREM
    • §4. THE GENERAL FORMULATION OF CAUCHY'S THEOREM
    • CHAPTER 9: CAUCHY'S INTEGRAL FORMULA AND ITS APPLICATIONS
    • §1. CAUCHY'S FORMULA
    • §2. THE TAYLOR EXPANSION OF AN ANALYTIC FUNCTION
    • §3. CONSEQUENCES OF CAUCHY'S INTEGRAL FORMULA
    • §4. THE LAURENT EXPANSION
    • §5. ISOLATED SINGULARITIES OF AN ANALYTIC FUNCTIUl'II
    • §6. THE INVERSE OF AN ANALYTIC FUNCTION
    • §7. MAPPING BY A RATIONAL FUNCTION
    • § 8. NORMAL FAMILIES
    • CHAPTER 10: THE RESIDUE THEOREM AND ITS APPLICATIONS
    • §1. THE RESIDUE THEOREM
    • §2. APPLICATION OF THE RESIDUE THEOREM TO THE EVALUATION OF DEFINITE INTEGRALS
    • §3. THE PARTIAL-FRACTION EXPANSION OF cot πz
    • §4. THE ARGUMENT PRINCIPLE
    • §5. APPLICATIONS OF THE ARGUMENT PRINCIPLE
    • CHAPTER 11: HARMONIC FUNCTIONS
    • §1. PRELIMINARY CONSIDERATIONS
    • §2. GAUSS'S MEAN-VALUE THEOREM.
    • §3. POISSON'S FORMULA
    • §4. HARMONIC MEASURE
    • §5. THE DIRICHLET PROBLEM
    • §6. HARNACK'S PRINCIPLE
    • CHAPTER 12: ANALYTIC CONTINUATION
    • §1. THE PRINCIPLE OF ANALYTIC CONTINUATION
    • §2. THE MONODROMY THEOREM
    • §3. THE INVERSE OF A RATIONAL FUNCTION
    • §4. HARMONIC CONTINUATION. THE REFLECTION PRINCIPLE
    • CHAPTER 13: ENTIRE FUNCTIONS
    • §1. INFINITE PRODUCTS
    • §2. PRODUCT REPRESENTATION OF THE FUNCTION w = sin πz
    • §3. THE WEIERSTRASS FACTORIZATION THEOREM
    • §4. JENSEN'S FORMULA. THE GROWTH OF ENTIRE FUNCTIONS
    • CHAPTER 14: PERIODIC FUNCTIONS
    • §1. DEFINITIONS OF SIMPLY AND DOUBLY PERIODIC FUNCTIONS
    • §2. REDUCTION OF SIMPLY PERIODIC FUNCTIONS TO THE EXPONENTIAL FUNCTION
    • §3. THE BASIC PROPERTIES OF DOUBLY PERIODIC FUNCTIONS
    • §4. THE WEIERSTRASS p-FUNCTION
    • §5. THE WEIERSTRASS ζ- AND σ-FUNCTIONS
    • §6, REPRESENTATION OF DOUBLY PERIODIC FUNCTIONS BY MEANS OF THE σ-FUNCTION
    • §7. THE DIFFERENTIAL EQUATION OF THE &a-FUNCTION
    • §8. REPRESENTATION OF DOUBLY PERIODIC FUNCTIONS AS RATIONAL FUNCTIONS OF p AND p'
    • §9. ADDITION THEOREM FOR DOUBLY PERIODIC FUNCTIONS
    • §10. DETERMINATION OF A DOUBLY PERIODIC FUNCTION WITH PRESCRIBED PRINCIPAL PARTS
    • §11. MAPPING BY A DOUBLY PERIODIC FUNCTION OF ORDER 2
    • §12. ELLIPTIC INTEGRALS
    • CHAPTER 15: THE EULER Γ-FUNCTION
    • §1. DEFINITION OF THE Γ-FUNCTION
    • §2. STIRLING'S FORMULA
    • §3. THE PRODUCT REPRESENTATION OF THE Γ-FUNCTION
    • CHAPTER 16: THE RIEMANN ζ-FUNCTION
    • §1. DEFINITION AND THE EULER PRODUCT FORMULA
    • §2. INTEGRAL REPRESENTATION OF THE ζ-FUNCTION
    • §3. ANALYTIC CONTINUATION OF THE ζ-FUNCTION
    • §4. RIEMANN'S FUNCTIONAL EQUATION
    • §5. THE ZEROS OF THE ζ-FUNCTION AND THE DISTRIBUTION OF PRIME NUMBERS
    • CHAPTER 17: THE THEORY OF CONFORMAL MAPPING
    • §1. THE RIEMANN MAPPING THEOREM
    • §2. CONSTRUCTION OF THE SOLUTION
    • §3. BOUNDARY CORRESPONDENCE UNDER CONFORMAL MAPPING
    • §4. THE CONNECTION BETWEEN CONFORMAL MAPPING AND THE DIRICHLET PROBLEM
    • §5. THE CONFORMAL MAPPING OF POLYGONS
    • §6, TRIANGLE FUNCTIONS
    • §7. THE PICARD THEOREM
    • INDEX
    • Back Cover
  • Additional Material
     
     
  • Reviews
     
     

    • This is a textbook by one of the masters of Complex Analysis. It is a crisp, direct, and surprisingly modern account of the basic material for a first course in Complex Analysis. ... In summary, the book remains an excellent reference for a first course in Complex Analysis. It contains over 300 exercises.
      MAA Reviews
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
AMS Chelsea Publishing
Volume: 310; 1969

It really is a gem, both in terms of its table of contents and the level of discussion. The exercises also look very good.

—Clifford Earle, Cornell University

This book has a soul and has passion.

—William Abikoff, University of Connecticut

This classic book gives an excellent presentation of topics usually treated in a complex analysis course, starting with basic notions (rational functions, linear transformations, analytic function), and culminating in the discussion of conformal mappings, including the Riemann mapping theorem and the Picard theorem. The two quotes above confirm that the book can be successfully used as a text for a class or for self-study.
Readership

Undergraduate and graduate students interested in complex analysis.
  • Front Cover
  • FOREWORD
  • CONTENTS
  • CHAPTER 1: THE CONCEPT OF AN ANALYTIC FUNCTION
  • §1. THE COMPLEX NUMBERS
  • §2. POINT SETS IN THE COMPLEX PLANE
  • §3. FUNCTIONS OF A COMPLEX VARIABLE
  • CHAPTER 2: GENERAL PROPERTIES OF RATIONAL FUNCTIONS
  • §1. THE n-TH POWER
  • §2. POLYNOMIALS
  • §3. RATIONAL FUNCTIONS
  • CHAPTER 3: LINEAR TRANSFORMATIONS
  • §1. BASIC PROPERTIES OF LINEAR TRANSFORMATIONS
  • §2. MAPPING PROBLEMS
  • §3. STEREOGRAPHlC PROJECTION
  • CHAPTER 4: MAPPING BY RATIONAL FUNCTIONS OF SECOND ORDER
  • CHAPTER 5: THE EXPONENTIAL FUNCTION AND ITS INVERSE. THE GENERAL POWER
  • §1. DEFINITION AND BASIC PROPERTIES OF THE EXPONENTIAL FUNCTION
  • §2. MAPPING BY MEANS OF THE EXPONENTIAL FUNCTION. THE LOGARITHM
  • §3. THE GENERAL POWER
  • CHAPTER 6: THE TRIGONOMETRIC FUNCTIONS
  • §1. THE SINE AND COSINE
  • §2. THE TANGENT AND THE COTANGENT
  • §3. THE MAPPINGS GIVEN BY THE FUNCTIONS tan z AND cot z. THEIR INVERSE FUNCTIONS
  • §4. THE MAPPINGS GIVEN BY THE FUNCTIONS sin z AND cos z. THE FUNCTIONS arc sin z AND arc cos z
  • §5. SURVEY OF THE RIEMANN SURFACES OF THE ELEMENTARY FUNCTIONS
  • CHAPTER 7: INFINITE SERIES WITH COMPLEX TERMS
  • §1. GENERAL THEOREMS
  • §2. POWER SERIES
  • CHAPTER 8: INTEGRATION IN THE COMPLEX DOMAIN. CAUCHY'S THEOREM
  • §1. COMPLEX LINE INTEGRALS
  • §2. THE PRIMITIVE FUNCTION
  • §3. CAUCHY'S THEOREM
  • §4. THE GENERAL FORMULATION OF CAUCHY'S THEOREM
  • CHAPTER 9: CAUCHY'S INTEGRAL FORMULA AND ITS APPLICATIONS
  • §1. CAUCHY'S FORMULA
  • §2. THE TAYLOR EXPANSION OF AN ANALYTIC FUNCTION
  • §3. CONSEQUENCES OF CAUCHY'S INTEGRAL FORMULA
  • §4. THE LAURENT EXPANSION
  • §5. ISOLATED SINGULARITIES OF AN ANALYTIC FUNCTIUl'II
  • §6. THE INVERSE OF AN ANALYTIC FUNCTION
  • §7. MAPPING BY A RATIONAL FUNCTION
  • § 8. NORMAL FAMILIES
  • CHAPTER 10: THE RESIDUE THEOREM AND ITS APPLICATIONS
  • §1. THE RESIDUE THEOREM
  • §2. APPLICATION OF THE RESIDUE THEOREM TO THE EVALUATION OF DEFINITE INTEGRALS
  • §3. THE PARTIAL-FRACTION EXPANSION OF cot πz
  • §4. THE ARGUMENT PRINCIPLE
  • §5. APPLICATIONS OF THE ARGUMENT PRINCIPLE
  • CHAPTER 11: HARMONIC FUNCTIONS
  • §1. PRELIMINARY CONSIDERATIONS
  • §2. GAUSS'S MEAN-VALUE THEOREM.
  • §3. POISSON'S FORMULA
  • §4. HARMONIC MEASURE
  • §5. THE DIRICHLET PROBLEM
  • §6. HARNACK'S PRINCIPLE
  • CHAPTER 12: ANALYTIC CONTINUATION
  • §1. THE PRINCIPLE OF ANALYTIC CONTINUATION
  • §2. THE MONODROMY THEOREM
  • §3. THE INVERSE OF A RATIONAL FUNCTION
  • §4. HARMONIC CONTINUATION. THE REFLECTION PRINCIPLE
  • CHAPTER 13: ENTIRE FUNCTIONS
  • §1. INFINITE PRODUCTS
  • §2. PRODUCT REPRESENTATION OF THE FUNCTION w = sin πz
  • §3. THE WEIERSTRASS FACTORIZATION THEOREM
  • §4. JENSEN'S FORMULA. THE GROWTH OF ENTIRE FUNCTIONS
  • CHAPTER 14: PERIODIC FUNCTIONS
  • §1. DEFINITIONS OF SIMPLY AND DOUBLY PERIODIC FUNCTIONS
  • §2. REDUCTION OF SIMPLY PERIODIC FUNCTIONS TO THE EXPONENTIAL FUNCTION
  • §3. THE BASIC PROPERTIES OF DOUBLY PERIODIC FUNCTIONS
  • §4. THE WEIERSTRASS p-FUNCTION
  • §5. THE WEIERSTRASS ζ- AND σ-FUNCTIONS
  • §6, REPRESENTATION OF DOUBLY PERIODIC FUNCTIONS BY MEANS OF THE σ-FUNCTION
  • §7. THE DIFFERENTIAL EQUATION OF THE &a-FUNCTION
  • §8. REPRESENTATION OF DOUBLY PERIODIC FUNCTIONS AS RATIONAL FUNCTIONS OF p AND p'
  • §9. ADDITION THEOREM FOR DOUBLY PERIODIC FUNCTIONS
  • §10. DETERMINATION OF A DOUBLY PERIODIC FUNCTION WITH PRESCRIBED PRINCIPAL PARTS
  • §11. MAPPING BY A DOUBLY PERIODIC FUNCTION OF ORDER 2
  • §12. ELLIPTIC INTEGRALS
  • CHAPTER 15: THE EULER Γ-FUNCTION
  • §1. DEFINITION OF THE Γ-FUNCTION
  • §2. STIRLING'S FORMULA
  • §3. THE PRODUCT REPRESENTATION OF THE Γ-FUNCTION
  • CHAPTER 16: THE RIEMANN ζ-FUNCTION
  • §1. DEFINITION AND THE EULER PRODUCT FORMULA
  • §2. INTEGRAL REPRESENTATION OF THE ζ-FUNCTION
  • §3. ANALYTIC CONTINUATION OF THE ζ-FUNCTION
  • §4. RIEMANN'S FUNCTIONAL EQUATION
  • §5. THE ZEROS OF THE ζ-FUNCTION AND THE DISTRIBUTION OF PRIME NUMBERS
  • CHAPTER 17: THE THEORY OF CONFORMAL MAPPING
  • §1. THE RIEMANN MAPPING THEOREM
  • §2. CONSTRUCTION OF THE SOLUTION
  • §3. BOUNDARY CORRESPONDENCE UNDER CONFORMAL MAPPING
  • §4. THE CONNECTION BETWEEN CONFORMAL MAPPING AND THE DIRICHLET PROBLEM
  • §5. THE CONFORMAL MAPPING OF POLYGONS
  • §6, TRIANGLE FUNCTIONS
  • §7. THE PICARD THEOREM
  • INDEX
  • Back Cover

  • This is a textbook by one of the masters of Complex Analysis. It is a crisp, direct, and surprisingly modern account of the basic material for a first course in Complex Analysis. ... In summary, the book remains an excellent reference for a first course in Complex Analysis. It contains over 300 exercises.
    MAA Reviews
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Powered by MathJax
Please select which format for which you are requesting permissions.