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The Location of Critical Points of Analytic and Harmonic Functions
 
The Location of Critical Points of Analytic and Harmonic Functions
Softcover ISBN:  978-0-8218-4643-8
Product Code:  COLL/34.S
List Price: $99.00
MAA Member Price: $89.10
AMS Member Price: $79.20
eBook ISBN:  978-1-4704-3179-2
Product Code:  COLL/34.E
List Price: $89.00
MAA Member Price: $80.10
AMS Member Price: $71.20
Softcover ISBN:  978-0-8218-4643-8
eBook: ISBN:  978-1-4704-3179-2
Product Code:  COLL/34.S.B
List Price: $188.00 $143.50
MAA Member Price: $169.20 $129.15
AMS Member Price: $150.40 $114.80
The Location of Critical Points of Analytic and Harmonic Functions
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The Location of Critical Points of Analytic and Harmonic Functions
Softcover ISBN:  978-0-8218-4643-8
Product Code:  COLL/34.S
List Price: $99.00
MAA Member Price: $89.10
AMS Member Price: $79.20
eBook ISBN:  978-1-4704-3179-2
Product Code:  COLL/34.E
List Price: $89.00
MAA Member Price: $80.10
AMS Member Price: $71.20
Softcover ISBN:  978-0-8218-4643-8
eBook ISBN:  978-1-4704-3179-2
Product Code:  COLL/34.S.B
List Price: $188.00 $143.50
MAA Member Price: $169.20 $129.15
AMS Member Price: $150.40 $114.80
  • Book Details
     
     
    Colloquium Publications
    Volume: 341950; 384 pp
    MSC: Primary 30

    This book is concerned with the critical points of analytic and harmonic functions. A critical point of an analytic function means a zero of its derivative, and a critical point of a harmonic function means a point where both partial derivatives vanish. The analytic functions considered are largely polynomials, rational functions, and certain periodic, entire, and meromorphic functions. The harmonic functions considered are largely Green's functions, harmonic measures, and various linear combinations of them. The interest in these functions centers around the approximate location of their critical points. The approximation is in the sense of determining minimal regions in which all the critical points lie or maximal regions in which no critical point lies. Throughout the book the author uses the single method of regarding the critical points as equilibrium points in fields of force due to suitable distribution of matter.

    The exposition is clear, complete, and well-illustrated with many examples.

    Readership

    Graduate students and research mathematicians interested in analyic and harmonic functions.

  • Table of Contents
     
     
    • Chapters
    • Chapter 1. Fundamental results
    • Chapter 2. Real polynomials
    • Chapter 3. Polynomials, continued
    • Chapter 4. Rational functions
    • Chapter 5. Rational functions with symmetry
    • Chapter 6. Analytic functions
    • Chapter 7. Green’s functions
    • Chapter 8. Harmonic functions
    • Chapter 9. Further harmonic functions
  • 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
Volume: 341950; 384 pp
MSC: Primary 30

This book is concerned with the critical points of analytic and harmonic functions. A critical point of an analytic function means a zero of its derivative, and a critical point of a harmonic function means a point where both partial derivatives vanish. The analytic functions considered are largely polynomials, rational functions, and certain periodic, entire, and meromorphic functions. The harmonic functions considered are largely Green's functions, harmonic measures, and various linear combinations of them. The interest in these functions centers around the approximate location of their critical points. The approximation is in the sense of determining minimal regions in which all the critical points lie or maximal regions in which no critical point lies. Throughout the book the author uses the single method of regarding the critical points as equilibrium points in fields of force due to suitable distribution of matter.

The exposition is clear, complete, and well-illustrated with many examples.

Readership

Graduate students and research mathematicians interested in analyic and harmonic functions.

  • Chapters
  • Chapter 1. Fundamental results
  • Chapter 2. Real polynomials
  • Chapter 3. Polynomials, continued
  • Chapter 4. Rational functions
  • Chapter 5. Rational functions with symmetry
  • Chapter 6. Analytic functions
  • Chapter 7. Green’s functions
  • Chapter 8. Harmonic functions
  • Chapter 9. Further harmonic functions
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
Please select which format for which you are requesting permissions.