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Softcover ISBN:  9780821846438 
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Softcover ISBN:  9780821846438 
Product Code:  COLL/34.S 
List Price:  $99.00 
MAA Member Price:  $89.10 
AMS Member Price:  $79.20 
eBook ISBN:  9781470431792 
Product Code:  COLL/34.E 
List Price:  $89.00 
MAA Member Price:  $80.10 
AMS Member Price:  $71.20 
Softcover ISBN:  9780821846438 
eBook ISBN:  9781470431792 
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 DetailsColloquium PublicationsVolume: 34; 1950; 384 ppMSC: 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 wellillustrated with many examples.
ReadershipGraduate 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


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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 wellillustrated with many examples.
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