Colloquium Publications 1950; 384 pp; softcover Volume: 34 ISBN10: 0821846434 ISBN13: 9780821846438 List Price: US$77 Member Price: US$61.60 Order Code: COLL/34.S
 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. Readership Graduate students and research mathematicians interested in analyic and harmonic functions. Table of Contents  Fundamental results
 Real polynomials
 Polynomials, continued
 Rational functions
 Rational functions with symmetry
 Analytic functions
 Green's functions
 Harmonic functions
 Further harmonic functions
 Bibliography
 Index
