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Problems and Theorems in Analysis II
Theory of Functions. Zeros. Polynomials. Determinants. Number Theory. Geometry
Langbeschreibung
Few mathematical books are worth translating 50 years after original publication. Polyá-Szegö is one! It was published in German in 1924, and its English edition was widely acclaimed when it appeared in 1972. In the past, more of the leading mathematicians proposed and solved problems than today. Their collection of the best in analysis is a heritage of lasting value.
Hauptbeschreibung
Problems and Theorems in Analysis I by Polyà/Szegö is also available in the Classics in Mathematics series (3-540-63640-4).
Inhaltsverzeichnis
Four. Functions of One Complex Variable. Special Part.- 1. Maximum Term and Central Index, Maximum Modulus and Number of Zeros.- 2. Schlicht Mappings.- 3. Miscellaneous Problems.- Five. The Location of Zeros.- 1. Rolle's Theorem and Descartes' Rule of Signs.- 2. The Geometry of the Complex Plane and the Zeros of Polynomials.- 3. Miscellaneous Problems.- Six. Polynomials and Trigonometric Polynomials.-
1 (1-7) Tchebychev Polynomials.-
2 (8-15) General Problems on Trigonometric Polynomials.-
3 (16-28) Some Special Trigonometric Polynomials.-
4 (29-38) Some Problems on Fourier Series.-
5 (39-43) Real Non-negative Trigonometric Polynomials.-
6 (44-49) Real Non-negative Polynomials.-
7 (50-61) Maximum-Minimum Problems on Trigonometric Polynomials.-
8 (62-66) Maximum-Minimum Problems on Polynomials.-
9 (67-76) The Lagrange Interpolation Formula.-
10 (77-83) The Theorems of S. Bernstein and A. Markov.-
11 (84-102) Legendre Polynomials and Related Topics.-
12 (103-113) Further Maximum-Minimum Problems on Polynomials.- Seven. Determinants and Quadratic Forms.-
1 (1-16) Evaluation of Determinants. Solution of Linear Equations.-
2 (17-34) Power Series Expansion of Rational Functions.-
3 (35-43.2) Generation of Positive Quadratic Forms.-
4 (44-54.4) Miscellaneous Problems.-
5 (55-72) Determinants of Systems of Functions.- Eight. Number Theory.- 1. Arithmetical Functions.- 2. Polynomials with Integral Coefficients and Integral-Valued Functions.- 3. Arithmetical Aspects of Power Series.- 4. Some Problems on Algebraic Integers.- 5. Miscellaneous Problems.- Nine. Geometric Problems.-
1 (1-25) Some Geometric Problems.- Errata.-
1 Additional Problems to Part One.- New Problems in EnglishEdition.- Author Index.- Topics.
1 (1-7) Tchebychev Polynomials.-
2 (8-15) General Problems on Trigonometric Polynomials.-
3 (16-28) Some Special Trigonometric Polynomials.-
4 (29-38) Some Problems on Fourier Series.-
5 (39-43) Real Non-negative Trigonometric Polynomials.-
6 (44-49) Real Non-negative Polynomials.-
7 (50-61) Maximum-Minimum Problems on Trigonometric Polynomials.-
8 (62-66) Maximum-Minimum Problems on Polynomials.-
9 (67-76) The Lagrange Interpolation Formula.-
10 (77-83) The Theorems of S. Bernstein and A. Markov.-
11 (84-102) Legendre Polynomials and Related Topics.-
12 (103-113) Further Maximum-Minimum Problems on Polynomials.- Seven. Determinants and Quadratic Forms.-
1 (1-16) Evaluation of Determinants. Solution of Linear Equations.-
2 (17-34) Power Series Expansion of Rational Functions.-
3 (35-43.2) Generation of Positive Quadratic Forms.-
4 (44-54.4) Miscellaneous Problems.-
5 (55-72) Determinants of Systems of Functions.- Eight. Number Theory.- 1. Arithmetical Functions.- 2. Polynomials with Integral Coefficients and Integral-Valued Functions.- 3. Arithmetical Aspects of Power Series.- 4. Some Problems on Algebraic Integers.- 5. Miscellaneous Problems.- Nine. Geometric Problems.-
1 (1-25) Some Geometric Problems.- Errata.-
1 Additional Problems to Part One.- New Problems in EnglishEdition.- Author Index.- Topics.
Biography of George PólyaBorn in Budapest, December 13, 1887, George Pólya initially studied law, then languages and literature in Budapest. He came to mathematics in order to understand philosophy, but the subject of his doctorate in 1912 was in probability theory and he promptly abandoned philosophy.After a year in Göttingen and a short stay in Paris, he received an appointment at the ETH in Zürich. His research was multi-faceted, ranging from series, probability, number theory and combinatorics to astronomy and voting systems. Some of his deepest work was on entire functions. He also worked in conformal mappings, potential theory, boundary value problems, and isoperimetric problems in mathematical physics, as well as heuristics late in his career. When Pólya left Europe in 1940, he first went to Brown University, then two years later to Stanford, where he remained until his death on September 7, 1985.
ISBN-13:
9783540636861
Veröffentl:
1997
Erscheinungsdatum:
11.12.1997
Seiten:
412
Autor:
George Polya
Gewicht:
622 g
Format:
235x155x23 mm
Serie:
Classics in Mathematics
Sprache:
Englisch
58,84 €*
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