Bücher online kaufen
|
| Der Artikel wird am Ende des Bestellprozesses zum Download zur Verfügung gestellt. |
Problems and Theorems in Analysis II
Theory of Functions. Zeros. Polynomials. Determinants. Number Theory. Geometry
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:
9783642619052
Veröffentl:
2012
Seiten:
392
Autor:
George Polya
Serie:
Classics in Mathematics
eBook Typ:
PDF
eBook Format:
EPUB
Kopierschutz:
1 - PDF Watermark
Sprache:
Englisch
58,84 €*
Lieferzeit: Sofort lieferbar
Alle Preise inkl. MwSt.