Theory of functions / by Konrad Knopp ; translated by Frederick Bagemihl.
Idioma: Inglés Lenguaje original: Alemán Editor: New York : Dover, c1945-c1947Descripción: 2 v. : il. ; 21 cmTítulos uniformes: Funktionentheorie. Inglés Tema(s): Functions of complex variablesOtra clasificación: 30-01pt. 1. Elements of the general theory of analytic functions. -- Section I Fundamental Concepts Chapter 1. Numbers and Points § 1. Prerequisites [1] § 2. The Plane and Sphere of Complex Numbers [2] § 8. Point Sets and Sets of Numbers [5] § 4. Paths, Regions, Continua [13] Chapter 2. Functions of a Complex Variable § 5; The Concept of a Most General (Singlevalued) Function of a Complex Variable [21] § 6. Continuity and Differentiability [23] § 7. The Cauchy-Riemann Differential Equations [28] Section II Integral Theorems Chapter 3. The Integral of a Continuous Function § 8. Definition of the Definite Integral [32] § 9. Existence Theorem for the Definite Integral [34] § 10. Evaluation of Definite Integrals [38] ll. Elementary Integral Theorems [44] Chapter 4. Cauchy’s Integral Theorem § 12. Formulation of the Theorem [47] § 13. Proof of the Fundamental Theorem [49] § 14. Simple Consequences and Extensions [55] Chapter 5. Cauchy’s Integral Formulas § 15. The Fundamental Formula [61] § 16. Integral Formulas for the Derivatives [62] Section III Series and the Expansion of Analytic Functions in Series Chapter 6. Series with Variable Terms § 17. Domain of Convergence [67] § 18. Uniform Convergence [71] § 19. Uniformly Convergent Series of Analytic Functions [73] Chapter 7. The Expansion of Analytic Functions in Power Series § 20. Expansion and Identity Theorems for Power Series [79] § 21. The Identity Theorem for Analytic Functions [85] Chapter 8. Analytic Continuation and Complete Definition of Analytic Functions § 22. The Principle of Analytic Continuation [92] 5 23. The Elementary Functions [96] § 24. Continuation by Means of Power Series and Complete Definition of Analytic Functions [98] § 25. The Monodromy Theorem [195] § 26. Examples of Multiple-valued Functions [107] Chapter 9. Entire Transcendental Functions § 27. Definitions [112] § 28. Behavior for Large | z | [112] Section IV Singularities Chapter 10. The Laurent Expansion § 29. The Expansion [117] § 30. Remarks and Examples [119] Chapter 11. The Various Types of Singularities § 31. Essential and Non-essential Singularities or Poles [123] § 32. Behavior of Analytic Functions at Infinity [126] § 33. The Residue Theorem [129] § 34. Inverses of Analytic Functions [134] § 35. Rational Functions [137]
pt. 2. Applications and continuation of the general theory. -- Section I Single-valued Functions Chapter 1. Entire Functions §1. Weierstrass’s Factor-theorem [1] §2. Proof of Weierstrass’s Factor-theorem [7] §3. Examples of Weierstrass’s Factor-theorem [22] Chapter 2. Meromorphic Functions §4. Mittag-Leffler’s Partial-fractions-theorem [34] §5. Proof of Mittag-Leffler’s Theorem [39] §6. Examples of Mittag-Leffler’s Theorem [42] Chapter 3. Periodic Functions §7. The Periods of Analytic Functions [58] §8. Simply Periodic Functions [64] §9. Doubly Periodic Functions; in Particular, Elliptic Functions [73] Section II Multiple-valued Functions Chapter 4. Root and Logarithm §10. Prefatory Remarks Concerning Multiplevalued Functions and Riemann Surfaces [93] §11. The Riemann Surfaces for p√z and log z [100] §12. The Riemann Surfaces for the Functions w = √[(z-a1)(z - a2) • • (z - ak)] [112] Chapter 5. Algebraic Functions §13. Statement of the Problem [119] §14. The Analytic Character of the Roots in the Small [121] §15. The Algebraic Function [126] Chapter 6. The Analytic Configuration §16. The Monogenic Analytic Function [135] §17. The Riemann Surface [139] §18. The Analytic Configuration [142]
| Item type | Home library | Shelving location | Call number | Materials specified | Status | Date due | Barcode | Course reserves |
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Instituto de Matemática, CONICET-UNS | Libros ordenados por tema | 30 K72fi (Browse shelf) | Part I | Available | A-8836 | ||
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Instituto de Matemática, CONICET-UNS | Libros ordenados por tema | 30 K72fi (Browse shelf) | Part II | Available | A-8837 |
Part 1 is translated, with minor changes in text, from the 5th German edition; pt. 2 is translated from the 4th German edition.
Traducción de: Funktionentheorie.
"First American edition."
Incluye referencias bibliográficas (v. 1, p. 141-142; v. 2, p. 147) e índices.
pt. 1. Elements of the general theory of analytic functions. --
Section I Fundamental Concepts --
Chapter 1. Numbers and Points --
§ 1. Prerequisites [1] --
§ 2. The Plane and Sphere of Complex Numbers [2] --
§ 8. Point Sets and Sets of Numbers [5] --
§ 4. Paths, Regions, Continua [13] --
Chapter 2. Functions of a Complex Variable --
§ 5; The Concept of a Most General (Singlevalued) Function of a Complex Variable [21] --
§ 6. Continuity and Differentiability [23] --
§ 7. The Cauchy-Riemann Differential Equations [28] --
Section II Integral Theorems --
Chapter 3. The Integral of a Continuous Function --
§ 8. Definition of the Definite Integral [32] --
§ 9. Existence Theorem for the Definite Integral [34] --
§ 10. Evaluation of Definite Integrals [38] --
ll. Elementary Integral Theorems [44] --
Chapter 4. Cauchy’s Integral Theorem --
§ 12. Formulation of the Theorem [47] --
§ 13. Proof of the Fundamental Theorem [49] --
§ 14. Simple Consequences and Extensions [55] --
Chapter 5. Cauchy’s Integral Formulas --
§ 15. The Fundamental Formula [61] --
§ 16. Integral Formulas for the Derivatives [62] --
Section III Series and the Expansion of Analytic Functions in Series --
Chapter 6. Series with Variable Terms --
§ 17. Domain of Convergence [67] --
§ 18. Uniform Convergence [71] --
§ 19. Uniformly Convergent Series of Analytic Functions [73] --
Chapter 7. The Expansion of Analytic Functions in Power Series --
§ 20. Expansion and Identity Theorems for Power Series [79] --
§ 21. The Identity Theorem for Analytic Functions [85] --
Chapter 8. Analytic Continuation and Complete Definition of Analytic Functions --
§ 22. The Principle of Analytic Continuation [92] --
5 23. The Elementary Functions [96] --
§ 24. Continuation by Means of Power Series and Complete Definition of Analytic Functions [98] --
§ 25. The Monodromy Theorem [195] --
§ 26. Examples of Multiple-valued Functions [107] --
Chapter 9. Entire Transcendental Functions --
§ 27. Definitions [112] --
§ 28. Behavior for Large | z | [112] --
Section IV Singularities --
Chapter 10. The Laurent Expansion --
§ 29. The Expansion [117] --
§ 30. Remarks and Examples [119] --
Chapter 11. The Various Types of Singularities --
§ 31. Essential and Non-essential Singularities or Poles [123] --
§ 32. Behavior of Analytic Functions at Infinity [126] --
§ 33. The Residue Theorem [129] --
§ 34. Inverses of Analytic Functions [134] --
§ 35. Rational Functions [137] --
pt. 2. Applications and continuation of the general theory. --
Section I Single-valued Functions --
Chapter 1. Entire Functions --
§1. Weierstrass’s Factor-theorem [1] --
§2. Proof of Weierstrass’s Factor-theorem [7] --
§3. Examples of Weierstrass’s Factor-theorem [22] --
Chapter 2. Meromorphic Functions --
§4. Mittag-Leffler’s Partial-fractions-theorem [34] --
§5. Proof of Mittag-Leffler’s Theorem [39] --
§6. Examples of Mittag-Leffler’s Theorem [42] --
Chapter 3. Periodic Functions --
§7. The Periods of Analytic Functions [58] --
§8. Simply Periodic Functions [64] --
§9. Doubly Periodic Functions; in Particular, Elliptic Functions [73] --
Section II Multiple-valued Functions --
Chapter 4. Root and Logarithm --
§10. Prefatory Remarks Concerning Multiplevalued Functions and Riemann Surfaces [93] --
§11. The Riemann Surfaces for p√z and log z [100] --
§12. The Riemann Surfaces for the Functions w = √[(z-a1)(z - a2) • • (z - ak)] [112] --
Chapter 5. Algebraic Functions --
§13. Statement of the Problem [119] --
§14. The Analytic Character of the Roots in the Small [121] --
§15. The Algebraic Function [126] --
Chapter 6. The Analytic Configuration --
§16. The Monogenic Analytic Function [135] --
§17. The Riemann Surface [139] --
§18. The Analytic Configuration [142] --
MR, 7,53e (pt. 1)
MR, 8,452e (pt. 2)
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