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1.

図書
図書
1. Elements of the theory of functions
by Konrad Knopp ; translated by Frederick Bagemihl
出版情報: New York : Dover Publications, c1952  140 p. ; 21 cm
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目次情報: 続きを見る
Complex Numbers and their Geometric Representation / Section I：
Foundations / Chapter I：
Introduction / 1：
The system of real numbers / 2：
Pointgs and vectors of the plane / 3：
The System of Complex Numbers and the Gaussian Plane of Numbers / Chapter II：
Historical remarks / 4：
Introduction of complex numbers / 5：
Notation
Equality and inequality / 6：
Addition and subtraction / 7：
Multiplication and division / 8：
Derived rules / 9：
Powers
The system of complex numbers as an extension of the system of real numbers / 10：
Trigonometric representation of complex numbers / 11：
Geometric representation of multiplication and division / 12：
Inequalities and absolute values / 13：
Examples
The Riemann Sphere of Numbers / Chapter III：
The stereographic projection / 14：
The Riemann sphere of numbers / 15：
The point infinity
Linear Functions and Circular Transformations / Section II：
Mapping by Means of Linear Functions / Chapter IV：
Mapping by means of entire linear functions / 16：
Mapping by means of the function w = 1/z / 17：
Mapping by means of arbitrary linear functions / 18：
Normal Forms and Particular Linear Mappings / Chapter V：
The group-property of linear transformations / 19：
Fixed points and normal forms / 20：
Particular linear mappings / 21：
Cross ratios
Further examples / 22：
Sets and Sequences / Section III：
Power Series
Point Sets and Sets of Numbers / Chapter VI：
Point sets / 23：
Sets of real numbers / 24：
The Bolzano-Weierstrass theorem / 25：
Sequences of Numbers / Chapter VII：
Infinite Series
Sequences of complex numbers / 26：
Sequences of real numbers / 27：
Infinite series / 28：
The circle of convergence / Chapter VIII：
Operations on power series / 30：
Analytic Functions and Conformal Mapping / Section IV：
Functions of a Complex Variable / Chapter IX：
The concept of a function of a complex variable / 31：
Limits of functions / 32：
Continuity / 33：
Differentiability / 34：
Properties of functions represented by power series / 35：
Analytic functions / Chapter X：
Conformal mapping / 37：
The Elementary Functions / Section V：
Power and Root / Chapter XI：
The Rational Functions
Power and root / 38：
The entire rational functions / 39：
The fractional rational functions / 40：
The Exponential, Trigonometric, and Hyperbolic Functions / Chapter XII：
The exponential function / 41：
The functions cos z and sin z / 42：
The functions tan z and cot z / 43：
The hyperbolic functions / 44：
The Logarithm, the Cyclometric Functions, and the Binomial Series / Chapter XIII：
The logarithm / 45：
The cyclometric functions / 46：
The binomial series and the general power Bibliography / 47：
Index
Complex Numbers and their Geometric Representation / Section I：
Foundations / Chapter I：
Introduction / 1：
2.

図書
図書
2. Infinite sequences and series
by Konrad Knopp ; translated by Frederick Bagemihl
出版情報: New York : Dover Publications, c1956  v, 186 p. ; 21 cm
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目次情報: 続きを見る
Foreword
Introduction and Prerequisites / Chapter 1：
Preliminary remarks concerning sequences and series / 1.1：
Real and complex numbers / 1.2：
Sets of numbers / 1.3：
Functions of a real and of a complex variable / 1.4：
Sequences and Series / Chapter 2：
Arbitrary sequences / 2.1：
Null sequences
Sequences and sets of numbers / 2.2：
Convergence and divergence / 2.3：
Cauchy's limit theorem and its generalizations / 2.4：
The main tests for sequences / 2.5：
Infinite series / 2.6：
The Main Tests for Infinite Series / Chapter 3：
Operating with Convergent Series
Series of positive terms: The first main test and the comparison tests of the first and second kind / 3.1：
The radical test and the ratio test / 3.2：
Series of positive, monotonically decreasing terms / 3.3：
The second main test / 3.4：
Absolute convergence / 3.5：
Operating with convergent series / 3.6：
Infinite products / 3.7：
Power Series / Chapter 4：
The circle of convergence / 4.1：
The functions represented by power series / 4.2：
Operating with power series / 4.3：
Expansion of composite functions
The inversion of a power series / 4.4：
Development of the Theory of Convergence / Chapter 5：
The theorems of Abel, Dini, and Pringsheim / 5.1：
Scales of convergence tests / 5.2：
Abel's partial summation / 5.3：
Lemmas
Special comparison tests of the second kind / 5.4：
Abel's and Dirichlet's tests and their generalizations / 5.5：
Series transformations / 5.6：
Multiplication of series / 5.7：
Expansion of the Elementary Functions / Chapter 6：
List of the elementary functions / 6.1：
The rational functions / 6.2：
The exponential function and the circular functions / 6.3：
The logarithmic function / 6.4：
The general power and the binomial series / 6.5：
The cyclometric functions / 6.6：
Numerical and Closed Evaluation of Series / Chapter 7：
Statement of the problem / 7.1：
Numerical evaluations and estimations of remainders / 7.2：
Closed evaluations Bibliography / 7.3：
Index
Foreword
Introduction and Prerequisites / Chapter 1：
Preliminary remarks concerning sequences and series / 1.1：
3.

図書
図書
3. Theory of sets
by E. Kamke ; translated by Frederick Bagemihl
出版情報: New York : Dover, 1950  vii, 144 p. ; 21 cm
シリーズ名: The Dover series in mathematics and physics
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