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: |