Theory of Functions / J. F. Ritt.

Format:

Book

Author/Creator:

Ritt, J. F., author.

Language:

English

Physical Description:

1 online resource

Place of Publication:

New York, NY : Columbia University Press, [1947]

Language Note:

In English.

Summary:

Examines functions such as the real number system, the theory of limits, linear point sets, derivatives, curves, and series among other mathematical theories.

Contents:

Frontmatter

Preface

Contents

I. The Real Number System

II. Theory of Limits

III. Linear Point Sets

IV. Functions and Continuity

V. The Derivative

VI. Riemann Integration

VII. Infinite Series of Numbers

VIII. Sequences of Functions

IX. Infinite Series of Functions

X. Functions of Two Variables

XI. Complex and Hypercomplex Numbers

XII. Limits and Point Sets (Complex Domain)

XIII. Curves and Regions

XIV. Derivatives

XV. Continuous Curves

XVI. Rectifiable Curves

XVII. Curvilinear Integrals

XVIII. Jordan Curves

XIX. Analysis Situs of the Triangle

XX. The Cauchy Integral Theorem for Triangles

XXI. Extension of the Cauchy Integral Theorem to Polygons

XXII. The Cauchy Integral Theorem for a Rectifiable Curve

XXIII. The Cauchy Integral Theorem for Several Contours

XXIV. Preliminaries for Cauchy Integral Formula

XXV. The Cauchy Integral Formula and the Derivatives of an Analytic Function

XXVI. Infinite Sequences and Infinite Series of Analytic Functions

XXVII. Power Series

XXVIII. Taylor's Expansion

XXIX. Liouville's Theorem and the Fundamental Theorem of Algebra

XXX. On the Zeros of Analytic Functions

XXXI. Laurent Series

XXXII. Singularities of Analytic Functions

XXXIII. Products and Quotients of Analytic Functions

XXXIV. Rational Functions

XXXV. The Functions ez , sin z, cos z

XXXVI. Periodic Functions

XXXVII. Indefinite Integrals, Logarithms

XXXVIII. Infinite Products

XXXIX. The Weierstrass Factorization Theorem

XL. Meromorphic Functions and Mittag-Leffler's Theorem

XLI. Theory of Residues

XLII. Certain Important Theorems

XLIII. Variation of the Amplitude of a Continuous Function along a Continuous Curve

XLIV. The Functions n√z, log z

XLV. Analytic Continuation

Notes:

Description based on online resource; title from PDF title page (publisher's Web site, viewed 08. Jul 2019)

ISBN:

0-231-89830-4

OCLC:

1100445124