Theory of Functions / / J. F. Ritt.

• Superior document: Title is part of eBook package: De Gruyter Columbia University Press eBook-Package Archive 1898-1999
• VerfasserIn: Ritt, J. F.,
• Place / Publishing House: New York, NY : : Columbia University Press, , [1947]; ©1947
• Year of Publication: 1947
• Language: English
• Physical Description: 1 online resource (184 p.)

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

Table of 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