A Source Book in Classical Analysis

Description

DjVu pp. 20-3 (pp. 8-11): Abbé Moigno's and Cauchy's proofs of the Fundamental Theorem of Calculus

pp. 60ff. are on the Cauchy-Riemann equations

The DjVu is bookmared, too! ☺

An understanding of the developments in classical analysis during the nineteenth century is vital to a full appreciation of the history of twentieth-century mathematical thought. It was during the nineteenth century that the diverse mathematical formulae of the eighteenth century were systematized and the properties of functions of real and complex variables clearly distinguished; and it was then that the calculus matured into the rigorous discipline of today, becoming in the process a dominant influence on mathematics and mathematical physics. This Source Book, a sequel to D. J. Struik's Source Book in Mathematics, 1200-1800, draws together more than eighty selections from the writings of the most influential mathematicians of the period. Thirteen chapters, each with an introduction by the editor, highlight the major developments in mathematical thinking over the century. All material is in English, and great care has been taken to maintain a high standard of accuracy both in translation and in transcription. Of particular value to historians and philosophers of science, the Source Book should serve as a vital reference to anyone seeking to understand the roots of twentieth-century mathematical thought.

MR0469612

This excellent book outlines the development of classical analysis in the 19th century by means of judiciously chosen selections from the writings of leading 19th-century analysts. The selections are grouped into 13 chapters: Foundations of real analysis, Foundations of complex analysis, Convergent expansions, Asymptotic expansions, Fourier series and integrals, Elliptic and Abelian integrals, Elliptic and automorphic functions, Ordinary differential equations (two chapters), Partial differential equations, Calculus of variations, Wave equations and characteristics, Integral equations. All selections not originally in English have been given first-rate translations. The various sections are well provided with penetrating introductions, and the selections themselves are amply annotated.

Reviewed by R. P. Boas Jr.