Garrett Birkhoff - Böcker

A carefully revised edition of the well-respected ODE text, whose unique treatment provides a smooth transition to critical understanding of proofs of basic theorems. First chapters present a rigorous treatment of background material; middle chapters deal in detail with systems of nonlinear differential equations; final chapters are devoted to the study of second-order linear differential equations. The power of the theory of ODE is illustrated throughout by deriving the properties of important special functions, such as Bessel functions, hypergeometric functions, and the more common orthogonal polynomials, from their defining differential equations and boundary conditions. Contains several hundred exercises. Prerequisite is a first course in ODE.

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.

A complete revision of the first edition this book. The author has added a chapter on turbulence, and has expanded the work on paradoxes and modeling. W.M. Elsasser said of the first edition, "A book such as this, concentrating as it does on the boundaries of fundamental progress, should be indispensable to all those engaged in hydrodynamical research who are concerned with the type of generalization that so often in the past has led to fundamental progress." Originally published in 1960. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

A complete revision of the first edition this book. The author has added a chapter on turbulence, and has expanded the work on paradoxes and modeling. W.M. Elsasser said of the first edition, "A book such as this, concentrating as it does on the boundaries of fundamental progress, should be indispensable to all those engaged in hydrodynamical research who are concerned with the type of generalization that so often in the past has led to fundamental progress." Originally published in 1960. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

This book presents modern algebra from first principles and is accessible to undergraduates or graduates. It combines standard materials and necessary algebraic manipulations with general concepts that clarify meaning and importance.This conceptual approach to algebra starts with a description of algebraic structures by means of axioms chosen to suit the examples, for instance, axioms for groups, rings, fields, lattices, and vector spaces. This axiomatic approach--emphasized by Hilbert and developed in Germany by Noether, Artin, Van der Waerden, et al., in the 1920s--was popularized for the graduate level in the 1940s and 1950s to some degree by the authors' publication of A Survey of Modern Algebra. The present book presents the developments from that time to the first printing of this book. This third edition includes corrections made by the authors.

This classic, written by two young instructors who became giants in their field, has shaped the understanding of modern algebra for generations of mathematicians and remains a valuable reference and text for self study and college courses.