Written by a professor at the U.S. Naval Academy, this classic textbook provides a clear, step-by-step introduction to the theory and application of ordinary differential equations. It is designed for students with a basic background in calculus, focusing on practical methods for solving first and second-order equations, linear equations with constant coefficients, and integration in series. Th…
This classic monograph provides a rigorous and systematic exposition of the theory of meromorphic functions—functions that are analytic in a domain except for isolated poles. Hayman focuses heavily on the Nevanlinna theory of value distribution, exploring how these functions behave near singularities and the frequency with which they take on specific values. The text is renowned for its clari…
This classic textbook, part of the Prentice-Hall Series in Automatic Computation, provides a rigorous foundation for the numerical analysis of ordinary differential equations (ODEs). It is particularly well-known for its systematic treatment of multi-step methods and its groundbreaking approach to "stiff" differential equations—problems where solutions vary on significantly different time sca…
This monograph explores the deep connections between algebraic number theory and group theory, specifically focusing on the structure of Galois groups and their central extensions. Fröhlich investigates how these extensions relate to the ideal class groups of algebraic number fields, providing a systematic treatment of the "genus field" and "central class field" concepts. It is a specialized r…
This textbook provides a rigorous introduction to multivariable calculus and mathematical analysis. It moves beyond elementary techniques to explore the theoretical foundations of differentiable manifolds, exterior algebra, and differential forms. Fleming emphasizes a modern approach to the subject, utilizing linear algebra to generalize classical theorems like Stokes' theorem and the Inverse F…
Originally a prominent Soviet textbook, this English translation provides a systematic and rigorous introduction to the foundations of mathematical analysis. Volume I focuses on the theory of limits as the central building block for calculus, establishing the properties of real numbers and functions of one and several variables. It provides a detailed account of differential and integral calcul…