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Extensively revised edition of a much-respected work examines thermodynamics of irreversible processes, general principles of statistical thermodynamics, assemblies of noninteracting structureless particles, and statistical theory. 1966 edition.
Elementary transformations and bilinear and quadratic forms; canonical reduction of equivalent matrices; subgroups of the group of equivalent transformations; and rational and classical canonical forms. 1952 edition. 275 problems.
One of the twentieth century's most eminent mathematical writers, Augustus De Morgan enriched his expositions with insights from history and psychology. On the Study and Difficulties of Mathematics represents some of his best work, containing points usually overlooked by elementary treatises, and written in a fresh and natural tone that provides a refreshing contrast to the mechanical character of common textbooks. Presuming only a knowledge of the rules of algebra and Euclidean theorems, De Morgan begins with some introductory remarks on the nature and objects of mathematics. He discusses the concept of arithmetical notion and its elementary rules, including arithmetical reactions and decimal fractions. Moving on to algebra, he reviews the elementary principles, examines equations of the first and second degree, and surveys roots and logarithms. De Morgan's book concludes with an exploration of geometrical reasoning that encompasses the formulation and use of axioms, the role of proportion, and the application of algebra to the measurement of lines, angles, the proportion of figures, and surfaces.
This classic work explains the theory and formulas behind Dirichlet's series and offers the first systematic account of Riesz's theory of the summation of series by typical means. Its authors rank among the most distinguished mathematicians of the twentieth century: G. H. Hardy is famous for his achievements in number theory and mathematical analysis, and Marcel Riesz's interests ranged from functional analysis to partial differential equations, mathematical physics, number theory, and algebra. Following an introduction, the authors proceed to a discussion of the elementary theory of the convergence of Dirichlet's series, followed by a look at the formula for the sum of the coefficients of a Dirichlet's series in terms of the order of the function represented by the series. They continue with an examination of the summation of series by typical means and of general arithmetic theorems concerning typical means. After a survey of Abelian and Tauberian theorems and of further developments of the theory of functions represented by Dirichlet's series, the text concludes with an exploration of the multiplication of Dirichlet's series.
A classic 1904 work, Nobel Laureate Ernest Rutherford describes his pioneering experiments with radioactivity. Includes a discussion of radioactive substances, examinations of the ionization theory of gases, methods of measurement, the nature of radiation, and the rate of emission of energy. Also includes properties of radiation, the continuous production of radioactive matter, radioactive emanations, more.
Written by the nineteenth-century French philosophical founder of positivism, this comprehensive map of mathematical science assigns to each part of the complex whole its true position and value.
The distinguished English mathematician, philosopher presents an alternative rendering of the theory of relativity, conceived long after Einstein's original groundbreaking papers; appropriate for upper-level undergraduates and graduate students. 1922 edition.
The author, a Nobel Laureate and one of the 20th century's most important logicians, asks and answers basic questions about the intersection of philosophy and higher mathematics. 1897 edition.
An almost entirely self-taught mathematical genius, George Green (1793 –1841) is best known for Green's theorem, which is used in almost all computer codes that solve partial differential equations. He also published influential essays, or papers, in the fields of hydrodynamics, electricity, and magnetism. This collection comprises his most significant works. The first paper, "An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism," which is also the longest and perhaps the most Important, appeared In 1828. It introduced the term potential as designating the result obtained by adding together the masses of all the particles of a system, each divided by its distance from a given point. Its three-part treatment first considers the properties of this function and then applies them, in the second and third parts, to the theories of magnetism and electricity. The following paper, "Mathematical Investigations concerning the Laws of the Equilibrium of Fluids analogous to the Electric Fluid," exhibits great analytical power, as does the next, "On the Determination of the Exterior and Interior Attractions of Ellipsoids of Variable Densities." Other highlights include the brief but absorbing paper, "On the Motion of Waves in a variable canal of small depth and width," and two of his most valuable memoirs, "On the Laws of Reflexlon and Refraction of Sound" and "On the Reflexlon and Refraction of Light at the common surface of two non-crystallized Media," which should be studied together.
Prized for its extensive coverage of classical material, this text is also well regarded for its unusual fullness of treatment and its comprehensive discussion of both theory and applications. The author developes the theory of elliptic integrals, beginning with formulas establishing the existence, formation, and treatment of all three types, and concluding with the most general description of these integrals in terms of the Riemann surface. The theories of Legendre, Abel, Jacobi, and Weierstrass are developed individually and correlated with the universal laws of Riemann. The important contributory theorems of Hermite and Liouville are also fully developed. 1910 ed.