Categories: MATHEMATICS & SCIENC

ADVANCED CALCULUS

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This classic text by a distinguished mathematician and former Professor of Mathematics at Harvard University, leads students familiar with elementary calculus into confronting and solving more theoretical problems of advanced calculus. In his preface to the first edition, Professor Widder also recommends various ways the book may be used as a text in both applied mathematics and engineering.Believing that clarity of exposition depends largely on precision of statement, the author has taken pains to state exactly what is to be proved in every case. Each section consists of definitions, theorems, proofs, examples and exercises. An effort has been made to make the statement of each theorem so concise that the student can see at a glance the essential hypotheses and conclusions.

THE ELEMENTARY THEORY OF ANALYTIC FUNCTIONS

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Noted mathematician offers basic treatment of theory of analytic functions of a complex variable, touching on analytic functions of several real or complex variables as well as the existence theorem for solutions of differential systems where data is analytic. Also included is a systematic, though elementary, exposition of theory of abstract complex manifolds of one complex dimension.Topics include power series in one variable, holomorphic functions, Cauchy’s integral, more. Exercises. 1973 edition.

FUNDAMENTALS OF THE THEORY OF METALS

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This comprehensive primer by a Nobel Physicist covers the electronic spectra of metals, electrical and thermal conductivities, galvanomagnetic and thermoelectrical phenomena, the behavior of metals in high-frequency fields, sound absorption, and Fermi-liquid phenomena. Addressing in detail all aspects of the energy spectra of electrons in metals and the theory of superconductivity, it continues to be a valuable resource for the field almost thirty years after its initial publication.Targeted at undergraduate students majoring in physics as well as graduate and postgraduate students, research workers, and teachers, this is an essential reference on the topic of electromagnetism and superconductivity in metals. No special knowledge of metals beyond a course in general physics is needed, although the author does presume a knowledge of quantum mechanics and quantum statistics.

COMPLEX VARIABLE METHODS IN ELASTIC

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The plane strain and generalized plane stress boundary value problems of linear elasticity are the focus of this graduate-level text, which formulates and solves these problems by employing complex variable theory. The text presents detailed descriptions of the three basic methods that rely on series representation, Cauchy integral representation, and the solution via continuation. Its five-part treatment covers functions of a complex variable, the basic equations of two-dimensional elasticity, plane and half-plane problems, regions with circular boundaries, and regions with curvilinear boundaries. Worked examples and sets of problems appear throughout the text. 1971 edition. 26 figures.

ELEMENTS OF THE THEORY OF FUNCTIONS

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Originally published in two volumes, this advanced-level text is based on courses and lectures given by the authors at Moscow State University and the University of Moscow.Reprinted here in one volume, the first part is devoted to metric and normal spaces. Beginning with a brief introduction to set theory and mappings, the authors offer a clear presentation of the theory of metric and complete metric spaces. The principle of contraction mappings and its applications to the proof of existence theorems in the theory of differential and integral equations receives detailed analysis, as do continuous curves in metric spaces — a topic seldom discussed in textbooks.Part One also includes discussions of other subjects, such as elements of the theory of normed linear spaces, weak sequential convergence of elements and linear functionals, adjoint operators, and linear operator equations. Part Two focuses on an exposition of measure theory, the Lebesque interval and Hilbert Space. Both parts feature numerous exercises at the end of each section and include helpful lists of symbols, definitions, and theorems.One-volume reprint of the two-volume edition published by the Graylock Press, Rochester, New York, 1957.

Studies in the Theory of Random Processes

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This text is devoted to the development of certain probabilistic methods in the specific field of stochastic differential equations and limit theorems for Markov processes. Specialists, researchers, and students in the field of probability will find it a source of important theorems as well as a remarkable amount of advanced material in compact form.The treatment begins by introducing the basic facts of the theory of random processes and constructing the auxiliary apparatus of stochastic integrals. All proofs are presented in full. Succeeding chapters explore the theory of stochastic differential equations, permitting the construction of a broad class of Markov processes on the basis of simple processes. The final chapters are devoted to various limit theorems connected with the convergence of a sequence of Markov chains to a Markov process with continuous time. Topics include the probability method of estimating how fast the sequence converges in the limit theorems and the precision of the limit theorems.

HANDBOOK OF MATHEMATICAL FUNCTIONS

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Despite the increasing use of computers, the basic need for mathematical tables continues. Tables serve a vital role in preliminary surveys of problems before programming for machine operation, and they are indispensable to thousands of engineers and scientists without access to machines. Because of automatic computers, however, and because of recent scientific advances, a greater variety of functions and a higher accuracy of tabulation than have been available until now are required.In 1954, a conference on mathematical tables, sponsored by M.I.T. and the National Science Foundation, met to discuss a modernization and extension of Jahnke and Emde's classical tables of functions. This volume, published 10 years later by the U.S. Department of Commerce, is the result. Designed to include a maximum of information and to meet the needs of scientists in all fields, it is a monumental piece of work, a comprehensive and self-contained summary of the mathematical functions that arise in physical and engineering problems.

ABRIKOSOV-METHODS OF QUANTUM FIELD THEOR

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Lucidly written and systematic in treatment, this book is a prominent work on many-body theory and its ramifications. Written by three members of the Institute for Physical Problems of the Academy of Sciences of the U.S.S.R., this work has been translated and revised by editor Richard A. Silverman, noted for his many translations of Russian works in the mathematical sciences.Using Green's functions for their basic methodological approach, the authors develop their material in seven connected chapters. The first chapter contains a preliminary discussion of several basic topics, including elementary excitations, the Fermi liquid, and second quantization. Chapters 2 and 3 present parallel methods of quantum field theory for T=O and T≠O, both involving the diagram technique. The final four chapters apply the technique and other information learned here to a discussion of the theory of the Fermi liquid, systems of interacting bosons, electromagnetic radiation in an absorbing medium, and the theory of superconductivity. Among the topics considered in these final chapters are electron-photon interactions, some properties of a degenerate plasma, the dilute nonideal Bose gas, properties of the spectrum of one-particle excitations near the cutoff point, molecular interaction forces, the basic system of equations for a superconductor, and the theory of superconducting alloys.

WHY SCIENCE DOES NOT DISPROVE GOD

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The renowned science writer, mathematician, and bestselling author of Fermat's Last Theorem masterfully refutes the overreaching claims the 'New Atheists,' providing millions of educated believers with a clear, engaging explanation of what science really says, how there's still much space for the Divine in the universe, and why faith in both God and empirical science are not mutually exclusive.A highly publicized coterie of scientists and thinkers, including Richard Dawkins, the late Christopher Hitchens, and Lawrence Krauss, have vehemently contended that breakthroughs in modern science have disproven the existence of God, asserting that we must accept that the creation of the universe came out of nothing, that religion is evil, that evolution fully explains the dazzling complexity of life, and more. In this much-needed book, science journalist Amir Aczel profoundly disagrees and conclusively demonstrates that science has not, as yet, provided any definitive proof refuting the existence of God.Why Science Does Not Disprove God is his brilliant and incisive analyses of the theories and findings of such titans as Albert Einstein, Roger Penrose, Alan Guth, and Charles Darwin, all of whose major breakthroughs leave open the possibility-- and even the strong likelihood--of a Creator. Bolstering his argument, Aczel lucidly discourses on arcane aspects of physics to reveal how quantum theory, the anthropic principle, the fine-tuned dance of protons and quarks, the existence of anti-matter and the theory of parallel universes, also fail to disprove God.

CLASSICAL MOMENT PROBLEM: AND SOME RELATED QUESTIONS IN ANAL

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The moment problem in mathematics focuses on a measure within a sequence over a temporal period. Issues associated with the moment problem involve probability theory as a measure of mean, variance, and so on.This text, written by a leading Soviet mathematician, provides a classic treatment of such topics that also involve:Linear algebra,Probability theory,Stochastic processes,Quantum fields,Signal processing and other related subjects.The treatment, which derives from lectures delivered by the author at Kharkov University, addresses infinite Jacobi matrices and their associated polynomials, the power moment problem, function theoretic methods in the moment problem, inclusion of the power moment problem in the spectral theory of operators, and trigonmetric and continuous analogies.