Considerable attention is devoted to physical applications of variational methods, e. G. Canonical equations, variational principles of mechanics, and conservation laws. The reader who merely wishes to become familiar with the most basic concepts and methods of the calculus of variations need only study the first chapter.

Based on a series of lectures given by I. The problems following each chapter were made specially for this English-language edition, and many of them comment further on corresponding parts of the text. Chapter 7 considers the application of variational methods to the study of systems with infinite degrees of freedom, and Chapter 8 deals with direct methods in the calculus of variations.

Gelfand at moscow state University, this book actually goes considerably beyond the material presented in the lectures. Dover Publications. M. Two appendices and suggestions for supplementary reading round out the text. Substantially revised and corrected by the translator, this inexpensive new edition will be welcomed by advanced undergraduate and graduate students of mathematics and physics.

. The aim is to give a treatment of the elements of the calculus of variations in a form both easily understandable and sufficiently modern. Students wishing a more extensive treatment, however, will find the first six chapters comprise a complete university-level course in the subject, including the theory of fields and sufficient conditions for weak and strong extrema.

Well-written, and scholarly, authoritative, Lagrange, this classic treatise begins with an introduction to the variational principles of mechanics including the procedures of Euler, and Hamilton. Ideal for a two-semester graduate course, the book includes a variety of problems, carefully chosen to familiarize the student with new concepts and to illuminate the general principles involved.

Moreover, engineering, or physics who does not intend to specialize in mechanics, it offers excellent grounding for the student of mathematics, but wants a thorough grasp of the underlying principles. The late professor lanczos dublin institute of advanced Studies was a well-known physicist and educator who brought a superb pedagogical sense and profound grasp of the principles of mechanics to this work, now available for the first time in an inexpensive Dover paperback edition.

Unlike many standard textbooks on advanced mechanics, historical, this present text eschews a primarily technical and formalistic treatment in favor of a fundamental, however, philosophical approach. Analytical mechanics is, a topic of perennial interest and usefulness in physics and engineering, of course, a discipline that boasts not only many practical applications, but much inherent mathematical beauty.

.

Each chapter ends with a series of exercises which should prove very useful in determining whether the material in that chapter has been thoroughly grasped. The clarity of exposition makes this book easily accessible to anyone who has mastered first-year calculus with some exposure to ordinary differential equations.

L. I regard this as a very useful book which I shall refer to frequently in the future. J. The author begins slowly, introducing the reader to the calculus of variations, and supplying lists of essential formulae and derivations. Synge, bulletin of the American Mathematical Society. Later chapters cover isoperimetric problems, dynamics of particles, Fermat's principle, geometrical optics, the Sturm-Liouville eigenvalue-eigenfunction problem, quantum mechanics, the theory of elasticity, and electrostatics.

.

Dover Publications. The subject is presented in its simplest, but with many explanatory details, and in a manner that conveys the geometric significance and theoretical and practical importance of the different concepts, figures and examples, most essential form, methods and results involved. The first chapters of the book focus on the basic concepts and facts of analytic geometry, the theory of space curves, and the foundations of the theory of surfaces, including problems closely related to the first and second fundamental forms.

. Problems at the end of each section with solutions at the end of the book will help students meaningfully review the material presented, and familiarize themselves with the manner of reasoning in differential geometry.

This enables the reader to infer generalized principles from concrete situations — departing from the traditional approach to tensors and forms in terms of purely differential-geometric concepts. The treatment of the calculus of variations of single and multiple integrals is based ab initio on Carathéodory's method of equivalent integrals.

The appendix, presents a reformulation of the principal concepts of the main text within the terminology of current global differential geometry, newly revised and enlarged for the Dover edition, thus bridging the gap between classical tensor analysis and the fundamentals of more recent global theories.

Other discussions include:• integral invariants• simple and direct derivations of Noether's theorems• Riemannian spaces with indefinite metricsThe emphasis in this book is on analytical techniques, with abundant problems, ranging from routine manipulative exercises to technically difficult problems encountered by those using tensor techniques in research activities.

A special effort has been made to collect many useful results of a technical nature, not generally discussed in the standard literature. Dover Publications. The aim of this book is to present a self-contained, engineers, adapted to the needs of physicists, reasonably modern account of tensor analysis and the calculus of exterior differential forms, and applied mathematicians.

To give a solid introduction to this burgeoning field, J. Pierce follows the brilliant formulations of Claude Shannon and describes such aspects of the subject as encoding and binary digits, entropy, efficient encoding, language and meaning, and the noisy channel. Uncommonly good. The most satisfying discussion to be found.

Scientific American. Behind the familiar surfaces of the telephone, radio, and television lies a sophisticated and intriguing body of knowledge known as information theory. R. This is the theory that has permitted the rapid development of all sorts of communication, from color television to the clear transmission of photographs from the vicinity of Jupiter.

Beginning with the origins of the field, Dr. Pierce worked for many years at the Bell Telephone Laboratories, where he became Director of Research in Communications Principles.

Dover Publications. In the second chapter professor mendelson discusses metric spaces, paying particular attention to various distance functions which may be defined on Euclidean n-space and which lead to the ordinary topology. The book's principal aim is to provide a simple, or sets, thorough survey of elementary topics in the study of collections of objects, that possess a mathematical structure.

The author begins with an informal discussion of set theory in Chapter 1, reserving coverage of countability for Chapter 5, where it appears in the context of compactness. Mendelson, a former professor of Mathematics at Smith College, has included many challenging and stimulating exercises to help students develop a solid grasp of the material presented.

Throughout the text, Dr. Dover Publications. Highly regarded for its exceptional clarity, imaginative and instructive exercises, and fine writing style, this concise book offers an ideal introduction to the fundamentals of topology. Chapter 3 takes up the concept of topological space, presenting it as a generalization of the concept of a metric space.

.

The book begins with a section that examines the origin of differential equations, defines basic terms and outlines the general solution of a differential equation-the solution that actually contains every solution of such an equation. An elementary college textbook for students of math, engineering and the sciences in general.

. The first includes a discussion of the legendre Differential Equation, Legendre Functions, the Bessel Differential Equation, Legendre Polynomials, and the Laguerre Differential Equation. This unusually well-written, skillfully organized introductory text provides an exhaustive survey of ordinary differential equations — equations which express the relationship between variables and their derivatives.

Throughout the book, every term is clearly defined and every theorem lucidly and thoroughly analyzed, and there is an admirable balance between the theory of differential equations and their application. Dover Publications. An abundance of solved problems and practice exercises enhances the value of Ordinary Differential Equations as a classroom text for undergraduate students and teaching professionals.

The book concludes with an in-depth examination of existence and uniqueness theorems about a variety of differential equations, as well as an introduction to the theory of determinants and theorems about Wronskians.

A stimulating excursion into pure mathematics aimed at "the mathematically traumatized, " but great fun for mathematical hobbyists and serious mathematicians as well. Dover Publications. The topics are so well motivated, the exposition so lucid and delightful, that the book's appeal should be virtually universal.

Exercises are included at the end of each chapter. 1976 edition. Dover Publications. Dover Publications. An elementary college textbook for students of math, engineering and the sciences in general.

Now available for the first time in paperback, this wide-ranging overview also contains an extensive 40-page appendix which provides detailed solutions to the numerous exercises included throughout the text. Students will find no better one-volume coverage of so many essential topics; moreover, elastomers, superconductivity, the book has been substantially revised and updated with additional material on Bessel functions, since its first publication, spherical harmonics, and other subjects.

The first four chapters review mathematical topics needed by theoretical and experimental physicists vector analysis, the calculus of variations, mathematical representation of periodic phenomena, theory of vibrations and waves, theory of functions of a complex variable, and more. Dover Publications. Dover Publications.

. Dover Publications.

He has also added a bibliography, containing suggestions for collateral and supplementary reading. Silverman's series of translations of outstanding Russian textbooks and monographs is well-known to people in the fields of mathematics, physics, and engineering. Dover Publications. A total of 107 problems will be found at the ends of the chapters, including many specially added to this English-language edition, and answers are given at the end of the text.

Dover Publications. An elementary college textbook for students of math, engineering and the sciences in general. 1962 edition. Richard silverman's excellent translation makes this book readily accessible to mathematicians and math students, as well as workers and students in the fields of physics and engineering.

Based on a series of lectures given by I. The problems following each chapter were made specially for this English-language edition, and many of them comment further on corresponding parts of the text. Chapter 7 considers the application of variational methods to the study of systems with infinite degrees of freedom, and Chapter 8 deals with direct methods in the calculus of variations.

Gelfand at moscow state University, this book actually goes considerably beyond the material presented in the lectures. Dover Publications. M. Two appendices and suggestions for supplementary reading round out the text. Substantially revised and corrected by the translator, this inexpensive new edition will be welcomed by advanced undergraduate and graduate students of mathematics and physics.

. The aim is to give a treatment of the elements of the calculus of variations in a form both easily understandable and sufficiently modern. Students wishing a more extensive treatment, however, will find the first six chapters comprise a complete university-level course in the subject, including the theory of fields and sufficient conditions for weak and strong extrema.

# The Variational Principles of Mechanics Dover Books on Physics

His book will be welcomed by students, mathematicians, engineers, physicists, and anyone interested in a clear masterly exposition of this all-important discipline. As the author remarks, there is a tremendous treasure of philosophical meaning" behind the great theories of Euler and Lagrange, Hamilton, Jacobi, and other mathematical thinkers.Well-written, and scholarly, authoritative, Lagrange, this classic treatise begins with an introduction to the variational principles of mechanics including the procedures of Euler, and Hamilton. Ideal for a two-semester graduate course, the book includes a variety of problems, carefully chosen to familiarize the student with new concepts and to illuminate the general principles involved.

Moreover, engineering, or physics who does not intend to specialize in mechanics, it offers excellent grounding for the student of mathematics, but wants a thorough grasp of the underlying principles. The late professor lanczos dublin institute of advanced Studies was a well-known physicist and educator who brought a superb pedagogical sense and profound grasp of the principles of mechanics to this work, now available for the first time in an inexpensive Dover paperback edition.

Unlike many standard textbooks on advanced mechanics, historical, this present text eschews a primarily technical and formalistic treatment in favor of a fundamental, however, philosophical approach. Analytical mechanics is, a topic of perennial interest and usefulness in physics and engineering, of course, a discipline that boasts not only many practical applications, but much inherent mathematical beauty.

.

# Calculus of Variations: with Applications to Physics and Engineering

Physicists and engineers who find variational methods evasive at times will find this book particularly helpful. This book by robert weinstock was written to fill the need for a basic introduction to the calculus of variations. Simply and easily written, with an emphasis on the applications of this calculus, it has long been a standard reference of physicists, engineers, and applied mathematicians.Each chapter ends with a series of exercises which should prove very useful in determining whether the material in that chapter has been thoroughly grasped. The clarity of exposition makes this book easily accessible to anyone who has mastered first-year calculus with some exposure to ordinary differential equations.

L. I regard this as a very useful book which I shall refer to frequently in the future. J. The author begins slowly, introducing the reader to the calculus of variations, and supplying lists of essential formulae and derivations. Synge, bulletin of the American Mathematical Society. Later chapters cover isoperimetric problems, dynamics of particles, Fermat's principle, geometrical optics, the Sturm-Liouville eigenvalue-eigenfunction problem, quantum mechanics, the theory of elasticity, and electrostatics.

.

# Differential Geometry Dover Books on Mathematics

This outstanding textbook by a distinguished mathematical scholar introduces the differential geometry of curves and surfaces in three-dimensional Euclidean space. The treatment of the theory of surfaces makes full use of the tensor calculus. The later chapters address geodesics, mappings of surfaces, special surfaces, and the absolute differential calculus and the displacement of Levi-Cività.Dover Publications. The subject is presented in its simplest, but with many explanatory details, and in a manner that conveys the geometric significance and theoretical and practical importance of the different concepts, figures and examples, most essential form, methods and results involved. The first chapters of the book focus on the basic concepts and facts of analytic geometry, the theory of space curves, and the foundations of the theory of surfaces, including problems closely related to the first and second fundamental forms.

. Problems at the end of each section with solutions at the end of the book will help students meaningfully review the material presented, and familiarize themselves with the manner of reasoning in differential geometry.

# Tensors, Differential Forms, and Variational Principles Dover Books on Mathematics

In the later, increasingly sophisticated chapters, the interaction between the concept of invariance and the calculus of variations is examined. This interaction is of profound importance to all physical field theories. Beginning with simple physical examples, the theory of tensors and forms is developed by a process of successive abstractions.This enables the reader to infer generalized principles from concrete situations — departing from the traditional approach to tensors and forms in terms of purely differential-geometric concepts. The treatment of the calculus of variations of single and multiple integrals is based ab initio on Carathéodory's method of equivalent integrals.

The appendix, presents a reformulation of the principal concepts of the main text within the terminology of current global differential geometry, newly revised and enlarged for the Dover edition, thus bridging the gap between classical tensor analysis and the fundamentals of more recent global theories.

Other discussions include:• integral invariants• simple and direct derivations of Noether's theorems• Riemannian spaces with indefinite metricsThe emphasis in this book is on analytical techniques, with abundant problems, ranging from routine manipulative exercises to technically difficult problems encountered by those using tensor techniques in research activities.

A special effort has been made to collect many useful results of a technical nature, not generally discussed in the standard literature. Dover Publications. The aim of this book is to present a self-contained, engineers, adapted to the needs of physicists, reasonably modern account of tensor analysis and the calculus of exterior differential forms, and applied mathematicians.

# An Introduction to Information Theory: Symbols, Signals and Noise Dover Books on Mathematics

He then goes beyond the strict confines of the topic to explore the ways in which information theory relates to physics, psychology, cybernetics, and art. R. Pierce has revised his well-received 1961 study of information theory for a second edition. Even more revolutionary progress is expected in the future.To give a solid introduction to this burgeoning field, J. Pierce follows the brilliant formulations of Claude Shannon and describes such aspects of the subject as encoding and binary digits, entropy, efficient encoding, language and meaning, and the noisy channel. Uncommonly good. The most satisfying discussion to be found.

Scientific American. Behind the familiar surfaces of the telephone, radio, and television lies a sophisticated and intriguing body of knowledge known as information theory. R. This is the theory that has permitted the rapid development of all sorts of communication, from color television to the clear transmission of photographs from the vicinity of Jupiter.

Beginning with the origins of the field, Dr. Pierce worked for many years at the Bell Telephone Laboratories, where he became Director of Research in Communications Principles.

# Introduction to Topology: Third Edition Dover Books on Mathematics

Originally conceived as a text for a one-semester course, it is directed to undergraduate students whose studies of calculus sequence have included definitions and proofs of theorems. Chapters 4 and 5 are devoted to a discussion of the two most important topological properties: connectedness and compactness.Dover Publications. In the second chapter professor mendelson discusses metric spaces, paying particular attention to various distance functions which may be defined on Euclidean n-space and which lead to the ordinary topology. The book's principal aim is to provide a simple, or sets, thorough survey of elementary topics in the study of collections of objects, that possess a mathematical structure.

The author begins with an informal discussion of set theory in Chapter 1, reserving coverage of countability for Chapter 5, where it appears in the context of compactness. Mendelson, a former professor of Mathematics at Smith College, has included many challenging and stimulating exercises to help students develop a solid grasp of the material presented.

Throughout the text, Dr. Dover Publications. Highly regarded for its exceptional clarity, imaginative and instructive exercises, and fine writing style, this concise book offers an ideal introduction to the fundamentals of topology. Chapter 3 takes up the concept of topological space, presenting it as a generalization of the concept of a metric space.

.

# Ordinary Differential Equations Dover Books on Mathematics

Dover Publications. In a disarmingly simple, step-by-step style that never sacrifices mathematical rigor, critically-important concepts to undergraduate students of mathematics, and Harry Pollard of Purdue University — introduce and explain complex, the authors — Morris Tenenbaum of Cornell University, engineering and the sciences.The book begins with a section that examines the origin of differential equations, defines basic terms and outlines the general solution of a differential equation-the solution that actually contains every solution of such an equation. An elementary college textbook for students of math, engineering and the sciences in general.

. The first includes a discussion of the legendre Differential Equation, Legendre Functions, the Bessel Differential Equation, Legendre Polynomials, and the Laguerre Differential Equation. This unusually well-written, skillfully organized introductory text provides an exhaustive survey of ordinary differential equations — equations which express the relationship between variables and their derivatives.

Throughout the book, every term is clearly defined and every theorem lucidly and thoroughly analyzed, and there is an admirable balance between the theory of differential equations and their application. Dover Publications. An abundance of solved problems and practice exercises enhances the value of Ordinary Differential Equations as a classroom text for undergraduate students and teaching professionals.

The book concludes with an in-depth examination of existence and uniqueness theorems about a variety of differential equations, as well as an introduction to the theory of determinants and theorems about Wronskians.

# Introduction to Graph Theory Dover Books on Mathematics

Requiring only high school algebra as mathematical background, Euler's formula, the book leads the reader from simple graphs through planar graphs, Platonic graphs, Euler walks, coloring, Hamilton walks, the genus of a graph, and a discussion of The Seven Bridges of Konigsberg. Every library should have several copies" — Choice.A stimulating excursion into pure mathematics aimed at "the mathematically traumatized, " but great fun for mathematical hobbyists and serious mathematicians as well. Dover Publications. The topics are so well motivated, the exposition so lucid and delightful, that the book's appeal should be virtually universal.

Exercises are included at the end of each chapter. 1976 edition. Dover Publications. Dover Publications. An elementary college textbook for students of math, engineering and the sciences in general.

# Theoretical Physics Dover Books on Physics

Although first published over 50 years ago, comprehensive survey, the book remains a solid, so well written and carefully planned that undergraduates as well as graduate students of theoretical and experimental physics will find it an indispensable reference they will turn to again and again. This material is followed by exhaustive coverage of mechanics including elasticity and fluid mechanics, kinetic theory and statistical mechanics, a highly detailed treatment of electromagnetic theory, and thorough discussions of thermodynamics, as well as relativistic mechanics, quantum mechanics and nuclear physics.Now available for the first time in paperback, this wide-ranging overview also contains an extensive 40-page appendix which provides detailed solutions to the numerous exercises included throughout the text. Students will find no better one-volume coverage of so many essential topics; moreover, elastomers, superconductivity, the book has been substantially revised and updated with additional material on Bessel functions, since its first publication, spherical harmonics, and other subjects.

The first four chapters review mathematical topics needed by theoretical and experimental physicists vector analysis, the calculus of variations, mathematical representation of periodic phenomena, theory of vibrations and waves, theory of functions of a complex variable, and more. Dover Publications. Dover Publications.

. Dover Publications.

# Fourier Series Dover Books on Mathematics

Richard A. Every chapter moves clearly from topic to topic and theorem to theorem, with many theorem proofs given. Dover Publications. The present book is another excellent text from this series, a valuable addition to the English-language literature on Fourier series. This edition is organized into nine well-defined chapters: trigonometric fourier series, operations on Fourier Series, Trigonometric Series with Decreasing Coefficients, Bessel Functions and Fourier-Bessel Series, Orthogonal Systems, Summation of Trigonometric Fourier Series, Double Fourier Series and the Fourier Integral, Convergence of Trigonometric Fourier Series, and the Eigenfunction Method and its Applications to Mathematical Physics.He has also added a bibliography, containing suggestions for collateral and supplementary reading. Silverman's series of translations of outstanding Russian textbooks and monographs is well-known to people in the fields of mathematics, physics, and engineering. Dover Publications. A total of 107 problems will be found at the ends of the chapters, including many specially added to this English-language edition, and answers are given at the end of the text.

Dover Publications. An elementary college textbook for students of math, engineering and the sciences in general. 1962 edition. Richard silverman's excellent translation makes this book readily accessible to mathematicians and math students, as well as workers and students in the fields of physics and engineering.