The Absolute Differential Calculus

Calculus of Tensors
Author: Tullio Levi-Civita
Publisher: Dover Publications
ISBN: 9780486446370
Category: Mathematics
Page: 452
View: 1319

Continue Reading →

A chief requirement in the study of relativity is knowledge of the absolute differential calculus, the subject that Einstein found necessary for developing his ideas mathematically. Tullio Levi-Civita was one of the founders of this field of mathematics, and he presents a clear, detailed exposition of the subject in this classic book. The first section of the three-part treatment examines functional determinants and matrices; systems of total differential equations; linear partial differential equations in complete systems; and algebraic foundations of the absolute differential calculus, concluding with a geometrical introduction to the theory of differential quadratic forms. Part two, a study of the fundamental quadratic form and the absolute differential calculus, focuses on covariant differentiation, invariants and differential parameters, and locally geodesic coordinates; Riemann's symbols and properties relating to curvature, Ricci's and Einstein's symbols, and geodesic deviation; relations between two different metrics referred to the same parameters, manifolds of constant curvature; and differential quadratic forms of class zero and class one; and some applications of intrinsic geometry. The third and final section explores physical applications, including the evolution of mechanics and geometrical optics and their relation to a four-dimensional world according to Einstein; and gravitational equations and general relativity.

The Absolute Differential Calculus (Calculus of Tensors)


Author: Tullio Levi-Civita
Publisher: Courier Corporation
ISBN: 0486316254
Category: Mathematics
Page: 452
View: 2985

Continue Reading →

Written by a distinguished mathematician, this classic examines the mathematical material necessary for a grasp of relativity theory. Covers introductory theories, fundamental quadratic forms, absolute differential calculus, and physical applications. 1926 edition.

Tensor Calculus


Author: J. L. Synge,A. Schild
Publisher: Courier Corporation
ISBN: 048614139X
Category: Mathematics
Page: 336
View: 1168

Continue Reading →

Fundamental introduction of absolute differential calculus and for those interested in applications of tensor calculus to mathematical physics and engineering. Topics include spaces and tensors; basic operations in Riemannian space, curvature of space, more.

Tensor and Vector Analysis

With Applications to Differential Geometry
Author: C. E. Springer
Publisher: Courier Corporation
ISBN: 048632091X
Category: Mathematics
Page: 256
View: 4075

Continue Reading →

Assuming only a knowledge of basic calculus, this text's elementary development of tensor theory focuses on concepts related to vector analysis. The book also forms an introduction to metric differential geometry. 1962 edition.

Tensors, Differential Forms, and Variational Principles


Author: David Lovelock,Hanno Rund
Publisher: Courier Corporation
ISBN: 048613198X
Category: Mathematics
Page: 400
View: 4062

Continue Reading →

Incisive, self-contained account of tensor analysis and the calculus of exterior differential forms, interaction between the concept of invariance and the calculus of variations. Emphasis is on analytical techniques. Includes problems.

Vector and Tensor Analysis with Applications


Author: A. I. Borisenko,I. E. Tarapov
Publisher: Courier Corporation
ISBN: 0486131904
Category: Mathematics
Page: 288
View: 3042

Continue Reading →

Concise, readable text ranges from definition of vectors and discussion of algebraic operations on vectors to the concept of tensor and algebraic operations on tensors. Worked-out problems and solutions. 1968 edition.

Applications of Tensor Analysis


Author: A J McConnell
Publisher: N.A
ISBN: 9781614276890
Category: Mathematics
Page: 332
View: 8631

Continue Reading →

2014 Reprint of 1957 Edition. Full facsimile of the original edition. Not reproduced with Optical Recognition Software. Formerly entitled "Applications of the Absolute Differential Calculus," this work applies tensorial methods to subjects within the realm of advanced college mathematics. In four major divisions, it explains the fundamental ideas and notation of tensor theory; covers the geometrical treatment of tensor algebra; introduces the theory of the differentiation of tensors; and applies mathematics to dynamics, electricity, elasticity and hydrodynamics.

Elements of Tensor Calculus


Author: A. Lichnerowicz
Publisher: Courier Dover Publications
ISBN: 0486805174
Category: Mathematics
Page: 176
View: 4841

Continue Reading →

Part I: rigorous presentation of tensor calculus as a develoment of vector analysis. Part II: important applications of tensor calculus. Concluding section: field equations of general relativity theory. 1962 edition.

The Concept of a Riemann Surface


Author: Hermann Weyl
Publisher: Courier Corporation
ISBN: 048613167X
Category: Mathematics
Page: 208
View: 6961

Continue Reading →

This classic on the general history of functions combines function theory and geometry, forming the basis of the modern approach to analysis, geometry, and topology. 1955 edition.

Tensor Analysis for Physicists


Author: Jan Arnoldus Schouten
Publisher: Courier Corporation
ISBN: 0486655822
Category: Science
Page: 277
View: 6130

Continue Reading →

This rigorous and advanced mathematical explanation of classic tensor analysis was written by one of the founders of tensor calculus. Its concise exposition of the mathematical basis of the discipline is integrated with well-chosen physical examples of the theory, including those involving elasticity, classical dynamics, relativity, and Dirac's matrix calculus. 1954 edition.

Differential Geometry


Author: Erwin Kreyszig
Publisher: Courier Corporation
ISBN: 0486318621
Category: Mathematics
Page: 384
View: 3030

Continue Reading →

An introductory textbook on the differential geometry of curves and surfaces in 3-dimensional Euclidean space, presented in its simplest, most essential form. With problems and solutions. Includes 99 illustrations.

Applications of Tensor Analysis


Author: A. J. McConnell
Publisher: Courier Corporation
ISBN: 0486603733
Category: Mathematics
Page: 318
View: 1205

Continue Reading →

Standard work applies tensorial methods to subjects within realm of advanced college mathematics. Text explains fundamental ideas and notation of tensor theory; covers geometrical treatment of tensor algebra; introduces theory of differentiation of tensors; and applies mathematics to dynamics, electricity, elasticity and hydrodynamics. 685 exercises, most with answers.

Representations of the Rotation and Lorentz Groups and Their Applications


Author: I. M. Gelfand, R. A. Minlos,Z. Ya. Shapiro
Publisher: Courier Dover Publications
ISBN: 0486823857
Category: Mathematics
Page: 384
View: 510

Continue Reading →

This monograph on the description and study of representations of the rotation group of three-dimensional space and of the Lorentz group features advanced topics and techniques crucial to many areas of modern theoretical physics. Prerequisites include a familiarity with the differential and integral calculus of several variables and the fundamentals of linear algebra. Suitable for advanced undergraduate and graduate students in mathematical physics, the book is also designed for mathematicians studying the representations of Lie groups, for whom it can serve as an introduction to the general theory of representation. The treatment encompasses all the basic material of the theory of representations used in quantum mechanics. The two-part approach begins with representations of the group of rotations of three-dimensional space, analyzing the rotation group and its representations. The second part, covering representations of the Lorentz group, includes an exploration of relativistic-invariant equations. The text concludes with three helpful supplements and a bibliography.

An Introduction to Differential Geometry


Author: T. J. Willmore
Publisher: Courier Corporation
ISBN: 0486282104
Category: Mathematics
Page: 336
View: 5866

Continue Reading →

This text employs vector methods to explore the classical theory of curves and surfaces. Topics include basic theory of tensor algebra, tensor calculus, calculus of differential forms, and elements of Riemannian geometry. 1959 edition.

The Variational Principles of Mechanics


Author: Cornelius Lanczos
Publisher: Courier Corporation
ISBN: 0486134709
Category: Science
Page: 464
View: 5853

Continue Reading →

Philosophic, less formalistic approach to analytical mechanics offers model of clear, scholarly exposition at graduate level with coverage of basics, calculus of variations, principle of virtual work, equations of motion, more.

Tensor Calculus

A Concise Course
Author: Barry Spain
Publisher: Courier Corporation
ISBN: 0486428311
Category: Mathematics
Page: 125
View: 4646

Continue Reading →

A compact exposition of the theory of tensors, this text also illustrates the power of the tensor technique by its applications to differential geometry, elasticity, and relativity. Explores tensor algebra, the line element, covariant differentiation, geodesics and parallelism, and curvature tensor. Also covers Euclidean 3-dimensional differential geometry, Cartesian tensors and elasticity, and the theory of relativity. 1960 edition.

Mathematical Analysis

An Introduction
Author: Andrew Browder
Publisher: Springer Science & Business Media
ISBN: 1461207150
Category: Mathematics
Page: 335
View: 7295

Continue Reading →

Among the traditional purposes of such an introductory course is the training of a student in the conventions of pure mathematics: acquiring a feeling for what is considered a proof, and supplying literate written arguments to support mathematical propositions. To this extent, more than one proof is included for a theorem - where this is considered beneficial - so as to stimulate the students' reasoning for alternate approaches and ideas. The second half of this book, and consequently the second semester, covers differentiation and integration, as well as the connection between these concepts, as displayed in the general theorem of Stokes. Also included are some beautiful applications of this theory, such as Brouwer's fixed point theorem, and the Dirichlet principle for harmonic functions. Throughout, reference is made to earlier sections, so as to reinforce the main ideas by repetition. Unique in its applications to some topics not usually covered at this level.

Essential Calculus with Applications


Author: Richard A. Silverman
Publisher: Courier Corporation
ISBN: 0486318591
Category: Mathematics
Page: 320
View: 1948

Continue Reading →

Calculus is an extremely powerful tool for solving a host of practical problems in fields as diverse as physics, biology, and economics, to mention just a few. In this rigorous but accessible text, a noted mathematician introduces undergraduate-level students to the problem-solving techniques that make a working knowledge of calculus indispensable for any mathematician. The author first applies the necessary mathematical background, including sets, inequalities, absolute value, mathematical induction, and other "precalculus" material. Chapter Two begins the actual study of differential calculus with a discussion of the key concept of function, and a thorough treatment of derivatives and limits. In Chapter Three differentiation is used as a tool; among the topics covered here are velocity, continuous and differentiable functions, the indefinite integral, local extrema, and concrete optimization problems. Chapter Four treats integral calculus, employing the standard definition of the Riemann integral, and deals with the mean value theorem for integrals, the main techniques of integration, and improper integrals. Chapter Five offers a brief introduction to differential equations and their applications, including problems of growth, decay, and motion. The final chapter is devoted to the differential calculus of functions of several variables. Numerous problems and answers, and a newly added section of "Supplementary Hints and Answers," enable the student to test his grasp of the material before going on. Concise and well written, this text is ideal as a primary text or as a refresher for anyone wishing to review the fundamentals of this crucial discipline.

Foundations of Mathematical Analysis


Author: Richard Johnsonbaugh,W.E. Pfaffenberger
Publisher: Courier Corporation
ISBN: 0486134776
Category: Mathematics
Page: 448
View: 697

Continue Reading →

Definitive look at modern analysis, with views of applications to statistics, numerical analysis, Fourier series, differential equations, mathematical analysis, and functional analysis. More than 750 exercises; some hints and solutions. 1981 edition.

Advanced Calculus

Revised
Author: Lynn Harold Loomis,Shlomo Sternberg
Publisher: World Scientific Publishing Company
ISBN: 9814583952
Category: Mathematics
Page: 596
View: 4828

Continue Reading →

An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades. This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis. The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives. In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds.