Tensors Differential Forms and Variational Principles

Author: David Lovelock
Publisher: Courier Corporation
ISBN: 9780486131986
Release Date: 2012-04-20
Genre: Mathematics

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.

Tensors Differential Forms and Variational Principles

Author: David Lovelock
Publisher: Courier Corporation
ISBN: 9780486658407
Release Date: 1975
Genre: Mathematics

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, with large number of problems, from routine manipulative exercises to technically difficult assignments.

The Variational Principles of Mechanics

Author: Cornelius Lanczos
Publisher: Courier Corporation
ISBN: 9780486134703
Release Date: 2012-04-24
Genre: Science

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 Analysis on Manifolds

Author: Richard L. Bishop
Publisher: Courier Corporation
ISBN: 9780486139234
Release Date: 2012-04-26
Genre: Mathematics

DIVProceeds from general to special, including chapters on vector analysis on manifolds and integration theory. /div

Vector and Tensor Analysis with Applications

Author: A. I. Borisenko
Publisher: Courier Corporation
ISBN: 9780486131900
Release Date: 2012-08-28
Genre: Mathematics

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.

Tensor and Vector Analysis

Author: C. E. Springer
Publisher: Courier Corporation
ISBN: 9780486320915
Release Date: 2013-09-26
Genre: Mathematics

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.

Calculus of Variations

Author: I. M. Gelfand
Publisher: Courier Corporation
ISBN: 9780486135014
Release Date: 2012-04-26
Genre: Mathematics

Fresh, lively text serves as a modern introduction to the subject, with applications to the mechanics of systems with a finite number of degrees of freedom. Ideal for math and physics students.

Differential Geometry

Author: Erwin Kreyszig
Publisher: Courier Corporation
ISBN: 9780486318622
Release Date: 2013-04-26
Genre: Mathematics

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.

Partial Differential Equations of Mathematical Physics

Author: S. L. Sobolev
Publisher: Courier Corporation
ISBN: 048665964X
Release Date: 1964
Genre: Science

This volume presents an unusually accessible introduction to equations fundamental to the investigation of waves, heat conduction, hydrodynamics, and other physical problems. Topics include derivation of fundamental equations, Riemann method, equation of heat conduction, theory of integral equations, Green's function, and much more. The only prerequisite is a familiarity with elementary analysis. 1964 edition.

Differential Forms

Author: M. Schreiber
Publisher: Springer Science & Business Media
ISBN: 9781461299400
Release Date: 2012-12-06
Genre: Mathematics

A working knowledge of differential forms so strongly illuminates the calculus and its developments that it ought not be too long delayed in the curriculum. On the other hand, the systematic treatment of differential forms requires an apparatus of topology and algebra which is heavy for beginning undergraduates. Several texts on advanced calculus using differential forms have appeared in recent years. We may cite as representative of the variety of approaches the books of Fleming [2], (1) Nickerson-Spencer-Steenrod [3], and Spivak [6]. . Despite their accommodation to the innocence of their readers, these texts cannot lighten the burden of apparatus exactly because they offer a more or less full measure of the truth at some level of generality in a formally precise exposition. There. is consequently a gap between texts of this type and the traditional advanced calculus. Recently, on the occasion of offering a beginning course of advanced calculus, we undertook the expe- ment of attempting to present the technique of differential forms with minimal apparatus and very few prerequisites. These notes are the result of that experiment. Our exposition is intended to be heuristic and concrete. Roughly speaking, we take a differential form to be a multi-dimensional integrand, such a thing being subject to rules making change-of-variable calculations automatic. The domains of integration (manifolds) are explicitly given "surfaces" in Euclidean space. The differentiation of forms (exterior (1) Numbers in brackets refer to the Bibliography at the end.

Gauge Theory and Variational Principles

Author: David Bleecker
Publisher: Courier Corporation
ISBN: 9780486151878
Release Date: 2013-01-18
Genre: Science

Covers principal fiber bundles and connections; curvature; particle fields, Lagrangians, and gauge invariance; inhomogeneous field equations; free Dirac electron fields; calculus on frame bundle; and unification of gauge fields and gravitation. 1981 edition

An Introduction to the Calculus of Variations

Author: Charles Fox
Publisher: Courier Corporation
ISBN: 0486654990
Release Date: 1950
Genre: Mathematics

In this highly regarded text for advanced undergraduate and graduate students, the author develops the calculus of variations both for its intrinsic interest and for its powerful applications to modern mathematical physics. Topics include first and second variations of an integral, generalizations, isoperimetrical problems, least action, special relativity, elasticity, more. 1963 edition.

Analysis and Algebra on Differentiable Manifolds

Author: Pedro M. Gadea
Publisher: Springer Science & Business Media
ISBN: 9789400759527
Release Date: 2012-12-30
Genre: Mathematics

This is the second edition of this best selling problem book for students, now containing over 400 completely solved exercises on differentiable manifolds, Lie theory, fibre bundles and Riemannian manifolds. The exercises go from elementary computations to rather sophisticated tools. Many of the definitions and theorems used throughout are explained in the first section of each chapter where they appear. A 56-page collection of formulae is included which can be useful as an aide-mémoire, even for teachers and researchers on those topics. In this 2nd edition: • 76 new problems • a section devoted to a generalization of Gauss’ Lemma • a short novel section dealing with some properties of the energy of Hopf vector fields • an expanded collection of formulae and tables • an extended bibliography Audience This book will be useful to advanced undergraduate and graduate students of mathematics, theoretical physics and some branches of engineering with a rudimentary knowledge of linear and multilinear algebra.

Curvature in Mathematics and Physics

Author: Shlomo Sternberg
Publisher: Courier Corporation
ISBN: 9780486292717
Release Date: 2013-04-17
Genre: Mathematics

Expert treatment introduces semi-Riemannian geometry and its principal physical application, Einstein's theory of general relativity, using the Cartan exterior calculus as a principal tool. Prerequisites include linear algebra and advanced calculus. 2012 edition.