Applied Exterior Calculus PDF Download

Author: Dominic G. B. Edelen
Publisher: Courier Corporation
ISBN: 0486438716
Category : Mathematics
Languages : en
Pages : 530

View

Book Description
This text begins with the essentials, advancing to applications and studies of physical disciplines, including classical and irreversible thermodynamics, electrodynamics, and the theory of gauge fields. Geared toward advanced undergraduates and graduate students, it develops most of the theory and requires only a familiarity with upper-division algebra and mathematical analysis. "Essential." — SciTech Book News. 1985 edition.

Author: Douglas N. Arnold
Publisher: SIAM
ISBN: 1611975530
Category : Mathematics
Languages : en
Pages : 126

View

Book Description
Computational methods to approximate the solution of differential equations play a crucial role in science, engineering, mathematics, and technology. The key processes that govern the physical world?wave propagation, thermodynamics, fluid flow, solid deformation, electricity and magnetism, quantum mechanics, general relativity, and many more?are described by differential equations. We depend on numerical methods for the ability to simulate, explore, predict, and control systems involving these processes. The finite element exterior calculus, or FEEC, is a powerful new theoretical approach to the design and understanding of numerical methods to solve partial differential equations (PDEs). The methods derived with FEEC preserve crucial geometric and topological structures underlying the equations and are among the most successful examples of structure-preserving methods in numerical PDEs. This volume aims to help numerical analysts master the fundamentals of FEEC, including the geometrical and functional analysis preliminaries, quickly and in one place. It is also accessible to mathematicians and students of mathematics from areas other than numerical analysis who are interested in understanding how techniques from geometry and topology play a role in numerical PDEs.

Author: Leo J. Grady
Publisher: Springer Science & Business Media
ISBN: 1849962901
Category : Computers
Languages : en
Pages : 371

View

Book Description
This unique text brings together into a single framework current research in the three areas of discrete calculus, complex networks, and algorithmic content extraction. Many example applications from several fields of computational science are provided.

Author: William L. Burke
Publisher: Cambridge University Press
ISBN: 9780521269292
Category : Mathematics
Languages : en
Pages : 440

View

Book Description
This is a self-contained introductory textbook on the calculus of differential forms and modern differential geometry. The intended audience is physicists, so the author emphasises applications and geometrical reasoning in order to give results and concepts a precise but intuitive meaning without getting bogged down in analysis. The large number of diagrams helps elucidate the fundamental ideas. Mathematical topics covered include differentiable manifolds, differential forms and twisted forms, the Hodge star operator, exterior differential systems and symplectic geometry. All of the mathematics is motivated and illustrated by useful physical examples.

Author: Lynn Harold Loomis
Publisher: World Scientific Publishing Company
ISBN: 9814583952
Category : Mathematics
Languages : en
Pages : 595

View

Book Description
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.

Author: Yves Talpaert
Publisher: CRC Press
ISBN: 9780824703851
Category : Mathematics
Languages : en
Pages : 480

View

Book Description
An introduction to differential geometry with applications to mechanics and physics. It covers topology and differential calculus in banach spaces; differentiable manifold and mapping submanifolds; tangent vector space; tangent bundle, vector field on manifold, Lie algebra structure, and one-parameter group of diffeomorphisms; exterior differential forms; Lie derivative and Lie algebra; n-form integration on n-manifold; Riemann geometry; and more. It includes 133 solved exercises.

Author: Erdogan Suhubi
Publisher: Elsevier
ISBN: 0124159281
Category : Technology & Engineering
Languages : en
Pages : 780

View

Book Description
Exterior analysis uses differential forms (a mathematical technique) to analyze curves, surfaces, and structures. Exterior Analysis is a first-of-its-kind resource that uses applications of differential forms, offering a mathematical approach to solve problems in defining a precise measurement to ensure structural integrity. The book provides methods to study different types of equations and offers detailed explanations of fundamental theories and techniques to obtain concrete solutions to determine symmetry. It is a useful tool for structural, mechanical and electrical engineers, as well as physicists and mathematicians. - Provides a thorough explanation of how to apply differential equations to solve real-world engineering problems - Helps researchers in mathematics, science, and engineering develop skills needed to implement mathematical techniques in their research - Includes physical applications and methods used to solve practical problems to determine symmetry

Author: R. W. R. Darling
Publisher: Cambridge University Press
ISBN: 9780521468008
Category : Mathematics
Languages : en
Pages : 288

View

Book Description
Introducing the tools of modern differential geometry--exterior calculus, manifolds, vector bundles, connections--this textbook covers both classical surface theory, the modern theory of connections, and curvature. With no knowledge of topology assumed, the only prerequisites are multivariate calculus and linear algebra.

Author: David Lovelock
Publisher: Courier Corporation
ISBN: 048613198X
Category : Mathematics
Languages : en
Pages : 402

View

Book Description
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.

Author: John G. Papastavridis
Publisher: Routledge
ISBN: 1351411616
Category : Mathematics
Languages : en
Pages : 444

View

Book Description
Tensor Calculus and Analytical Dynamics provides a concise, comprehensive, and readable introduction to classical tensor calculus - in both holonomic and nonholonomic coordinates - as well as to its principal applications to the Lagrangean dynamics of discrete systems under positional or velocity constraints. The thrust of the book focuses on formal structure and basic geometrical/physical ideas underlying most general equations of motion of mechanical systems under linear velocity constraints. Written for the theoretically minded engineer, Tensor Calculus and Analytical Dynamics contains uniquely accessbile treatments of such intricate topics as: tensor calculus in nonholonomic variables Pfaffian nonholonomic constraints related integrability theory of Frobenius The book enables readers to move quickly and confidently in any particular geometry-based area of theoretical or applied mechanics in either classical or modern form.