Methods of Differential Geometry in Analytical Mechanics PDF Download

Author: M. de León
Publisher: Elsevier
ISBN: 0080872697
Category : Science
Languages : en
Pages : 495

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Book Description
The differential geometric formulation of analytical mechanics not only offers a new insight into Mechanics, but also provides a more rigorous formulation of its physical content from a mathematical viewpoint.Topics covered in this volume include differential forms, the differential geometry of tangent and cotangent bundles, almost tangent geometry, symplectic and pre-symplectic Lagrangian and Hamiltonian formalisms, tensors and connections on manifolds, and geometrical aspects of variational and constraint theories.The book may be considered as a self-contained text and only presupposes that readers are acquainted with linear and multilinear algebra as well as advanced calculus.

Author: Allan Struthers
Publisher: Springer
ISBN: 3030205061
Category : Technology & Engineering
Languages : en
Pages : 514

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Book Description
This book is designed to serve as a textbook for a course on ordinary differential equations, which is usually a required course in most science and engineering disciplines and follows calculus courses. The book begins with linear algebra, including a number of physical applications, and goes on to discuss first-order differential equations, linear systems of differential equations, higher order differential equations, Laplace transforms, nonlinear systems of differential equations, and numerical methods used in solving differential equations. The style of presentation of the book ensures that the student with a minimum of assistance may apply the theorems and proofs presented. Liberal use of examples and homework problems aids the student in the study of the topics presented and applying them to numerous applications in the real scientific world. This textbook focuses on the actual solution of ordinary differential equations preparing the student to solve ordinary differential equations when exposed to such equations in subsequent courses in engineering or pure science programs. The book can be used as a text in a one-semester core course on differential equations, alternatively it can also be used as a partial or supplementary text in intensive courses that cover multiple topics including differential equations.

Author: Dr. Praveen Saraswat
Publisher: Thakur Publication Private Limited
ISBN: 9354801382
Category : Education
Languages : en
Pages : 392

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Book Description
Buy Latest e-books on "Differential Calculus & Integral Calculus" for B.Sc. 1st Sem (Maths Boo) especially designed for U.P. State universities by Thakur Publication

Author: Wolfgang Bertram
Publisher: American Mathematical Soc.
ISBN: 0821840916
Category : Mathematics
Languages : en
Pages : 218

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Book Description
The aim of this work is to lay the foundations of differential geometry and Lie theory over the general class of topological base fields and -rings for which a differential calculus has been developed, without any restriction on the dimension or on the characteristic. Two basic features distinguish the author's approach from the classical real (finite or infinite dimensional) theory, namely the interpretation of tangent- and jet functors as functors of scalar extensions and the introduction of multilinear bundles and multilinear connections which generalize the concept of vector bundles and linear connections.

Author: Joseph L. McCauley
Publisher: Cambridge University Press
ISBN: 1107328136
Category : Business & Economics
Languages : en
Pages : 219

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Book Description
Stochastic calculus provides a powerful description of a specific class of stochastic processes in physics and finance. However, many econophysicists struggle to understand it. This book presents the subject simply and systematically, giving graduate students and practitioners a better understanding and enabling them to apply the methods in practice. The book develops Ito calculus and Fokker–Planck equations as parallel approaches to stochastic processes, using those methods in a unified way. The focus is on nonstationary processes, and statistical ensembles are emphasized in time series analysis. Stochastic calculus is developed using general martingales. Scaling and fat tails are presented via diffusive models. Fractional Brownian motion is thoroughly analyzed and contrasted with Ito processes. The Chapman–Kolmogorov and Fokker–Planck equations are shown in theory and by example to be more general than a Markov process. The book also presents new ideas in financial economics and a critical survey of econometrics.

Author: Dipankar De
Publisher: John Wiley & Sons
ISBN: 1119795621
Category : Mathematics
Languages : en
Pages : 516

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Book Description
INTRODUCTION TO DIFFERENTIAL GEOMETRY WITH TENSOR APPLICATIONS This is the only volume of its kind to explain, in precise and easy-to-understand language, the fundamentals of tensors and their applications in differential geometry and analytical mechanics with examples for practical applications and questions for use in a course setting. Introduction to Differential Geometry with Tensor Applications discusses the theory of tensors, curves and surfaces and their applications in Newtonian mechanics. Since tensor analysis deals with entities and properties that are independent of the choice of reference frames, it forms an ideal tool for the study of differential geometry and also of classical and celestial mechanics. This book provides a profound introduction to the basic theory of differential geometry: curves and surfaces and analytical mechanics with tensor applications. The author has tried to keep the treatment of the advanced material as lucid and comprehensive as possible, mainly by including utmost detailed calculations, numerous illustrative examples, and a wealth of complementing exercises with complete solutions making the book easily accessible even to beginners in the field. Groundbreaking and thought-provoking, this volume is an outstanding primer for modern differential geometry and is a basic source for a profound introductory course or as a valuable reference. It can even be used for self-study, by students or by practicing engineers interested in the subject. Whether for the student or the veteran engineer or scientist, Introduction to Differential Geometry with Tensor Applications is a must-have for any library. This outstanding new volume: Presents a unique perspective on the theories in the field not available anywhere else Explains the basic concepts of tensors and matrices and their applications in differential geometry and analytical mechanics Is filled with hundreds of examples and unworked problems, useful not just for the student, but also for the engineer in the field Is a valuable reference for the professional engineer or a textbook for the engineering student

Author: Su Buchin
Publisher: World Scientific Publishing Company
ISBN: 9813104104
Category : Mathematics
Languages : en
Pages : 149

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Book Description
This book is a set of notes based on lectures delivered by Prof. Su Buchin at Fudan University, Shanghai in 1978 and 1979 to graduate students as well as teachers from other institutions in China. Some selected topics in global differential geometry are dealt with. Certain areas of classical differential geometry based on modern approach are presented in Lectures 1, 3 and 4. Lecture 2 is on integral geometry on the Euclidean plane. It is abridged from W Blaschke's Vorlesungen Ulber Integralgeometrie. In Lecture 5, Cartan's exterior differential forms are introduced. Fruitful applications in this area by Profs S S Chern and C C Hsiung are also discussed.

Author: John Christopher Atkinson
Publisher:
ISBN:
Category : English language
Languages : en
Pages : 686

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Book Description

Author: Karl Kunisch
Publisher: Springer Science & Business Media
ISBN: 3764389230
Category : Mathematics
Languages : en
Pages : 346

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Book Description
Contains contributions originating from the 'Conference on Optimal Control of Coupled Systems of Partial Differential Equations', held at the 'Mathematisches Forschungsinstitut Oberwolfach' in March 2008. This work covers a range of topics such as controllability, optimality systems, model-reduction techniques, and fluid-structure interactions.

Author: Anil Kumar Sharma
Publisher: Discovery Publishing House
ISBN: 9788183560948
Category : Vector analysis
Languages : en
Pages : 312

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Book Description
Contents: Differentiation and Integration of Vectors, Multiple Vectors, Gradient, Divergence and Curl, Green s Gauss s and Stoke s Theorem.