Fundamentals of Tensor Calculus for Engineers with a Primer on Smooth Manifolds PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Fundamentals of Tensor Calculus for Engineers with a Primer on Smooth Manifolds PDF full book. Access full book title Fundamentals of Tensor Calculus for Engineers with a Primer on Smooth Manifolds by Uwe Mühlich. Download full books in PDF and EPUB format.
Author: Uwe Mühlich
Publisher: Springer
ISBN: 3319562649
Category : Science
Languages : en
Pages : 134
Get Book Here
Book Description
This book presents the fundamentals of modern tensor calculus for students in engineering and applied physics, emphasizing those aspects that are crucial for applying tensor calculus safely in Euclidian space and for grasping the very essence of the smooth manifold concept. After introducing the subject, it provides a brief exposition on point set topology to familiarize readers with the subject, especially with those topics required in later chapters. It then describes the finite dimensional real vector space and its dual, focusing on the usefulness of the latter for encoding duality concepts in physics. Moreover, it introduces tensors as objects that encode linear mappings and discusses affine and Euclidean spaces. Tensor analysis is explored first in Euclidean space, starting from a generalization of the concept of differentiability and proceeding towards concepts such as directional derivative, covariant derivative and integration based on differential forms. The final chapter addresses the role of smooth manifolds in modeling spaces other than Euclidean space, particularly the concepts of smooth atlas and tangent space, which are crucial to understanding the topic. Two of the most important concepts, namely the tangent bundle and the Lie derivative, are subsequently worked out.
Author: Uwe Mühlich
Publisher: Springer
ISBN: 3319562649
Category : Science
Languages : en
Pages : 134
Get Book Here
Book Description
This book presents the fundamentals of modern tensor calculus for students in engineering and applied physics, emphasizing those aspects that are crucial for applying tensor calculus safely in Euclidian space and for grasping the very essence of the smooth manifold concept. After introducing the subject, it provides a brief exposition on point set topology to familiarize readers with the subject, especially with those topics required in later chapters. It then describes the finite dimensional real vector space and its dual, focusing on the usefulness of the latter for encoding duality concepts in physics. Moreover, it introduces tensors as objects that encode linear mappings and discusses affine and Euclidean spaces. Tensor analysis is explored first in Euclidean space, starting from a generalization of the concept of differentiability and proceeding towards concepts such as directional derivative, covariant derivative and integration based on differential forms. The final chapter addresses the role of smooth manifolds in modeling spaces other than Euclidean space, particularly the concepts of smooth atlas and tangent space, which are crucial to understanding the topic. Two of the most important concepts, namely the tangent bundle and the Lie derivative, are subsequently worked out.
Author: Peter Schiavone
Publisher: Professional Publications Incorporated
ISBN:
Category : Education
Languages : en
Pages : 138
Get Book Here
Book Description
Calculus Refresher for the FE Exam was written in response to the requests of countless FE candidates. Many engineers report having more difficulty with problems involving calculus than with anything else on the FE exam. Almost everyone can benefit from a concise review of the subject! The author provides background theory, clear explanatory text, relevant examples, and FE-style practice problems (with solutions).
Author: John Perry
Publisher:
ISBN:
Category : Calculus
Languages : en
Pages : 398
Get Book Here
Book Description
Author: Michael Stone
Publisher: Cambridge University Press
ISBN: 1139480618
Category : Science
Languages : en
Pages : 821
Get Book Here
Book Description
An engagingly-written account of mathematical tools and ideas, this book provides a graduate-level introduction to the mathematics used in research in physics. The first half of the book focuses on the traditional mathematical methods of physics – differential and integral equations, Fourier series and the calculus of variations. The second half contains an introduction to more advanced subjects, including differential geometry, topology and complex variables. The authors' exposition avoids excess rigor whilst explaining subtle but important points often glossed over in more elementary texts. The topics are illustrated at every stage by carefully chosen examples, exercises and problems drawn from realistic physics settings. These make it useful both as a textbook in advanced courses and for self-study. Password-protected solutions to the exercises are available to instructors at www.cambridge.org/9780521854030.
Author: Robert Wasserman
Publisher: Oxford University Press, USA
ISBN: 9780198510598
Category : Language Arts & Disciplines
Languages : en
Pages : 468
Get Book Here
Book Description
This book sets forth the basic principles of tensors and manifolds and describes how the mathematics underlies elegant geometrical models of classical mechanics, relativity and elementary particle physics.
Author: Bernard F. Schutz
Publisher: Cambridge University Press
ISBN: 9780521277037
Category : Science
Languages : en
Pages : 396
Get Book Here
Book Description
This textbook develops general relativity and its associated mathematics from a minimum of prerequisites, leading to a physical understanding of the theory in some depth.
Author: Frank Nielsen
Publisher: Springer
ISBN: 3030025209
Category : Technology & Engineering
Languages : en
Pages : 395
Get Book Here
Book Description
This book focuses on information geometry manifolds of structured data/information and their advanced applications featuring new and fruitful interactions between several branches of science: information science, mathematics and physics. It addresses interrelations between different mathematical domains like shape spaces, probability/optimization & algorithms on manifolds, relational and discrete metric spaces, computational and Hessian information geometry, algebraic/infinite dimensional/Banach information manifolds, divergence geometry, tensor-valued morphology, optimal transport theory, manifold & topology learning, and applications like geometries of audio-processing, inverse problems and signal processing. The book collects the most important contributions to the conference GSI’2017 – Geometric Science of Information.
Author: M. Crampin
Publisher: Cambridge University Press
ISBN: 9780521231909
Category : Mathematics
Languages : en
Pages : 408
Get Book Here
Book Description
An introduction to geometrical topics used in applied mathematics and theoretical physics.
Author: Bernard Schutz
Publisher: Cambridge University Press
ISBN: 0521887054
Category : Science
Languages : en
Pages : 411
Get Book Here
Book Description
Second edition of a widely-used textbook providing the first step into general relativity for undergraduate students with minimal mathematical background.
Author: Shun-ichi Amari
Publisher: Springer
ISBN: 4431559787
Category : Mathematics
Languages : en
Pages : 378
Get Book Here
Book Description
This is the first comprehensive book on information geometry, written by the founder of the field. It begins with an elementary introduction to dualistic geometry and proceeds to a wide range of applications, covering information science, engineering, and neuroscience. It consists of four parts, which on the whole can be read independently. A manifold with a divergence function is first introduced, leading directly to dualistic structure, the heart of information geometry. This part (Part I) can be apprehended without any knowledge of differential geometry. An intuitive explanation of modern differential geometry then follows in Part II, although the book is for the most part understandable without modern differential geometry. Information geometry of statistical inference, including time series analysis and semiparametric estimation (the Neyman–Scott problem), is demonstrated concisely in Part III. Applications addressed in Part IV include hot current topics in machine learning, signal processing, optimization, and neural networks. The book is interdisciplinary, connecting mathematics, information sciences, physics, and neurosciences, inviting readers to a new world of information and geometry. This book is highly recommended to graduate students and researchers who seek new mathematical methods and tools useful in their own fields.
