Fundamentals of Tensor Calculus for Engineers with a Primer on Smooth Manifolds

Nonfiction, Science & Nature, Science, Physics, Mechanics, Mathematics, Applied, Technology
Cover of the book Fundamentals of Tensor Calculus for Engineers with a Primer on Smooth Manifolds by Uwe Mühlich, Springer International Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Uwe Mühlich ISBN: 9783319562643
Publisher: Springer International Publishing Publication: April 18, 2017
Imprint: Springer Language: English
Author: Uwe Mühlich
ISBN: 9783319562643
Publisher: Springer International Publishing
Publication: April 18, 2017
Imprint: Springer
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from Springer International Publishing

Cover of the book Limbo Reapplied by Uwe Mühlich
Cover of the book Reclamation of Arid Lands by Uwe Mühlich
Cover of the book Hodgkin Lymphoma by Uwe Mühlich
Cover of the book Bamboo by Uwe Mühlich
Cover of the book Simulation and Optimization of Digital Circuits by Uwe Mühlich
Cover of the book Natural and Artificial Reasoning by Uwe Mühlich
Cover of the book Rules and Reasoning by Uwe Mühlich
Cover of the book From beliefs to dynamic affect systems in mathematics education by Uwe Mühlich
Cover of the book Small-Gauge Vitrectomy for Diabetic Retinopathy by Uwe Mühlich
Cover of the book Chocolate, Politics and Peace-Building by Uwe Mühlich
Cover of the book Fibrous Proteins: Structures and Mechanisms by Uwe Mühlich
Cover of the book Precision Agriculture: Technology and Economic Perspectives by Uwe Mühlich
Cover of the book Leadership Today by Uwe Mühlich
Cover of the book Information Security and Cryptology - ICISC 2014 by Uwe Mühlich
Cover of the book Toward Scientific Medicine by Uwe Mühlich
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy