Introduction to Differential Geometry with Tensor Applications

This book provides a comprehensive introduction to differential geometry with tensor applications, covering the theory of tensors, curves, and surfaces, and their applications in Newtonian mechanics. It includes detailed calculations, illustrative examples, and exercises with complete solutions, making it accessible to beginners and a valuable reference for professionals.

Format: Hardback
Length: 512 pages
Publication date: 24 May 2022
Publisher: John Wiley & Sons Inc

Explains 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.
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.
• Explains 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.

The book is divided into three parts. The first part provides an introduction to the basic theory of differential geometry, including curves and surfaces. The second part discusses the theory of tensors, including their definition, properties, and applications. The third part applies the theory of tensors to various problems in analytical mechanics, including rigid body dynamics, fluid mechanics, and electromagnetism.

Throughout the book, the author emphasizes the importance of visualizing the concepts and equations in differential geometry. He uses numerous illustrations and diagrams to help the reader understand the topics better. The examples are carefully chosen to demonstrate the practical applications of the theory and to provide the reader with a hands-on experience.

In addition to the theoretical material, the book includes a wealth of exercises with complete solutions. These exercises are designed to help the reader practice the concepts and techniques discussed in the book. The solutions are detailed and provide a step-by-step guide to solving the problems.

Whether you are a student studying differential geometry or a practicing engineer or scientist interested in the field, Introduction to Differential Geometry with Tensor Applications is a must-have for any library. This book provides a comprehensive and accessible introduction to the basic theory of differential geometry and its applications in analytical mechanics. With its clear and concise writing style, numerous illustrations, and comprehensive exercises, this book is an excellent resource for anyone looking to gain a deeper understanding of the subject.

Weight: 834g
Dimension: 229 x 160 x 32 (mm)
ISBN-13: 9781119795629