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Introduction to Differential Geometry with Tensor Applications

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Absolute differential

Associate tensors
Bianchi Identity
Binormal
Category=PBMP
Christoffel symbols
Codazzi equation
Conjugate tensors
Contraction
Contravariant tensor
Covariant tensor
Curl of a vector
Curvature tensor
Developable
Divergence
Einstein tensor
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
First fundamental form
Fundamental tensor
Gauss's equation
Gaussian curvature
Gauss’s equation
Geodesic coordinates
Geodesic curvature
Helix
Inner product
Intrinsic derivative
Invarants
Isometry
Jacobian
Kronecker delta
Length of a Vector
Mean curvature
Metric tensor
Meusnier's theorem
Meusnier’s theorem
Minkowski space time
Normal curvature
Null vector
Osculating plane
Outer multiplication
Quotient law
Reciprocal tensor
Ricci tensor
Ricci Theorem
Riemann-Christoffel tensor
Riemannian metric
Riemannian space
Second fundamental form
Serret-Frenet formulii
Skew symmetric tensors
Space curve
Summation convention
Surface Curve
Symmetric tensor
Tangent vectors
Tensor algebra
Tensor derivative
Third fundamental form
Torsion
Total curvature
Unit Vector
Vector space
Weingarten's formula
Weingarten’s formula
Zero Vector

Product details

  • ISBN 9781119795629
  • Weight: 454g
  • Dimensions: 10 x 10mm
  • Publication Date: 24 May 2022
  • Publisher: John Wiley & Sons Inc
  • Publication City/Country: US
  • Product Form: Hardback
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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
About

Dipankar De, PhD, received his BSc and MSc in mathematics from the University of Calcutta, India and his PhD in mathematics from Tripura University, India. He has over 40 years of teaching experience and is an associate professor and guest lecturer in India. He has published many research papers in various reputed journal in the field of fuzzy mathematics and differential geometry.