Concepts from Tensor Analysis and Differential Geometry
eBook - PDF

Concepts from Tensor Analysis and Differential Geometry

  1. 128 pages
  2. English
  3. PDF
  4. Available on iOS & Android
eBook - PDF

Concepts from Tensor Analysis and Differential Geometry

About this book

Concepts from Tensor Analysis and Differential Geometry discusses coordinate manifolds, scalars, vectors, and tensors. The book explains some interesting formal properties of a skew-symmetric tensor and the curl of a vector in a coordinate manifold of three dimensions. It also explains Riemann spaces, affinely connected spaces, normal coordinates, and the general theory of extension. The book explores differential invariants, transformation groups, Euclidean metric space, and the Frenet formulae. The text describes curves in space, surfaces in space, mixed surfaces, space tensors, including the formulae of Gaus and Weingarten. It presents the equations of two scalars K and Q which can be defined over a regular surface S in a three dimensional Riemannian space R. In the equation, the scalar K, which is an intrinsic differential invariant of the surface S, is known as the total or Gaussian curvature and the scalar U is the mean curvature of the surface. The book also tackles families of parallel surfaces, developable surfaces, asymptotic lines, and orthogonal ennuples. The text is intended for a one-semester course for graduate students of pure mathematics, of applied mathematics covering subjects such as the theory of relativity, fluid mechanics, elasticity, and plasticity theory.

Frequently asked questions

Yes, you can cancel anytime from the Subscription tab in your account settings on the Perlego website. Your subscription will stay active until the end of your current billing period. Learn how to cancel your subscription.
At the moment all of our mobile-responsive ePub books are available to download via the app. Most of our PDFs are also available to download and we're working on making the final remaining ones downloadable now. Learn more here.
Perlego offers two plans: Essential and Complete
  • Essential is ideal for learners and professionals who enjoy exploring a wide range of subjects. Access the Essential Library with 800,000+ trusted titles and best-sellers across business, personal growth, and the humanities. Includes unlimited reading time and Standard Read Aloud voice.
  • Complete: Perfect for advanced learners and researchers needing full, unrestricted access. Unlock 1.4M+ books across hundreds of subjects, including academic and specialized titles. The Complete Plan also includes advanced features like Premium Read Aloud and Research Assistant.
Both plans are available with monthly, semester, or annual billing cycles.
We are an online textbook subscription service, where you can get access to an entire online library for less than the price of a single book per month. With over 1 million books across 1000+ topics, we’ve got you covered! Learn more here.
Look out for the read-aloud symbol on your next book to see if you can listen to it. The read-aloud tool reads text aloud for you, highlighting the text as it is being read. You can pause it, speed it up and slow it down. Learn more here.
Yes! You can use the Perlego app on both iOS or Android devices to read anytime, anywhere — even offline. Perfect for commutes or when you’re on the go.
Please note we cannot support devices running on iOS 13 and Android 7 or earlier. Learn more about using the app.
Yes, you can access Concepts from Tensor Analysis and Differential Geometry by Tracy Y. Thomas, Richard Bellman in PDF and/or ePUB format, as well as other popular books in Mathematics & Differential Geometry. We have over one million books available in our catalogue for you to explore.

Information

Publisher
Academic Press
Year
2016
Print ISBN
9781483230184
eBook ISBN
9781483263717
Topic
Mathematics
Subtopic
Differential Geometry
Index
Mathematics

Table of contents

  1. Front Cover
  2. Concepts from Tensor Analysis and Differential Geometry
  3. Copyright Page
  4. Table of Contents
  5. Preface
  6. Chapter 1. Coordinate Manifolds
  7. Chapter 2. Sealars
  8. Chapter 3. Vectors and Tensors
  9. Chapter 4. A Special Skew-symmetric Tensor
  10. Chapter 5. The Vector Product. Curl of a Vector
  11. Chapter 6. Riemann Spaces
  12. Chapter 7. Affinely Connected Spaces
  13. Chapter 8. Normal Coordinates
  14. Chapter 9. General Theory of Extension
  15. Chapter 10. Absolute Differentiation
  16. Chapter 11. Differential Invariants
  17. Chapter 12. Transformation Groups
  18. Chapter 13. Euclidean Metrie Space
  19. Chapter 14. Homogeneous and Isotropic Tensors
  20. Chapter 15. Curves in Space. Frenet Formulae
  21. Chapter 16. Surfaces in Space
  22. Chapter 17. Mixed Surface and Space Tensors. Coordinate Extension and Absolute Differentiation
  23. Chapter 18. Formulae of Gauss and Weingarten
  24. Chapter 19. Gaussian and Mean Curvature of a Surface
  25. Chapter 20. Equations of Gauss and Codazzi
  26. Chapter 21. Principal Curvatures and Principal Directions
  27. Chapter 22. Asymptotic Lines
  28. Chapter 23. Orthogonal Ennuples and Normal Congruences
  29. Chapter 24. Families of Parallel Surfaces
  30. Chapter 25. Developable Surfaces. Minimal Surfaces
  31. General References
  32. Subject Index