Vector Analysis and Cartesian Tensors by Bourne and Kendall

In summary, the conversation is discussing the search for useful resources for a teaching assistant job in a multivariable calculus class. One book by Bourne and Kendall is mentioned, with positive observations on its treatment of vector analysis and Cartesian tensors. However, it is noted that the book may be lacking in certain topics. Other recommendations for books on vector analysis with tensors are also requested, with one suggestion being "Vectors" by P. Moon and D.E. Spencer, which follows the contravariant/covariant notation convention and was co-authored by a student of Dirk Struik.
  • #1
Whitehole
132
4
I have to do a teaching assistant job on a multivariable calculus class, I have to survey books that can be useful as resources. Has anyone used this book by Bourne and Kendall? I noticed that the treatment of vector analysis seems good and the chapter on Cartesian tensors seem to be a good intro for undergrads. I just noticed that the topics of the book seems to be lacking, i.e. Lagrange multipliers, etc.

Can anyone also recommend other good books on vector analysis with some tensors included, i.e. vector calculus in tensor notations, etc.
 
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  • #2
While certainly not a modern book one of the coauthors was a student of Dirk Struik:

Vectors by P. Moon and D.E. Spencer D.Van Nostrand Company Inc (1965)

notation follows the contravariant/covariant convention
 

1. What is vector analysis?

Vector analysis is a branch of mathematics that deals with the study of vectors and their properties. It involves the manipulation of vectors using mathematical operations such as addition, subtraction, and multiplication to solve problems in various fields such as physics, engineering, and computer science.

2. What are Cartesian tensors?

Cartesian tensors, also known as Cartesian coordinate tensors, are mathematical objects that represent the geometric properties of a multi-dimensional space. They are used in vector analysis to describe the magnitude and direction of vectors in a rectangular coordinate system.

3. What topics are covered in "Vector Analysis and Cartesian Tensors" by Bourne and Kendall?

This book covers a wide range of topics including vector algebra, vector calculus, vector fields, line and surface integrals, the gradient, divergence and curl operators, and the use of Cartesian tensors in solving problems in mechanics and electromagnetism.

4. Is this book suitable for beginners?

Yes, this book is suitable for beginners as it starts with basic concepts and gradually introduces more advanced topics. It also includes numerous examples and exercises to help readers understand and apply the concepts.

5. How can "Vector Analysis and Cartesian Tensors" be applied in real life?

Vector analysis and Cartesian tensors have various applications in real life, such as in engineering, physics, and computer graphics. They are used to solve problems involving forces, motion, and fluid dynamics, as well as in the analysis and design of structures and machines.

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