Tensor Analysis on Manifolds (1980)

by Richard L. Bishop

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Proceeds from general to special, including chapters on vector analysis on manifolds and integration theory.

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Abandoned after two chapters, that is after chapter 1: when a book that starts at chapter 0 it acts as a warning sign to me and I was right to be wary. This is a book by a mathematician for mathematicians and it might very well be excellent for its intended audience. I am not a mathematician, however, and I found it completely useless for my needs. Hence, I haven't rated the book because it may not actually be bad, just inappropriate for me.

Arbieroo | Jul 17, 2020 |

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1980

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"Sie bedeutet einen wahren Triumph der durch Gauss, Riemann, Christoffel, Ricci . . . begründeten Methoden des allgemeinen Differentialcalculus." Albert Einstein, 1915

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Since its development by Ricci between 1887 and 1896, tensor analysis has had a rather restricted outlook despite its striking success as a mathematical tool in the general theory of relativity and its adaptability to a wide range of problems in differential equations, geometry, and physics.

Since we cannot hope to convey the significance of set theory, it is mostly for the sake of logical completeness and to fix our notation that we give the definitions and deduce the facts that follow.

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