EAN: 9781461478669

INTRODUCTION TO TENSOR ANALYSIS AND THE CALCULU...

Tensor calculus is a must for researchers dealing with natural phenomena as well as for highly
qualified engineers working with man-made technological equipment. This textbook was conceived
as a self-contained introduction to tensor calculus and grown out of the lecture notes for a
course continually taught by the author at Drexel University. The text contains over 150
exercises and is divided into four parts. The first part focuses on tensors in Euclidean spaces
and includes chapters on subjects such as covariant differentiation. The second part focuses on
tensors in embedded surfaces  and includes chapters on the curvature tensor and Gauss's
theorem. The third part covers applications of tensor calculus and contains chapters on
equations of classical mechanics  equations of continuum mechanics  and Einstein's Theory of
Relativity. The fourth and final chapter explains the rules and applications of the calculus of
moving surfaces. Though the book's approach is informal and avoids a formalization of the
subject  it maintains a respectable level of rigor and reflects the author's deep passion for
the subject. Moreover  it focuses on concrete objects and appeals to the reader's intuition
with regard to such fundamental concepts as the Euclidean space  surface  and length. It is
intended for advanced undergraduate students (and first-year graduate students) in technical
fields  and assumes a solid understanding of linear algebra and multivariable calculus.

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