This concise introduction to a fundamental branch of applied mathematics is indispensable for mathematicians, physicists, and engineers. Highly readable, it covers the fundamentals of vector and tensor analysis, applying the theory to specific physics and engineering problems, with a particular emphasis on its applications in fluid dynamics.

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The authors initiate the discussion with the definition of vectors and explore algebraic operations on vectors. The concept of vectors is then naturally extended to tensors. Chapter Three delves into algebraic operations on tensors. Subsequently, the authors systematically examine the differential and integral calculus of vector and tensor functions in space and time. The book concludes by exploring vector and tensor analysis from both basic and more advanced perspectives.

The strength of the book lies in the thorough problem-solving approach with complete solutions provided at the end of each chapter. Additionally, each chapter incorporates ample exercise material. Geared towards advanced undergraduates and graduate students in mathematics, physics, and engineering, this work is self-contained and accessible to students with a solid background in calculus.

“Vector and Tensor Analysis With Applications” is part of the SELECTED RUSSIAN PUBLICATIONS IN THE MATHEMATICAL SCIENCES series, several of which have been previously published by Dover. The authors are esteemed Russian mathematicians and specialists in gas dynamics and numerical analysis. Richard A. Silverman, the series editor, as well as the editor and translator of this volume, has revised and enhanced the original edition, including the addition of a bibliography.

Vector and Tensor Analysis with Applications by A. Borisenko (1968)

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