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Vector analysis

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Tensor calculus is a prerequisite for many tasks in physics and engineering. This book introduces the symbolic and the index notation side by side and offers easy access to techniques in the field by focusing on algorithms in index notation. It explains the required algebraic tools and contains numerous exercises with answers, making it suitable for self study for students and researchers in areas such as solid mechanics, fluid mechanics, and electrodynamics. ContentsAlgebraic ToolsTensor Analysis in Symbolic Notation and in Cartesian CoordinatesAlgebra of Second Order TensorsTensor Analysis in Curvilinear CoordinatesRepresentation of Tensor FunctionsAppendices: Solutions to the Problems; Cylindrical Coordinates and Spherical Coordinates

Calculus of tensors. --- Vector analysis.

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The main thread running through this somewhat unorthodox approach to the special theory of relativity is the Pythagorean theorem. It appears in its most elementary geometric form in the very beginning of this monograph. Then it reappears in algebraic garb, it is further modified and finally reinterpreted to play the role of one of the main characters in the special theory of relativity. The first four chapters are easily accessible to high school sophomores or juniors. The remaining part of the book may be a little difficult for students who never studied physics, although the author actually employs only the notion of impact and presupposes no background in physics. With the aid of the vector geometry introduced earlier, he leads the reader from the impact conservation laws to the famous formula e=mc^2.

Pythagorean theorem. --- Dynamics. --- Relativity (Physics) --- Vector analysis.

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Vectors in 2 or 3 Dimensions provides an introduction to vectors from their very basics. The author has approached the subject from a geometrical standpoint and although applications to mechanics will be pointed out and techniques from linear algebra employed, it is the geometric view which is emphasised throughout.Properties of vectors are initially introduced before moving on to vector algebra and transformation geometry. Vector calculus as a means of studying curves and surfaces in 3 dimensions and the concept of isometry are introduced later, providing a stepping stone to mo

Vector analysis. --- Vector algebra. --- Algebra, Vector --- Algebras, Linear --- Vector analysis --- Algebra, Universal --- Mathematics --- Numbers, Complex --- Quaternions --- Spinor analysis --- Vector algebra

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This book provides a comprehensive foundation in Probabilistic Normed (PN) Spaces for anyone conducting research in this field of mathematics and statistics. It is the first to fully discuss the developments and the open problems of this highly relevant topic, introduced by A N Serstnev in the early 1960s as a response to problems of best approximations in statistics. The theory was revived by Claudi Alsina, Bert Schweizer and Abe Sklar in 1993, who provided a new, wider definition of a PN space which quickly became the standard adopted by all researchers. This book is the first wholly up-to-d

Normed linear spaces. --- Linear normed spaces --- Normed vector spaces --- Banach spaces --- Functional analysis --- Vector analysis