Tensor Analysis

Tensor analysis is a prerequisite for many tasks in engineering and physics. By focusing on algorithms in the coordinate representation of tensors, this graduate textbook offers easy access to techniques in the field. It imparts the required algebraic aids and contains numerous exercises with answers, making it suitable for taught courses and self study for students and researchers in areas such as fluid dynamics, solid mechanics, and electrodynamics. While a variety of textbooks on mathematical aspects of tensor analysis are available, this book focuses on the practical aspects allowing engineers to directly apply the methods learned in three dimensions. By using carefully chosen language an emphasis lies on conveying symbolic and index notation in parallel, thus allowing for immediate applications e.g. in continuum mechanics, electrodynamics, or signal processing. Students with basic knowledge in linear algebra will get an understanding of the methods on an algorithmic level, rather than by means of visualization and metaphors which are hard to apply to practical problems. 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