Vector and Tensor Analysis
"Remarkably comprehensive, concise and clear." — Industrial Laboratories "Considered as a condensed text in the classical manner, the book can well be recommended." — Nature Here is a clear introduction to classic vector and tensor analysis for students of engineering and mathematical physics. Chapters range from elementary operations and applications of geometry, to application of vectors to mechanics, partial differentiation, integration, and tensor analysis. More than 200 problems are included throughout the book.
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angle angular velocity called cartesian tensor center of mass Christoffel symbols contravariant tensor contravariant vector coordinate system covariant vector curve curvilinear coordinates cylinder cylindrical coordinates deﬁned deﬁnition denote the position-vectors differential equation equal evaluate the line example expressions external forces ﬁgure ﬁnd ﬁxed point follows formulas frame of reference geometry given point gyroscope Hence i2 and i3 inertia introduce j-th particle Let us consider line integral line of action linear function magnitude mixed tensor origin orthogonal outer product parallel parametric lines perpendicular physical components Problem Proof of Equation prove rectangular cartesian coordinates relative tensors respect right side rotation scalar ﬁeld scalar triple products second order set of quantities shown in Figure sphere sufﬁx surface integral system of particles tangent tensor character tion transformation unit vectors unit vectors i1 vector ﬁeld vector product write x3 axis yields