Problems and Worked Solutions in Vector Analysis"A handy book like this," noted The Mathematical Gazette, "will fill a great want." Devoted to fully worked out examples, this unique text constitutes a self-contained introductory course in vector analysis for undergraduate and graduate students of applied mathematics. Opening chapters define vector addition and subtraction, show how to resolve and determine the direction of two or more vectors, and explain systems of coordinates, vector equations of a plane and straight line, relative velocity and acceleration, and infinitely small vectors. The following chapters deal with scalar and vector multiplication, axial and polar vectors, areas, differentiation of vector functions, gradient, curl, divergence, and analytical properties of the position vector. Applications of vector analysis to dynamics and physics are the focus of the final chapter, including such topics as moving rigid bodies, energy of a moving rigid system, central forces, equipotential surfaces, Gauss's theorem, and vector flow. |
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angular applied assume axes axis becomes called centre circle closed coefficients constant coordinates corresponding couple curve determined differential direction displacement distance dr/dt draw drawn element equal equation example expression extremity figure find first fixed flow follows force function given grad Hence hold initial integral intersection joining latter length limit mass meet method motion moving multiplication normal obtained operation opposite origin parallel parallelogram passing perpendicular plane positive projection Prove quantity radius referred relation represents respectively resultant right angles rotation scalar components scalar value Sect Show shown sides Similarly space squares stands straight line substituting suppose surface taken tangent terminal point triangle unit vector vanishes variable velocity volume write written