The use of vectors not only simplifies treatments of differential geometry, mechanics, hydrodynamics, and electrodynamics, but also makes mathematical and physical concepts more tangible and easy to grasp. This text for undergraduates was designed as a short introductory course to give students the tools of vector algebra and calculus, as well as a brief glimpse into these subjects' manifold applications. The applications are developed to the extent that the uses of the potential function, both scalar and vector, are fully illustrated. Moreover, the basic postulates of vector analysis are brought to the foreground, placing their logical structure in sharp relief.
Because the concept of a vector has been greatly generalized in geometry and mathematical physics, this text concludes with a brief introduction to abstract vector spaces, together with the ideas of linear dependence, basis, and dimension. The exposition of these abstract concepts is kept simple and clear. Numerous figures appear throughout the text.
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VECTOR ALGEBRA 1 Vectors
Addition of Vectors
Subtraction of Vectors
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a x b Advanced Calculus algebra angle axis basis boundary called centroid charge q circle circuit integral closed curve closed surface components compute conductor const constant coordinates coplanar defined denote density derivatives dextral differential dimensions direction distance div f divergence theorem dot-multiplying dx dy dyadic equal equation of motion Example field fluid formula given gradient Green's theorem harmonic hence irrotational Laplace's equation line integral line vectors linear linearly dependent mathematical numbers obtain orthogonal orthonormal parallel parametric equations particle perpendicular plane curve point function position vector Prob PROBLEMS Proof prove ratio rectangular region rot f rot g ru x r scalar simply connected solution step path stream-lines surface integral tangent triangle ABC u x v unit vector values vector area vector f vector potential vector space velocity z-axis zero