This course develops the geometrical ideas of two and three dimensional vector calculus. It is good preparation for advanced engineering and physics courses, Classical Mechanics, Statics, Kinematics, Dynamics and Vibrations, Electromagnetics and Wave Propagation, Fluid Flow and Elasticity.
Vector Algebra; Scalar and Vector Products; vector identities; lines, planes and vector geometry. Vector functions; diferentiation; space curves, velocity, acceleration; curvature and torsion. Scalar and Vector Fields; gradients and level lines; flow lines; divergence and flux; curl and circulation; Laplacian and tension. Orthogonal curvilinear coordinates. Line, surface and volume integrals. The theorems of Gauss, Stokes and Helmholtz. Orthogonal matrices and rotations in 3 dimensions. Quaternions. Vector equations of Classical Mechanics.
"...work examples, since even the very simplest formulae, by the infinite variety of transformations of which they are capable, will perplex the learner for a time. But that which forms the chief difficulty to the beginner, is one of the grandest advantages to him who has acquired even a moderate proficiency in the use of the Calculus." (P.G. Tait)Return to: Department of Mathematics and Statistics, University of New Mexico.
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Last updated: Sat Jan 26 13:26:41 MST 2013