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Differentiation of vector-valued functions; rules of vector differentiation; derivatives of vector products; some applications of vector differentiation.

Integration of vector-valued functions; definite, indefinite and line integrals of vector-valued functions; some applications of integration of vector-valued functions.

An introduction to applications of vectors in mechanics - forces and their resultants; equilibrium under the action of concurrent forces; work done by constant and variable forces; kinetic and potential energy; conservation of energy principle; moment of a force about a point.

An introduction to applications of vectors in mechanics - displacements, velocities and accelerations; relative velocities and accelerations; motion of a particle in tangential and normal components; motion of a particle in radial and transverse components (polar coordinates).

An introduction to the applications of vectors in mechanics - motion of a particle along a path of constant radius; motion of a particle in cylindrical coordinates; motion in rotating and fixed frames.

Arc length and curvature of parametric curves; tangential, normal and binormal vectors to a parametric curve; osculating, normal and rectifying planes to a parametric curve; Frenet-Serret formulas.