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A geodesic is a locally length-minimizing curve. Equivalently, it is a path that a particle which is not accelerating would follow. In the plane, the geodesics are straight ...

Zygmund (1988, p. 192) noted that there exists a number alpha_0 in (0,1) such that for each alpha>=alpha_0, the partial sums of the series sum_(n=1)^(infty)n^(-alpha)cos(nx) ...

Macdonald's plane partition conjecture proposes a formula for the number of cyclically symmetric plane partitions (CSPPs) of a given integer whose Ferrers diagrams fit inside ...

Roughly speaking, a tangent vector is an infinitesimal displacement at a specific point on a manifold. The set of tangent vectors at a point P forms a vector space called the ...

The word quadrature has (at least) three incompatible meanings. Integration by quadrature either means solving an integral analytically (i.e., symbolically in terms of known ...

In analysis, the phrase "Riesz-Fischer theorem" is used to describe a number of results concerning the convergence of Cauchy sequences in L-p spaces. The theorem is named for ...

A vector bundle is special class of fiber bundle in which the fiber is a vector space V. Technically, a little more is required; namely, if f:E->B is a bundle with fiber R^n, ...

The Wiener-Hopf method is a powerful technique which enables certain linear partial differential equations subject to boundary conditions on semi-infinite domains to be ...

Calculus I

The difference between the measured or inferred value of a quantity x_0 and its actual value x, given by Deltax=x_0-x (sometimes with the absolute value taken) is called the ...