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Multivariable Calculus

Pre-Calculus

_8phi_7[a,qa^(1/2),-qa^(1/2),b,c,d,e,q^(-N); a^(1/2),-a^(1/2),(aq)/b,(aq)/c,(aq)/d,(aq)/e,aq^(N+1);q,(aq^(N+2))/(bcde)] ...

The Boy surface is a nonorientable surface that is one possible parametrization of the surface obtained by sewing a Möbius strip to the edge of a disk. Two other ...

The Cauchy principal value of a finite integral of a function f about a point c with a<=c<=b is given by ...

The term "cylinder" has a number of related meanings. In its most general usage, the word "cylinder" refers to a solid bounded by a closed generalized cylinder (a.k.a. ...

A Gray code is an encoding of numbers so that adjacent numbers have a single digit differing by 1. The term Gray code is often used to refer to a "reflected" code, or more ...

An ideal is a subset I of elements in a ring R that forms an additive group and has the property that, whenever x belongs to R and y belongs to I, then xy and yx belong to I. ...

The lemniscate, also called the lemniscate of Bernoulli, is a polar curve defined as the locus of points such that the the product of distances from two fixed points (-a,0) ...

The pedal of a curve C with respect to a point O is the locus of the foot of the perpendicular from O to the tangent to the curve. More precisely, given a curve C, the pedal ...