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The circle through the cusp of the arbelos and the tangent points of the first Pappus circle, which is congruent to the two Archimedes' circles. If AB=r and AC=1, then the ...

Differential calculus is that portion of "the" calculus dealing with derivatives. Among his many other talents, Major General Stanley in Gilbert and Sullivan's operetta the ...

An infinite-dimensional differential calculus on the Wiener space, also called stochastic calculus of variations.

The Schwarzian derivative is defined by D_(Schwarzian)=(f^(''')(x))/(f^'(x))-3/2[(f^('')(x))/(f^'(x))]^2. The Feigenbaum constant is universal for one-dimensional maps if its ...

In the notation of Watson (1966), theta=zd/(dz).

An atlas is a collection of consistent coordinate charts on a manifold, where "consistent" most commonly means that the transition functions of the charts are smooth. As the ...

The idea of a velocity vector comes from classical physics. By representing the position and motion of a single particle using vectors, the equations for motion are simpler ...

The derivative of a function represents an infinitesimal change in the function with respect to one of its variables. The "simple" derivative of a function f with respect to ...

Calculus I

Let M^n be a compact n-dimensional oriented Riemannian manifold without boundary, let O be a group representation of pi_1(M) by orthogonal matrices, and let E(O) be the ...