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Let f and g be nonnegative and continuous functions on the closed interval [a,b], then the solid of revolution obtained by rotating the curves f(x) and g(x) about the x-axis ...

A procedure for finding the quadratic factors for the complex conjugate roots of a polynomial P(x) with real coefficients. (1) Now write the original polynomial as ...

A root-finding algorithm used in LU decomposition. It solves the N^2 equations i<j l_(i1)u_(1j)+l_(i2)u_(2j)+...+l_(ii)u_(ij)=a_(ij)i=j ...

An algorithm for finding roots for quartic equations with complex roots.

A root-finding algorithm which converges to a complex root from any starting position. To motivate the formula, consider an nth order polynomial and its derivatives, P_n(x) = ...

In order to find a root of a polynomial equation a_0x^n+a_1x^(n-1)+...+a_n=0, (1) consider the difference equation a_0y(t+n)+a_1y(t+n-1)+...+a_ny(t)=0, (2) which is known to ...

If x_0 is an ordinary point of the ordinary differential equation, expand y in a Taylor series about x_0. Commonly, the expansion point can be taken as x_0=0, resulting in ...

An algorithm for computing an Egyptian fraction.

A generalization of the Bulirsch-Stoer algorithm for solving ordinary differential equations.

An algorithm for computing an Egyptian fraction (Stewart 1992).