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The second-order ordinary differential equation (d^2y)/(dx^2)-2x(dy)/(dx)+lambday=0. (1) This differential equation has an irregular singularity at infty. It can be solved ...

A matrix used in the Jacobi transformation method of diagonalizing matrices. The Jacobi rotation matrix P_(pq) contains 1s along the diagonal, except for the two elements ...

An algorithm for finding a graph's spanning tree of minimum length. It sorts the edges of a graph in order of increasing cost and then repeatedly adds edges that bridge ...

Long division is an algorithm for dividing two numbers, obtaining the quotient one digit at a time. The example above shows how the division of 123456/17 is performed to ...

Nonparametric estimation is a statistical method that allows the functional form of a fit to data to be obtained in the absence of any guidance or constraints from theory. As ...

A method of proof which proceeds by stating a proposition and then showing that it results in a contradiction, thus demonstrating the proposition to be false. In the words of ...

Rodrigues' rotation formula gives an efficient method for computing the rotation matrix R in SO(3) corresponding to a rotation by an angle theta about a fixed axis specified ...

Given a simple harmonic oscillator with a quadratic perturbation, write the perturbation term in the form alphaepsilonx^2, x^..+omega_0^2x-alphaepsilonx^2=0, (1) find the ...

The method of d'Alembert provides a solution to the one-dimensional wave equation (partial^2y)/(partialx^2)=1/(c^2)(partial^2y)/(partialt^2) (1) that models vibrations of a ...

Let alpha_i and A_i be algebraic numbers such that the A_is differ from zero and the alpha_is differ from each other. Then the expression ...