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The word adjoint has a number of related meanings. In linear algebra, it refers to the conjugate transpose and is most commonly denoted A^(H). The analogous concept applied ...

Following the work of Fuchs in classifying first-order ordinary differential equations, Painlevé studied second-order ordinary differential equation of the form ...

Partial derivatives are defined as derivatives of a function of multiple variables when all but the variable of interest are held fixed during the differentiation. (1) The ...

At least one power series solution will be obtained when applying the Frobenius method if the expansion point is an ordinary, or regular, singular point. The number of roots ...

A curve on a surface whose tangents are always in the direction of principal curvature. The equation of the lines of curvature can be written |g_(11) g_(12) g_(22); b_(11) ...

Also known as the total curvature. The linear element of the indicatrix ds_P=sqrt(ds_T^2+ds_B^2).

Fermat's last theorem is a theorem first proposed by Fermat in the form of a note scribbled in the margin of his copy of the ancient Greek text Arithmetica by Diophantus. The ...

A Fourier series is an expansion of a periodic function f(x) in terms of an infinite sum of sines and cosines. Fourier series make use of the orthogonality relationships of ...

An expression is called "well-defined" (or "unambiguous") if its definition assigns it a unique interpretation or value. Otherwise, the expression is said to not be ...

Critical damping is a special case of damped simple harmonic motion x^..+betax^.+omega_0^2x=0, (1) in which D=beta^2-4omega_0^2=0, (2) where beta is the damping constant. ...