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de Rham cohomology is a formal set-up for the analytic problem: If you have a differential k-form omega on a manifold M, is it the exterior derivative of another differential ...

The acceleration of an element of fluid, given by the convective derivative of the velocity v, (Dv)/(Dt)=(partialv)/(partialt)+v·del v, where del is the gradient operator.

For any function f:A->B (where A and B are any sets), the kernel (also called the null space) is defined by Ker(f)={x:x in Asuch thatf(x)=0}, so the kernel gives the elements ...

An orthogonal basis of vectors is a set of vectors {x_j} that satisfy x_jx_k=C_(jk)delta_(jk) and x^mux_nu=C_nu^mudelta_nu^mu, where C_(jk), C_nu^mu are constants (not ...

Two vectors u and v whose dot product is u·v=0 (i.e., the vectors are perpendicular) are said to be orthogonal. In three-space, three vectors can be mutually perpendicular.

The scalar triple product of three vectors A, B, and C is denoted [A,B,C] and defined by [A,B,C] = A·(BxC) (1) = B·(CxA) (2) = C·(AxB) (3) = det(ABC) (4) = |A_1 A_2 A_3; B_1 ...

Pre-Calculus

The convective derivative is a derivative taken with respect to a moving coordinate system. It is also called the advective derivative, derivative following the motion, ...

A projection is the transformation of points and lines in one plane onto another plane by connecting corresponding points on the two planes with parallel lines. This can be ...

The Reynolds transport theorem, also called simply the Reynolds theorem, is an important result in fluid mechanics that's often considered a three-dimensional analog of the ...