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The finite volume method is a numerical method for solving partial differential equations that calculates the values of the conserved variables averaged across the volume. ...

Suppose f(x) is continuous at a stationary point x_0. 1. If f^'(x)>0 on an open interval extending left from x_0 and f^'(x)<0 on an open interval extending right from x_0, ...

A differential k-form can be integrated on an n-dimensional manifold. The basic example is an n-form alpha in the open unit ball in R^n. Since alpha is a top-dimensional ...

The technique of extracting the content from geometric (tensor) equations by working in component notation and rearranging indices as required. Index gymnastics is a ...

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

The simplest interpretation of the Kronecker delta is as the discrete version of the delta function defined by delta_(ij)={0 for i!=j; 1 for i=j. (1) The Kronecker delta is ...

In n-dimensional Lorentzian space R^n=R^(1,n-1), the light cone C^(n-1) is defined to be the subset consisting of all vectors x=(x_0,x_1,...,x_(n-1)) (1) whose squared ...

A four-vector a_mu is said to be lightlike if its four-vector norm satisfies a_mua^mu=0. One should note that the four-vector norm is nothing more than a special case of the ...

1. Find a complete system of invariants, or 2. Decide when two metrics differ only by a coordinate transformation. The most common statement of the problem is, "Given metrics ...

The index associated to a metric tensor g on a smooth manifold M is a nonnegative integer I for which index(gx)=I for all x in M. Here, the notation index(gx) denotes the ...