منابع مشابه
Differential Forms
Differentials are an important topic in algebraic geometry, allowing the use of some classical geometric arguments in the context of varieties over any field. We will use them to define the genus of a curve, and to analyze the ramification of morphisms between curves. Although differentials remain important for arbitrary varieties, we will restrict our treatment to the case of nonsingular varie...
متن کاملDifferential Forms
We’ve hit the big three theorems of vector calculus: Green’s, Stokes’, and the Divergence Theorem (although Green’s theorem is really a pretty obvious special case of Stokes’ theorem). But it’s an amazing fact that all of these theorems are really special cases of an even larger theorem that unifies all that we’ve studied so far. This new theory also extends what we’ve done to spaces of arbitra...
متن کاملDifferential Forms and Integration
a f(x) dx (which one would use for instance to compute the work required to move a particle from a to b). For simplicity we shall restrict attention here to functions f : R → R which are continuous on the entire real line (and similarly, when we come to differential forms, we shall only discuss forms which are continuous on the entire domain). We shall also informally use terminology such as “i...
متن کاملDiscrete Differential Forms
The emergence of computers as an essential tool in scientific research has shaken the very foundations of differential modeling. Indeed, the deeply-rooted abstraction of smoothness, or differentiability, seems to inherently clash with a computer’s ability of storing only finite sets of numbers. While there has been a series of computational techniques that proposed discretizations of differenti...
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ژورنال
عنوان ژورنال: Journal of Nonlinear Mathematical Physics
سال: 1998
ISSN: 1776-0852
DOI: 10.2991/jnmp.1998.5.3.3