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  2. Nevanlinna theory - Wikipedia

    en.wikipedia.org/wiki/Nevanlinna_theory

    The Second Fundamental Theorem allows to give an upper bound for the characteristic function in terms of N(r,a). For example, if f is a transcendental entire function, using the Second Fundamental theorem with k = 3 and a 3 = ∞, we obtain that f takes every value infinitely often, with at most two exceptions, proving Picard's Theorem.

  3. Second law of thermodynamics - Wikipedia

    en.wikipedia.org/wiki/Second_law_of_thermodynamics

    In 1865, the German physicist Rudolf Clausius stated what he called the "second fundamental theorem in the mechanical theory of heat" in the following form: [75] = where Q is heat, T is temperature and N is the "equivalence-value" of all uncompensated transformations involved in a cyclical process. Later, in 1865, Clausius would come to define ...

  4. Second fundamental form - Wikipedia

    en.wikipedia.org/wiki/Second_fundamental_form

    The second fundamental form of a parametric surface S in R 3 was introduced and studied by Gauss. First suppose that the surface is the graph of a twice continuously differentiable function, z = f(x,y), and that the plane z = 0 is tangent to the surface at the origin. Then f and its partial derivatives with respect to x and y vanish at (0,0).

  5. Fundamental theorem of calculus - Wikipedia

    en.wikipedia.org/wiki/Fundamental_theorem_of...

    The fundamental theorem of calculus is a theorem that links the concept of differentiating a function (calculating its slopes, or rate of change at each point in time) with the concept of integrating a function (calculating the area under its graph, or the cumulative effect of small contributions). Roughly speaking, the two operations can be ...

  6. Gauss–Codazzi equations - Wikipedia

    en.wikipedia.org/wiki/Gauss–Codazzi_equations

    In Riemannian geometry and pseudo-Riemannian geometry, the Gauss–Codazzi equations (also called the Gauss–Codazzi–Weingarten-Mainardi equations or Gauss–Peterson–Codazzi formulas [1]) are fundamental formulas that link together the induced metric and second fundamental form of a submanifold of (or immersion into) a Riemannian or pseudo-Riemannian manifold.

  7. List of theorems called fundamental - Wikipedia

    en.wikipedia.org/wiki/List_of_theorems_called...

    In mathematics, a fundamental theorem is a theorem which is considered to be central and conceptually important for some topic. For example, the fundamental theorem of calculus gives the relationship between differential calculus and integral calculus . [ 1 ]

  8. Dynkin's formula - Wikipedia

    en.wikipedia.org/wiki/Dynkin's_formula

    In mathematics — specifically, in stochastic analysis — Dynkin's formula is a theorem giving the expected value of any suitably smooth function applied to a Feller process at a stopping time. It may be seen as a stochastic generalization of the (second) fundamental theorem of calculus. It is named after the Russian mathematician Eugene Dynkin.

  9. First and second fundamental theorems of invariant theory

    en.wikipedia.org/wiki/First_and_second...

    In algebra, the first and second fundamental theorems of invariant theory concern the generators and the relations of the ring of invariants in the ring of polynomial functions for classical groups (roughly the first concerns the generators and the second the relations). [1] The theorems are among the most important results of invariant theory.