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Hace 1 día · Johann Carl Friedrich Gauss (German: Gauß [kaʁl ˈfʁiːdʁɪç ˈɡaʊs] ⓘ; Latin: Carolus Fridericus Gauss; 30 April 1777 – 23 February 1855) was a German mathematician, astronomer, geodesist, and physicist who contributed to many fields in mathematics and science.
Hace 4 días · Euler's constant (sometimes called the Euler–Mascheroni constant) is a mathematical constant, usually denoted by the lowercase Greek letter gamma ( γ ), defined as the limiting difference between the harmonic series and the natural logarithm, denoted here by log : Here, ⌊·⌋ represents the floor function .
Hace 3 días · v. t. e. A pendulum is a body suspended from a fixed support so that it swings freely back and forth under the influence of gravity. When a pendulum is displaced sideways from its resting, equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back towards the equilibrium position.
Hace 5 días · Expressing the conservative forces by a potential Π and nonconservative forces by the generalized forces Q, the equation of motion follow from Euler--Lagrange's equations. d dt(∂L ∂˙qi) − ∂L ∂qi = Qi, i = 1, 2, …, 3n − k. The Lagrangian L = K − Π describes the conservative forces. The force field F ( x) is said to be ...
Hace 1 día · The beta function (also known as Euler's integral of the first kind) is important in calculus and analysis due to its close connection to the gamma function, which is itself a generalization of the factorial function. Many complex integrals can be reduced to expressions involving the beta function.
Hace 3 días · Multistep Methods. The methods of Euler, Heun, Runge--Kutta, and Taylor are called single-step methods (or one-step methods) because they use only the information from one previous point to compute the successive point; that is, only the initial point (x0, y0) is used to compute (x1, y1) and, in general, yk is needed to compute yk+1.
Hace 4 días · Two of the most widely used electronic-structure theory methods, namely, Hartree–Fock and Kohn–Sham density functional theory, require the iterative solution of a set of Schrödinger-like equations. The speed of convergence of such a process depends on the complexity of the system under investigation, the self-consistent-field algorithm employed, and the initial guess for the density ...
