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  2. Fraction - Wikipedia

    en.wikipedia.org/wiki/Fraction

    [14] [15] It is said to be an improper fraction, or sometimes top-heavy fraction, [16] if the absolute value of the fraction is greater than or equal to 1. Examples of proper fractions are 2/3, −3/4, and 4/9, whereas examples of improper fractions are 9/4, −4/3, and 3/3.

  3. Partial fraction decomposition - Wikipedia

    en.wikipedia.org/wiki/Partial_fraction_decomposition

    In algebra, the partial fraction decomposition or partial fraction expansion of a rational fraction (that is, a fraction such that the numerator and the denominator are both polynomials) is an operation that consists of expressing the fraction as a sum of a polynomial (possibly zero) and one or several fractions with a simpler denominator.

  4. Irreducible fraction - Wikipedia

    en.wikipedia.org/wiki/Irreducible_fraction

    Two fractions ⁠ a / b ⁠ and ⁠ c / d ⁠ are equal or equivalent if and only if ad = bc.) For example, ⁠ 1 / 4 ⁠ , ⁠ 5 / 6 ⁠ , and ⁠ −101 / 100 ⁠ are all irreducible fractions. On the other hand, ⁠ 2 / 4 ⁠ is reducible since it is equal in value to ⁠ 1 / 2 ⁠ , and the numerator of ⁠ 1 / 2 ⁠ is less than the ...

  5. Continued fraction - Wikipedia

    en.wikipedia.org/wiki/Continued_fraction

    Continued fractions can also be applied to problems in number theory, and are especially useful in the study of Diophantine equations. In the late eighteenth century Lagrange used continued fractions to construct the general solution of Pell's equation, thus answering a question that had fascinated mathematicians for more than a thousand years. [9]

  6. Lists of integrals - Wikipedia

    en.wikipedia.org/wiki/Lists_of_integrals

    Integration is the basic operation in integral calculus.While differentiation has straightforward rules by which the derivative of a complicated function can be found by differentiating its simpler component functions, integration does not, so tables of known integrals are often useful.

  7. Improper integral - Wikipedia

    en.wikipedia.org/wiki/Improper_integral

    An improper Riemann integral of the first kind, where the region in the plane implied by the integral is infinite in extent horizontally. The area of such a region, which the integral represents, may be finite (as here) or infinite. An improper Riemann integral of the second kind, where the implied region is infinite vertically.

  8. Fractionating column - Wikipedia

    en.wikipedia.org/wiki/Fractionating_column

    A fractionating column or fractional column is equipment used in the distillation of liquid mixtures to separate the mixture into its component parts, or fractions, based on their differences in volatility. Fractionating columns are used in small-scale laboratory distillations as well as large-scale industrial distillations.

  9. Helmholtz decomposition - Wikipedia

    en.wikipedia.org/wiki/Helmholtz_decomposition

    The Helmholtz decomposition in three dimensions was first described in 1849 [9] by George Gabriel Stokes for a theory of diffraction. Hermann von Helmholtz published his paper on some hydrodynamic basic equations in 1858, [10] [11] which was part of his research on the Helmholtz's theorems describing the motion of fluid in the vicinity of vortex lines. [11]

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