How Do You Spell STURM'S INTERVAL?

Pronunciation: [stˈɜːmz ˈɪntəvə͡l] (IPA)

The spelling of the word "Sturm's interval" can be a bit tricky to decipher. In IPA phonetic transcription, it is pronounced as /stɜːmz ˈɪntəvəl/. The word "Sturm" is pronounced with a long "e" sound and is accented on the first syllable. The "s" at the end of the word is pronounced with a "z" sound due to the following vowel. "Interval" is pronounced with an emphasis on the second syllable and the "a" is pronounced as "uh". Overall, Sturm's interval refers to a range of values where a polynomial function switches signs.

STURM'S INTERVAL Meaning and Definition

  1. Sturm's interval refers to a concept in mathematics, specifically in the field of real analysis and the theory of real polynomials. It is named after the 19th-century French mathematician and physicist Jacques Charles François Sturm.

    In mathematics, a polynomial is an expression consisting of variables, coefficients, and exponents, combined using arithmetic operations such as addition, subtraction, multiplication, and exponentiation. Sturm's interval provides a method for counting the number of real roots within a certain range for a given real polynomial function.

    To understand Sturm's interval, one begins by obtaining a sequence of polynomials derived from the original polynomial function, known as Sturm polynomials. This sequence is generated by systematically taking derivatives and changing signs. By analyzing the variation in the number of sign changes between adjacent polynomials within a specific interval, one can determine the number of distinct real roots present within that interval.

    Sturm's interval plays a critical role in solving problems related to real polynomials and is particularly useful in the context of root isolation and root counting. Based on the changes in sign, one can establish an upper bound for the number of real roots in a given interval, facilitating further analysis and calculation.

    Overall, Sturm's interval provides a powerful tool for investigating the properties of real polynomials and determining the number of real roots they possess within specific intervals. Its application extends to various branches of mathematics, including calculus, algebra, and numerical analysis.

  2. The distance between the anterior and posterior foci or focal points in the eye.

    A practical medical dictionary. By Stedman, Thomas Lathrop. Published 1920.

Common Misspellings for STURM'S INTERVAL

  • aturm's interval
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  • xturm's interval
  • dturm's interval
  • eturm's interval
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  • srurm's interval
  • sfurm's interval
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  • syurm's interval
  • s6urm's interval
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  • styrm's interval
  • sthrm's interval
  • stjrm's interval
  • stirm's interval
  • st8rm's interval
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  • stuem's interval
  • studm's interval

Etymology of STURM'S INTERVAL

The term "Sturm's interval" is named after the French mathematician Jacques Charles François Sturm. Sturm's interval is a concept in mathematics, specifically in the theory of real algebraic curves and the study of Sturm-Liouville theory. Sturm-Liouville theory deals with ordinary differential equations and their associated eigenvalue problems.

Sturm made significant contributions to the study of ordinary differential equations in the 19th century. He developed a method to count the number of real roots of a polynomial equation in a given interval, known as the Sturm sequence or Sturm chain. The intervals on which the polynomial changes sign are referred to as "Sturm's intervals".

Sturm's work laid the foundation for the development of the theory of real algebraic curves and their properties.

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