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Calculus: meaning, definitions and examples

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calculus

 

[ˈkælkjələs ]

Definition

Context #1 | Noun

mathematics

Calculus is a branch of mathematics that deals with the finding and properties of derivatives and integrals of functions, by methods originally based on the summation of infinitesimal differences.

Synonyms

differential calculus, integral calculus, mathematical analysis.

Which Synonym Should You Choose?

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Word Description / Examples
calculus

General usage referring to the entire field of study that deals with rates of change and accumulation of quantities.

  • Calculus is a required course for engineering students.
  • She excelled in her calculus class and decided to major in mathematics.
mathematical analysis

Broader context encompassing calculus as well as other areas of advanced mathematics that deal with functions, limits, and infinity.

  • Mathematical analysis provides the rigorous foundation for understanding calculus concepts.
  • He published several papers on topics in mathematical analysis during his career.
differential calculus

Specific context of calculus focused on the concept of the derivative, rates of change, and slopes of curves.

  • Differential calculus is used to find the slope of a tangent line to a curve at any point.
  • The concept of limits is fundamental to understanding differential calculus.
integral calculus

Specific context of calculus that deals with the concept of the integral, accumulation of quantities, and areas under or between curves.

  • Integral calculus is crucial for computing the area under a curve.
  • In physics, integral calculus is often used to determine the total work done by a force over a distance.

Examples of usage

  • Studying calculus helps us understand the rate of change of quantities.
  • The fundamental theorem of calculus connects the concept of integration with that of differentiation.

Interesting Facts

Etymology

  • The word 'calculus' comes from the Latin word 'calculus', which means 'small stone' used for counting.
  • It was first used in the 17th century to describe a new approach to solving problems in mathematics.
  • The term reflects how early mathematicians used stones or pebbles to perform calculations.

History

  • Calculus was developed independently by Isaac Newton and Gottfried Wilhelm Leibniz in the late 17th century.
  • The subject was controversial in its early days, leading to disputes over who invented it first.
  • Fermat and Descartes also contributed ideas that laid the groundwork for calculus before its formal advent.

Applications

  • Calculus is essential in physics for understanding motion, forces, and energy.
  • It is heavily used in economics to model changes in cost and profit over time.
  • Biologists apply calculus to study population dynamics and changes in ecosystems.

Science

  • In biology, calculus aids in modeling how populations grow and change over time.
  • Astronomers use calculus to calculate the orbits of planets and the trajectories of spacecraft.
  • Chemists apply calculus to understand reaction rates and how substances interact.

Education

  • Many high schools and colleges offer calculus courses as part of STEM education, emphasizing its importance in science and engineering.
  • Despite its challenges, mastering calculus is a significant accomplishment for students and opens doors to advanced studies.
  • Tutoring in calculus has emerged as a popular service, with numerous online resources available for students needing extra help.

Translations

Translations of the word "calculus" in other languages:

🇵🇹 cálculo

🇮🇳 कलन

🇩🇪 Infinitesimalrechnung

🇮🇩 kalkulus

🇺🇦 диференційне числення

🇵🇱 rachunek różniczkowy

🇯🇵 微積分 (びせきぶん)

🇫🇷 calcul

🇪🇸 cálculo

🇹🇷 hesap

🇰🇷 미적분학 (微積分學)

🇸🇦 حساب التفاضل والتكامل

🇨🇿 kalkulus

🇸🇰 kalkulus

🇨🇳 微积分 (wēijīfēn)

🇸🇮 infinitesimalni račun

🇮🇸 heildareikning

🇰🇿 есептеу

🇬🇪 კალკულუსი

🇦🇿 hesablama

🇲🇽 cálculo

Word Frequency Rank

Ranked #10,084, this word falls into high-advanced vocabulary. It appears less frequently but is valuable for expressing precise meanings in specific contexts.