calculus
Sign in to saveCalculus is the mathematical study of continuous change, and the principal precursor of modern mathematical analysis. Originally called infinitesimal calculus or the calculus of infinitesimals, it has two major branches, differential calculus and integral calculus. Differential calculus analyses instantaneous rates of change and the slopes of curves; integral calculus analyses accumulation of quantities and areas under or between curves. These two branches are related to each other by the fundamental theorem of calculus. Calculus uses convergence of infinite sequences and infinite series to a
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Calculus is the mathematical study of continuous change, with two main branches: differential calculus, which analyzes how things change at any given moment, and integral calculus, which analyzes how quantities accumulate over time. It matters because these tools allow mathematicians and scientists to understand and predict how systems change and grow, from the motion of objects to the spread of diseases.
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Article
30 sectionsContents
- Etymology
- Primary concepts and basic notation
- Limits and infinitesimals
- Differential calculus
- Leibniz notation
- Integral calculus
- Fundamental theorem
- Advanced topics
- Multivariable and vector calculus
- Differential equations
- Real analysis
- Complex analysis
- Calculus of variations
- History
- Ancient precursors
- Egypt and Babylon
- Greece
- China
- Medieval
- Middle East
- India
- Europe
- Modern
- Foundations
- Significance
- Applications
- See also
- References
- Further reading
- External links
Calculus is the mathematical study of continuous change, and the principal precursor of modern mathematical analysis. Originally called infinitesimal calculus or the calculus of infinitesimals, it has two major branches, differential calculus and integral calculus. Differential calculus analyses instantaneous rates of change and the slopes of curves; integral calculus analyses accumulation of quantities and areas under or between curves. These two branches are related to each other by the fundamental theorem of calculus. Calculus uses convergence of infinite sequences and infinite series to a well-defined mathematical limit.
Calculus is the "mathematical backbone" for solving problems in which variable quantities change with time or another reference value. It has also been called "the basic instrument of physical science".