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  2. Institutiones calculi integralis - Wikipedia

    en.wikipedia.org/wiki/Institutiones_calculi...

    Institutiones calculi integralis (Foundations of integral calculus) is a three-volume textbook written by Leonhard Euler and published in 1768. It was on the subject of integral calculus and contained many of Euler's discoveries about differential equations .

  3. A Course of Pure Mathematics - Wikipedia

    en.wikipedia.org/wiki/A_Course_of_Pure_Mathematics

    the book is organized into the following chapters. i. real variables; ii. functions of real variables; iii. complex numbers; iv. limits of functions of a positive integral variable; v. limits of functions of a continuous variable. continuous and discontinuous functions; vi. derivatives and integrals; vii. additional theorems in the differential ...

  4. Grigorii Fikhtengol'ts - Wikipedia

    en.wikipedia.org/wiki/Grigorii_Fikhtengol'ts

    Fikhtengol'ts's books on analysis are widely used in Middle and Eastern European, as well as Chinese universities, due to their exceptionally detailed and well-organized presentation of material on mathematical analysis. For unknown reasons, these books have not gained the same level of fame in universities in other parts of the world.

  5. 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.

  6. Archimedes Palimpsest - Wikipedia

    en.wikipedia.org/wiki/Archimedes_Palimpsest

    Using this method, Archimedes was able to solve several problems now treated by integral calculus, which was given its modern form in the seventeenth century by Isaac Newton and Gottfried Leibniz. Among those problems were that of calculating the center of gravity of a solid hemisphere , the center of gravity of a frustum of a circular ...

  7. Calculus - Wikipedia

    en.wikipedia.org/wiki/Calculus

    Calculus is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations. Originally called infinitesimal calculus or "the calculus of infinitesimals", it has two major branches, differential calculus and integral calculus.

  8. Riemann integral - Wikipedia

    en.wikipedia.org/wiki/Riemann_integral

    The Darboux integral is defined whenever the Riemann integral is, and always gives the same result. Conversely, the gauge integral is a simple but more powerful generalization of the Riemann integral and has led some educators to advocate that it should replace the Riemann integral in introductory calculus courses. [12]

  9. Lebesgue integral - Wikipedia

    en.wikipedia.org/wiki/Lebesgue_integral

    English translation by Laurence Chisholm Young, with two additional notes by Stefan Banach. Shilov, G. E.; Gurevich, B. L. (1977). Integral, measure and derivative: a unified approach. Translated from the Russian and edited by Richard A. Silverman. Dover Books on Advanced Mathematics. New York: Dover Publications Inc. xiv+233. ISBN 0-486-63519-8.

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