Abstract
We develop the integral calculus. In this chapter we introduce curvilinear and surface integrals and obtain some fundamental and widely used integral formulas generalizing the classical Newton–Leibniz formula.
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Notes
- 1.
G.P. Joule (1818–1889) – British physicist who discovered the law of thermal action of a current and also determined, independently of Mayer, the mechanical equivalent of heat.
- 2.
J.P. Mayer (1814–1878) – German scholar, a physician by training; he stated the law of conservation and transformation of energy and found the mechanical equivalent of heat.
- 3.
N.L.S. Carnot (1796–1832) – French engineer, one of the founders of thermodynamics.
- 4.
M. Faraday (1791–1867) – outstanding British physicist, creator of the concept of an electromagnetic field.
- 5.
A.M. Ampère (1775–1836) – French physicist and mathematician, one of the founders of modern electrodynamics.
- 6.
Biot (1774–1862), Savart (1791–1841) – French physicists.
- 7.
G. Green (1793–1841) – British mathematician and mathematical physicist. Newton’s grave in Westminster Abbey is framed by five smaller gravestones with brilliant names: Faraday, Thomson (Lord Kelvin), Green, Maxwell, and Dirac.
- 8.
L.E.J. Brouwer (1881–1966) – well-known Dutch mathematician. A number of fundamental theorems of topology are associated with his name, as well as an analysis of the foundations of mathematics that leads to the philosophico-mathematical concepts called intuitionism.
- 9.
The classical Stokes theorem (13.34) is meant.
- 10.
Élie Cartan (1869–1951) – outstanding French geometer.
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Zorich, V.A. (2016). Line and Surface Integrals. In: Mathematical Analysis II. Universitext. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48993-2_5
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DOI: https://doi.org/10.1007/978-3-662-48993-2_5
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