Augustin-Louis, Baron Cauchy summary

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Augustin-Louis, Baron Cauchy, (born Aug. 21, 1789, Paris, France—died May 23, 1857, Sceaux), French mathematician, pioneer of analysis and group theory. After a career as a military engineer in Napoleon’s navy, he wrote a treatise in 1813 that became the basis of the theory of complex variables. He also clarified the theory of calculus by developing the concepts of limits and continuity, laid the foundations for the mathematical theory of elasticity, and made important contributions to number theory. He is considered one of the greatest mathematicians of the modern era.

elasticity Summary

Elasticity, ability of a deformed material body to return to its original shape and size when the forces causing the deformation are removed. A body with this ability is said to behave (or respond) elastically. To a greater or lesser extent, most solid materials exhibit elastic behaviour, but there

An illustration of the difference between average and instantaneous rates of changeThe graph of f(t) shows the secant between (t, f(t)) and (t + h, f(t + h)) and the tangent to f(t) at t. As the time interval h approaches zero, the secant (average speed) approaches the tangent (actual, or instantaneous, speed) at (t, f(t)).

calculus Summary

Calculus, branch of mathematics concerned with the calculation of instantaneous rates of change (differential calculus) and the summation of infinitely many small factors to determine some whole (integral calculus). Two mathematicians, Isaac Newton of England and Gottfried Wilhelm Leibniz of

The transformation of a circular region into an approximately rectangular regionThis suggests that the same constant (π) appears in the formula for the circumference, 2πr, and in the formula for the area, πr2. As the number of pieces increases (from left to right), the “rectangle” converges on a πr by r rectangle with area πr2—the same area as that of the circle. This method of approximating a (complex) region by dividing it into simpler regions dates from antiquity and reappears in the calculus.

analysis Summary

Analysis, a branch of mathematics that deals with continuous change and with certain general types of processes that have emerged from the study of continuous change, such as limits, differentiation, and integration. Since the discovery of the differential and integral calculus by Isaac Newton and

mathematics Summary

Mathematics, the science of structure, order, and relation that has evolved from elemental practices of counting, measuring, and describing the shapes of objects. It deals with logical reasoning and quantitative calculation, and its development has involved an increasing degree of idealization and