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Johann Bernoulli: On the scientific achievements The scientific achievements of Johann Bernoullis are closely linked to those of his brother Jakob ). Above all, the creation of modern foundations for the infinitesimal calculus should be mentioned here - php homework assignments on domyhomework.club , which took place in close correspondence with the German mathematician Gottfried Wilhelm Leibniz (1646 to 1716). Despite (or perhaps because of) their work on often identical mathematical subjects, the personal relationship between the Bernoulli brothers was a very strained one (which, incidentally - do my homework for me please , was also true of Johann's relationship with his son Daniel). In particular, Johann's excessive ambition and his bossiness based on it led to disputes (often fought out in public). Despite these human weaknesses, John Bernoulli is probably one of the most important mathematicians of his time. He played a major role in spreading the modern concept of the infinitesimal calculus in Europe - https://domyhomework.club/geometry-homework/ . While his brother Jakob had used the term "integral" for the first time in 1690, Johann Bernoulli created that of the integral calculus ("Calculus integralis"). His "Lectiones mathematicae de methodo integralium" (Mathematical Lessons on the Integral Method), published in 1691/92, is considered the first work on integral calculus ever. It contains recent results by Johann Bernoulli on special mathematical curves, such as envelope curves or logarithmic spirals, as well as on catacouplings (focal lines or focal surfaces) occurring in optics. Furthermore, he dealt with (the integration of) differential equations, among other things he gave a solution formula for the Bernoullian differential equation y' + f(x) ⋅y + g(x)⋅ yn = 0 (today named after him). More information: | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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