By Lokenath Debnath
This ebook basically serves as a ancient study monograph at the biographical cartoon and occupation of Leonhard Euler and his significant contributions to varied components within the mathematical and actual sciences. It includes fourteen chapters describing Euler's works on quantity concept, algebra, geometry, trigonometry, differential and imperative calculus, research, endless sequence and endless items, usual and elliptic integrals and particular features, usual and partial differential equations, calculus of diversifications, graph conception and topology, mechanics and ballistic examine, elasticity and fluid mechanics, physics and astronomy, likelihood and information. The e-book is written to supply a definitive effect of Euler's own existence in addition to of the diversity, strength, and intensity of his designated contributions. This tricentennial tribute commemorates Euler the nice guy and Euler the common mathematician of all time. in keeping with the author's traditionally inspired approach to instructing, unique awareness is given to illustrate that Euler's paintings had served because the foundation of analysis and advancements of mathematical and actual sciences for the final three hundred years. An try can be made to check his learn and its relation to present arithmetic and technology. in response to a chain of Euler's outstanding contributions, the historic improvement of many various matters of mathematical sciences is traced with a linking observation in order that it places the reader on the leading edge of present learn.
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Extra resources for The Legacy of Leonhard Euler: A Tricentennial Tribute
Sample text
His new methodology of science led him to believe in the total reformulation that not only imparted expected and unprecedented power to science, but bound it indissolubly to mathematics. It was Galileo who remarkably discovered the more radical, more effective and more practical methods for modern science. He demonstrated the profound effectiveness of his approach to science through his own work. ” Galileo himself was convinced that nature is simple, orderly, and mathematically designed which can be documented by his own famous 1610 quotation: “Philosophy [nature] is written in that great book which ever lies before our eyes — I mean the universe — but we cannot understand it if we do not first ...
Although Newton first discovered calculus in 1664-1666, and communicated his ideas and results through manuscripts and letters to selected friends from 1666 onwards, however, he never published his manuscripts during 1664-1686. In his two letters addressed to Leibniz in 1676, Newton made no mention of his 1671 manuscript “Treatise of the method of series and fluxions” which contained algorithms and rules of differential calculus (similar to those of Leibniz) and their applications to problems of tangents and curvatures of plane curves.
After a century of slow progress, the revival of the projective geometry received considerable attention by Gaspard Monge (1746-1818) and his ´ school at the Ecole Polytechnique. Monge’s extensive work in descriptive geometry, ordinary and partial differential equations won the remarkable admiration from mathematical scientists of the world. His greatest student was Poncelet who published his famous Treatise on the Projective Properties of Figures in 1822 which he subsequently expanded and revised this treatise and later published in two volumes entitled Applications d’analyse et de g´eom´etrie (1862-1864).