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Loading... Second Year Calculus: From Celestial Mechanics to Special Relativityby David M. Bressoud
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Sign up for LibraryThing to find out whether you'll like this book. No current Talk conversations about this book. As the title indicates, this work is has an unusual emphasis on physics; reflecting the author's inspiration, the appendix includes an excerpt from Freeman Dyson's speech "Missed Opportunities", which contains the stunning claim that if mathematicians had been keeping up with contemporary physics, in the 19th century they would have discovered "Einstein's theory of special relativity, the theory of topological groups and their linear representations, and probably large pieces of the theory of hyperbolic differential equations and functional analysis." Bressoud backs up the first part of this claim (through a textbook for multivariable calculus of all things!), concluding with a fast-paced crash-course on the historical development of the theory of electricity and a formal derivation of special relativity based only on the scientific knowledge at the time of Maxwell. With aesthetic unity unusual for math textbooks, the book opens with F=ma and a presentation of Newton's Law of Gravitation, derives all the mathematical formalism from physical concepts, and concludes with a derivation of E=mc^2 from F=ma. Taking its pedagogical inspiration from Apostol's Calculus and Edwards's Advanced Calculus, the work is also mathematically sophisticated and modern. I finished the book grateful that I now have a far more developed physical intuition of this branch of math and an understanding of theoretical details of celestial mechanics and electromagnetism, in just 360 pages of uncluttered mathematical writing. ( ) no reviews | add a review
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Second Year Calculus: From Celestial Mechanics to Special Relativity covers multi-variable and vector calculus, emphasizing the historical physical problems which gave rise to the concepts of calculus. The book carries us from the birth of the mechanized view of the world in Isaac Newton's Mathematical Principles of Natural Philosophy in which mathematics becomes the ultimate tool for modelling physical reality, to the dawn of a radically new and often counter-intuitive age in Albert Einstein's Special Theory of Relativity in which it is the mathematical model which suggests new aspects of that reality. The development of this process is discussed from the modern viewpoint of differential forms. Using this concept, the student learns to compute orbits and rocket trajectories, model flows and force fields, and derive the laws of electricity and magnetism. These exercises and observations of mathematical symmetry enable the student to better understand the interaction of physics and mathematics. No library descriptions found. |
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Google Books — Loading... GenresMelvil Decimal System (DDC)515Natural sciences and mathematics Mathematics AnalysisLC ClassificationRatingAverage:
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