本書介紹了相對論的數(shù)學(xué)基礎(chǔ)的相關(guān)理論知識。目標讀者是數(shù)學(xué)、其他科學(xué)和工程專業(yè)的高年級本科生和研究生。讀者應(yīng)了解高等微積分的基礎(chǔ)知識、一些解微分方程的技巧、一些線性代數(shù)知識以及集合論和群論的基礎(chǔ)知識。本書適合對相對論的數(shù)學(xué)方面感興趣的高年級本科生、研究生以及數(shù)學(xué)研究人員閱讀參考。This book has three main goals. First， it explores a selection of topics from the early period of the theory of relativity， focusing on particular aspects that are interesting or unusual. These include the twin paradox; relativistic mechanics and its interaction with Maxwell's laws; the earliest triumphs of general relativity relating to the orbit of Mercury and the deflection of light passing near the sun; and the surprising bizarre metric of Kurt G？del， in which time travel is possible. Second， it provides an exposition of the differential geometry needed to understand these topics on a level that is intended to be accessible to those with just two years of university-level mathematics as background. Third， it reflects on the historical development of the subject and its significance for our understanding of what reality is and how we can know about the physical universe. The book also takes note of historical prefigurations of relativity， such as Euler's 1744 result that a particle moving on a surface and subject to no tangential acceleration will move along a geodesic， and the work of Lorentz and Poincaré on space-time coordinate transformations between two observers in motion at constant relative velocity.The book is aimed at advanced undergraduate mathematics， science， and engineering majors （and， of course， at any interested person who knows a little university-level mathematics）. The reader is assumed to know the rudiments of advanced calculus， a few techniques for solving differential equations， some linear algebra， and basics of set theory and groups.
鄂公網(wǎng)安備 42010302001612號 