This book studies the interplay between mathematical analysis and differential geometry as well as the foundations of these two fields. The development of a unified approach to topological vector spaces, differential geometry and algebraic and differential topology of function manifolds led to the broad expansion of global analysis. This book serves as a self-contained reference on both the prerequisites for further study and the recent research results which have played a decisive role in the advancement of global analysis.

Edward John Routh (1831-1907) was a highly successful mathematics coach at Cambridge. He also contributed to the foundations of control theory and to the modern treatment of mechanics. Published between 1896 and 1902, this revised two-volume textbook offers extensive coverage of statics, with formulae and examples throughout.