On The Analytical Representation Of Direction

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.

The writings of Newton, Leibniz, Pascal, Riemann, Bernoulli, and others in a comprehensive selection of 125 treatises dating from the Renaissance to the late 19th century — most unavailable elsewhere.

Discusses theories of atmospheric circulation, covering such topics as atmospheric structure, vorticity, atmospheric wave motion, models of the wind, and moisture processes.

The Wonder of Quantum Spin is a confection of the history and the science of quantum spin sprinkled with quotations and excerpts from pioneers who lived and breathed science. The book unfolds two centuries of the golden era in mathematics and physics, where first glimpses of spin appeared nearly 200 years ago in the mathematics of rotations. In these studies, spinors emerged as a new entity that changes sign after a 360 degree rotation, reminiscent of the Mobius geometry. A century later, quantum spins described by spinors was discovered in physics in atomic spectra. This led to the discovery of antimatter and raised the possibility of parity violation. It gave the first warning that protons and neutrons are not elementary. As we approach the centennial of the discovery, the spin mystique prevails as we have no clue of what exactly is spinning. Nevertheless, the theoretical framework underlying the spin determines why we exist, and explains the mysteries of the 3000-year-old phenomenon of magnetism. This book showcases MRI - one of the most important medical advances of the 20th century with a tantalizing history of the application of nuclear spin to humanity. It narrates fascinating spin tales of the precision measurements of electron and muon spin magnetic moments displaying a mindboggling confrontation between theory and experiment that remains our ambassador to quantum physics.

The methods of time-efficient simulation of surface-excited wave propagation in plate-like multilayered composites are presented. The mathematical model of wave propagation in laminated plate based on the elasticity theory is transformed and then solved in wavenumber-frequency domain. The numerical methods for computation of inverse transform in time-space domain are developed and used for analysis of wave and energy propagation phenomena occurring in composite plates due to surface excitation.

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.