Böcker av Leonid P. Lebedev

This book started its life as a series of lectures given by the second author from the 1970's onwards to students in their third and fourth years in the Department of Mathematics at the Rostov State University.

The tensorial nature of a quantity permits us to formulate transformation rules for its components under a change of basis. This book offers a self-contained treatment of tensors, tensor fields, and their applications.

Fully supported with underlying mechanical concepts, this revised new edition includes exercises and examples throughout in its concise and accessible introduction to functional analysis, including new material on essential inequalities and imbedding results.

This is a book for those who enjoy thinking about how and why Nature can be described using mathematical tools. Approximating Perfection considers the background behind mechanics as well as the mathematical ideas that play key roles in mechanical applications. Concentrating on the models of applied mechanics, the book engages the reader in the types of nuts-and-bolts considerations that are normally avoided in formal engineering courses: how and why models remain imperfect, and the factors that motivated their development. The opening chapter reviews and reconsiders the basics of calculus from a fully applied point of view; subsequent chapters explore selected topics from solid mechanics, hydrodynamics, and the natural sciences. Emphasis is placed on the logic that underlies modeling in mechanics and the many surprising parallels that exist between seemingly diverse areas. The mathematical demands on the reader are kept to a minimum, so the book will appeal to a wide technical audience.

Presents the basics of micropolar continuum including short but comprehensive introduction of stress and strain measures, derivation of motion equations. This book demonstrates the difference between Cosserat and the classic theory. It also considers more specific problems related to the constitutive modeling.