For students: Numerous exercises with answers and solutions, plots and tables
For researchers: Vast references to the relevant Russian literature not well known or unavailable for an English speaking reader
For engineers: Numerous problems on deformation, buckling and vibrations of thin-walled structural elements with a comparison of results obtained by asymptotic, analytical and numerical approaches
The construction of solutions of singularly perturbed systems of equations and boundary value problems that are characteristic for the mechanics of thin-walled structures are the main focus of the book. The theoretical results are supplemented by the analysis of problems and exercises. Some of the topics are rarely discussed in the textbooks, for example, the Newton polyhedron, which is a generalization of the Newton polygon for equations with two or more parameters. After introducing the important concept of the index of variation for functions special attention is devoted to eigenvalue problems containing a small parameter. The main part of the book deals with methods of asymptotic solutions of linear singularly perturbed boundary and boundary value problems without or with turning points, respectively. As examples, one-dimensional equilibrium, dynamics and stability problems for rigid bodies and solids are presented in detail. Numerous exercises and examples as well as vast references to the relevant Russian literature not well known for an English speaking reader makes this a indispensable textbook on the topic. Β
Topics
Ordinary Differential Equations
Partial Differential Equations
Mechanics