Product Description
This book contains the basics of group analysis of differential equations and its applications to various problems on nonlinear mechanics and physics. The consistent presentation of Lie group theory is illustrated by plentiful examples. For the first time the systematic group analysis of main postulates of classical and relativistic mechanics is given. Symmetries and conservation laws of differential equations are studied. Specific equations and problems of mechanics and physics are considered and exact solutions are given for equations of dynamics of ridgid body, heat transfer equations, wave equations, equations of hydrodynamics, the Thomas-Fermi equations, etc.
Special attention is paid to the application of group analysis to developing asymptotic methods of applied mathematics in problems with small parameter. The methods developed are used to solve basic equations (Van Der Pol's equation, Duffing equation, etc) encountered in the theory of nonlinear oscillations. This book will be valuable source for a wide range of scientists, engineers and students in the fields of applied mathematics, mechanics and physics. ... Read more

Product Description
Thermal Quadrupoles describes a novel and powerful method which allows design engineers firstly to model a linear problem in heat conduction, then build a solution in an explicit form and finally obtain a numerical solution. It constitutes a modelling and calculation tool based on a very efficient and systematic methodological approach.

The chapters in this book increase in complexity from a rapid presentation of the method for one dimensional transient problems in Chapter one, to non-uniform boundary conditions or inhomogeneous media in Chapter six. In addition, a wide range of corrected problems of contemporary interest are presented mainly in Chapters three and six with their numerical implementation in MATLAB language. This book covers the whole scope of linear problems and presents a wide range of concrete issues of contemporary interest such as harmonic excitations of buildings, transfer in composite media, thermal contact resistance and moving material heat transfer. Extensions of this method to coupled transfers in a semi-transparent medium and to mass transfer in porous media are considered respectively in Chapters seven and eight. Chapter nine is devoted to practical numerical methods that can be used to inverse the Laplace transform.

Written from an engineering perspective, with applications to real engineering problems, this book will be of significant interest not only to researchers, lecturers and graduate students in mechanical engineering (thermodynamics) and process engineers needing to model a heat transfer problem to obtain optimized operating conditions, but also to researchers interested in the simulation or design of experiments where heat transfer plays a significant role. ... Read more

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Provides the first self-contained account of integro-differential equations of the Barbashin type and partial integral operators--including existence, uniqueness, stability, and perturbation results. ... Read more