The book consists of two parts. The first part consists of seven chapters and presents a new software for package Maple of releases 6-10. The tools represented in this chapters increase the range and efficiency of use of Maple on Windows platform owing to the innovations in three basic directions: (1) elimination of a series of basic defects and shortcomings, (2) extending of capabilities of a series of standard tools, and (3) replenishment of Maple by new means which increase capabilities of its program environment, including the means which improve the level of compatibility of releases 6 - 10. The basic attention is devoted to additional tools created in the process of practical use and testing the Maple of releases 4 - 10 which by some parameters extend essentially the opportunities of the package and facilitate the work with it. The considerable attention is also devoted to the means providing package compatibility of releases 6-10.

Whereas the algorithms of physical and engineering problems of the second part mainly use the finite element method (FEM). Actually, this is an essential tool for undergraduates or early postgraduates, as well as a reference book for engineers and scientists who want to develop quickly finite-element programs or implant their own Fortran programs into computer algebra system Maple. The FEM adapted for Maple appears to be an interesting one.

The eighth chapter of the book considers questions of a computer solution in Maple of basic problems of thermal conductivity having important value to solve many applied problems of thermal physics as well as a combination of problems in the theory of elasticity and plasticity. The solution in the package environment for the following problems is considered to be: linear (1) and non-linear (2) stationary problems of thermal conductivity as well as linear (3) and non-linear (4) non-stationary problems of thermal conductivity. In particular, linear non-stationary heat conductivity equation is one of the main equations describing convective heat exchange and mass exchange occurring in the systems of various physical natures. Whereas the last problem keeps not only the great independent value for definition of non-stationary temperature fields in various matters and materials, but it is also an important component of more complex physical and engineering problems having rather wide fields of appendices as well.

In the ninth chapter the four problems of linear mechanics of deformable bodies are considered. The main relations concerning the description of tensely deformable state and the relations for resilient bodies are established. Each problem is solved by the finite element method. The main principles of solution of the next practically important problems are presented: (1) the definition of geometrical parameters of cross-sections of bodies, (2) the calculation of rod constructions at static loads, (3) the plane problem of the theory of elasticity, and (4) the contact problem of two elastic bodies. The indicated problems represent the applied interest; therefore Maple programs corresponding to them for a number of the appendices are taken into consideration.

In the tenth chapter the dynamic problems of the theory of elasticity representing major practical interest in designing the objects of mechanical engineering are considered. The main problems here are: the definition of own and forced oscillations of elastic bodies as well as the research of the behavior of elastic systems at short-term loads. The problems considered in the chapter generate the practical interest for the research of the indicated questions. The main principles of solution of the other practically important problems are represented: (1) research of our own and forced oscillations of the linear rod systems, (2) the plane problem of the theory of elasticity at dynamical loads, (3) a dynamical problem of shells of arbitrary configuration, and (4) a geometrically non-linear problem of the theory of elasticity at dynamical loads.

In the eleventh chapter the five problems of hydrodynamics having the important applied value and allowing to solve many engineering problems which are linked with the flow around bodies, oscillations of constructions in a liquid, a percussion impulse action onto a liquid, etc. are considered. The following problems are represented: an vortex-free motion of a liquid in terms of potential of speeds (1), the flow function (2), the Navier-Stokes equations describing common movement of a liquid (3), a solution of the Navier-Stokes equations in the terms of a vortical function of the flow (4), widely used in the applied problems of hydromechanics, and (5) a non-stationary movement of a compressed liquid described by the potential of speeds.

In the twelfth chapter the following problems of hydromechanics which play an important role in the research of problems are considered: (1) hydrodynamic lubrication between movable surfaces, (2) models of movement of the non-Newtonian liquid, (3) the problem of convective heat exchange and mass transfer for an incompressible liquid, (4) a model of convective heat exchange in a liquid, and (5) the models of movement of a liquid in hydraulic system.

When solving dynamic problems of solid mechanics there is a necessity of the definition of moments of inertia of masses of bodies of complex geometrical forms as well as systems of bodies with respect to various axes of coordinates. For example, the thirteenth chapter considers the problems of the definition of moments of inertia of masses of bodies with complex geometrical forms and systems of such bodies. By tools of Maple the following interesting problems are studied: (1) the calculation of moments of inertia of a solid; (2) the calculation of moments of inertia of the system of solids; (3) the non-linear oscillations of mechanical systems; (4) the derivation and solution of equations of motion of a mechanical system with concentrated parameters, and (5) the calculation of transitional torsion oscillations in a mechanical transmission.

The problems of moving of transport along the uneven way are of great interest. When the transport moves along the uneven way upon elements of its hanger bracket a rather large loads affect, which in turn, decrease longevity of elements of hanger bracket and all carrier as a whole, and also essentially influence onto its comfortable quality. In this connection the fourteenth chapter of the book considers the following interesting problems: (1) movements of a carrier on an uneven way; (2) the stationary random oscillations of a carrier; (3) movements of a car on an uneven railway path; (4) dynamics of pneumatic vibration extinguisher with steady magnets, and (5) models of moving gas in a pneumatic system.

Finally, the fifteenth chapter is devoted to the application of Maple for solution of optimization problems. In this chapter the problem of minimizing function of real variables under the assumption that no constraint is imposed on the values of these variables is considered in the light of different standpoints.

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