2006, X, 321 p. 204 illus., Softcover
ISBN: 3-540-30685-4
About this textbook
This book is an introduction to modern numerical methods in
engineering. It covers applications in fluid mechanics,
structural mechanics, and heat transfer as the most relevant
fields for engineering disciplines such as computational
engineering, scientific computing, mechanical engineering as well
as chemical and civil engineering. The content covers all aspects
in the interdisciplinary field which are essential for an ''up-to-date''
engineer.
Written for:
Students, scientists, industrial engineers in mechanical
engineering
Table of contents
Series: Encyclopaedia of Mathematical Sciences, Vol. 3
2006, Approx. 470 p. 108 illus., Hardcover
ISBN: 3-540-28246-7
About this book
The main purpose of the book is to acquaint mathematicians,
physicists and engineers with classical mechanics as a whole, in
both its traditional and its contemporary aspects. As such, it
describes the fundamental principles, problems, and methods of
classical mechanics, with the emphasis firmly laid on the working
apparatus, rather than the physical foundations or applications.
Chapters cover the n-body problem, symmetry groups of mechanical
systems and the corresponding conservation laws, the problem of
the integrability of the equations of motion, the theory of
oscillations and perturbation theory.
Written for:
Mathematicians, physicists, astronomers
Table of contents
1 Basic Principles of Classical Mechanics.- 2 The n-Body Problem.-
3 Symmetry Groups and Order Reduction.- 4 Variational Principles
and Methods.- 5 Integrable Systems and Integration Methods.- 6
Perturbation Theory for Integrable Systems.- 7 Non-Integrable
Systems.- 8 Theory of Small Oscillations.- 9 Tensor Invariants of
Equations of Dynamics.- References
Series: Advances in Mathematics, Vol. 10
2006, XIV, 340 p., Hardcover
ISBN: 0-387-30804-0
About this book
M-Solid Varieties of Algebras provides a complete and systematic
introduction to the fundamentals of the hyperequational theory of
universal algebra, offering the newest results on M-solid
varieties of semirings and semigroups. The book aims to develop
the theory of M-solid varieties as a system of mathematical
discourse that is applicable in several concrete situations. It
applies the general theory to two classes of algebraic
structures, semigroups and semirings. Both these varieties and
their subvarieties play an important role in computer science.
A unique feature of this book is the use of Galois connections to
integrate different topics. Galois connections form the abstract
framework not only for classical and modern Galois theory,
involving groups, fields and rings, but also for many other
algebraic, topological, ordertheoretical, categorical and logical
theories. This concept is used throughout the whole book, along
with the related topics of closure operators, complete lattices,
Galois closed subrelations and conjugate pairs of completely
additive closure operators.
Written for:
Researchers in the fields of universal algebra, semigroups, and
semirings, researchers in theoretical computer science, students
and lecturers in these fields
Table of contents
Series: Springer Series in Computational Mathematics, Vol. 31
2006, XVII, 644 p. 153 illus., Hardcover
ISBN: 3-540-30663-3
About this book
Numerical methods that preserve properties of Hamiltonian
systems, reversible systems, differential equations on manifolds
and problems with highly oscillatory solutions are the subject of
this book. A complete self-contained theory of symplectic and
symmetric methods, which include Runge-Kutta, composition,
splitting, multistep and various specially designed integrators,
is presented and their construction and practical merits are
discussed. The long-time behaviour of the numerical solutions is
studied using a backward error analysis (modified equations)
combined with KAM theory. The book is illustrated by many
figures, it treats applications from physics and astronomy and
contains many numerical experiments and comparisons of different
approaches. The second edition is substantially revised and
enlarged, with many improvements in the presentation and
additions concerning in particular non-canonical Hamiltonian
systems, highly oscillatory mechanical systems, and the dynamics
of multistep methods.
Written for:
Graduate students and researchers
Series: Nonconvex Optimization and Its Applications, Vol. 83
2006, X, 298 p. 44 illus., Hardcover
ISBN: 0-387-30063-5
About this book
Large-Scale Nonlinear Optimization reviews and discusses recent
advances in the development of methods and algorithms for
nonlinear optimization and its applications, focusing on the
large-dimensional case, the current forefront of much research.
The chapters of the book, authored by some of the most active and
well-known researchers in nonlinear optimization, give an updated
overview of the field from different and complementary
standpoints, including theoretical analysis, algorithmic
development, implementation issues and applications.
Written for:
Researchers in applied mathematics, advanced engineering, and
computer science; also recommended for further reading within
graduate studies, postgraduate and doctoral programs
Table of contents
Series: Lecture Notes in Mathematics, Vol. 1884
2006, XII, 557 p., Softcover
ISBN: 3-540-32059-8
About this book
Many of problems of the natural sciences lead to nonlinear
partial differential equations. However, only a few of them have
succeeded in being solved explicitly. Therefore different methods
of qualitative analysis such as the asymptotic methods play a
very important role. This is the first book in the world
literature giving a systematic development of a general
asymptotic theory for nonlinear partial differential equations
with dissipation. Many typical well-known equations are
considered as examples, such as: nonlinear heat equation, KdVB
equation, nonlinear damped wave equation, Landau-Ginzburg
equation, Sobolev type equations, systems of equations of
Boussinesq, Navier-Stokes and others.
Written for:
Researchers and graduate students in Mathematics, Physics and
Engineering
Table of contents
Preliminary results.- Asymptotically weak nonlinearity.- Critical
Noncenvective Equations.- Critical Convective Equations, Self-similar
Solutions.- Subcritical Nonconvective Equations.- Subcritical
Convective Equations.- Bibliography.- Subject Index.