Series: Developments in Mathematics, Vol. 35
1st ed. 2015, X, 232 p. 251 illus., 55 illus. in
Hardcover
ISBN 978-3-319-26307-6
* Presents and explains a general, efficient, and elegant method of a
solution for boundary value problems for an elliptic system of partial
differential equations
* Shows in detail a methodology for constructing a boundary integral
equation method (BIEM), and all the attending mathematical
properties are derived with full rigor
* Develops and employs a numerical scheme directly related to the
BIEMs to compute approximate solutions
This book presents and explains a general, efficient, and elegant method for solving the
Dirichlet, Neumann, and Robin boundary value problems for the extensional deformation
of a thin plate on an elastic foundation. The solutions of these problems are obtained
both analytically*by means of direct and indirect boundary integral equation methods
(BIEMs)*and numerically, through the application of a boundary element technique. The
text discusses the methodology for constructing a BIEM, deriving all the attending
mathematical properties with full rigor. The model investigated in the book can serve
as a template for the study of any linear elliptic two-dimensional problem with constant
coefficients. The representation of the solution in terms of single-layer and double-layer
potentials is pivotal in the development of a BIEM, which, in turn, forms the basis for the
second part of the book, where approximate solutions are computed with a high degree
of accuracy.
The book is intended for graduate students and researchers in the fields of boundary
integral equation methods, computational mechanics and, more generally, scientists
working in the areas of applied mathematics and engineering. Given its detailed
presentation of the material, the book can also be used as a text in a specialized
graduate course on the applications of the boundary element method to the numerical
computation of solutions in a wide variety of problems.
Series: Graduate Texts in Mathematics, Vol. 171
2015, X, 432 p. 50 illus., 1 illus. in
Hardcover
ISBN 978-3-319-26652-7
* Includes a substantial addition of unique and enriching exercises
* Exists as one of the few Works to combine both the geometric parts
of Riemannian geometry and analytic aspects of the theory
* Presents a new approach to the Bochner technique for tensors that
considerably simplifies the material
Intended for a one year course, this text serves as a single source, introducing readers
to the important techniques and theorems, while also containing enough background
on advanced topics to appeal to those students wishing to specialize in Riemannian
geometry. This is one of the few Works to combine both the geometric parts of
Riemannian geometry and the analytic aspects of the theory. The book will appeal to a
readership that have a basic knowledge of standard manifold theory, including tensors,
forms, and Lie groups.
Important revisions to the third edition include:
* a substantial addition of unique and enriching exercises scattered throughout the text;
* inclusion of an increased number of coordinate calculations of connection and
curvature;
* addition of general formulas for curvature on Lie Groups and submersions;
* integration of variational calculus into the text allowing for an early treatment of the
Sphere theorem using a proof by Berger;
* incorporation of several recent results about manifolds with positive curvature;
* presentation of a new simplifying approach to the Bochner technique for tensors with
application to bound topological quantities with general lower curvature bounds.
Series: Universitext
2015, XXI, 644 p. 41 illus.
Hardcover
ISBN 978-3-662-48991-8
* Thoroughness of coverage, from elementary to very advanced
* Clarity of exposition
* Originality and variety of exercises and examples
* Complete logical rigor of discussion
* Various new appendices
* Useful not only to mathematicians, but also to physicists and
engineers
This second English edition of a very popular two-volume work presents a thorough first
course in analysis, leading from real numbers to such advanced topics as differential forms
on manifolds; asymptotic methods; Fourier, Laplace, and Legendre transforms; elliptic
functions; and distributions. Especially notable in this course are the clearly expressed
orientation toward the natural sciences and the informal exploration of the essence and
the roots of the basic concepts and theorems of calculus. Clarity of exposition is matched
by a wealth of instructive exercises, problems, and fresh applications to areas seldom
touched on in textbooks on real analysis.
The main difference between the second and first English editions is the addition of a
series of appendices to each volume. There are six of them in the first volume and five in
the second. The subjects of these appendices are diverse. They are meant to be useful
to both students (in mathematics and physics) and teachers, who may be motivated by
different goals. Some of the appendices are surveys, both prospective and retrospective.
The final survey establishes important conceptual connections between analysis and
other parts of mathematics.
This second volume presents classical analysis in its current form as part of a unified
mathematics. It shows how analysis interacts with other modern fields of mathematics
such as algebra, differential geometry, differential equations, complex analysis, and
functional analysis. This book provides a firm foundation for advanced work in any of
these directions.
gThe textbook of Zorich seems to me the most successful of the available comprehensive
textbooks of analysis for mathematicians and physicists.
Series: Springer Monographs in Mathematics
1st ed. 2016, Approx. 415 p.
Hardcover
ISBN 978-1-4471-6788-4
* Contains many applications to coding theory, algebraic geometry,
incidence geometry, design theory, graph theory, and group theory
* Provides detailed studies of quadrics, Hermitian varieties, Grassmann
varieties, Veronese and Segre varieties
* Unique being the only book of its kind
This book is the second edition of the third and last volume of a treatise on projective
spaces over a finite field, also known as Galois geometries. This volume completes the
trilogy comprised of plane case (first volume) and three dimensions (second volume).
This revised edition includes much updating and new material. It is a mostly selfcontained
study of classical varieties over a finite field, related incidence structures and
particular point sets in finite n-dimensional projective spaces.
General Galois Geometries is suitable for PhD students and researchers in combinatorics
and geometry. The separate chapters can be used for courses at postgraduate level.
Series: Progress in Mathematics, Vol. 313
1st ed. 2016, Approx. 280 p.
Hardcover
ISBN 978-3-319-26337-3
* Solves the 16th Hilbert problem (restricted to algebraic limit cycles)
based on generic assumptions
* Presents a detailed analysis of transpositional relations, a
generalization of the Hamiltonian principle
* Features the Nambu bracket as central tool in the authors' approach
on solving inverse problems in ODEs
This book focuses on finding all ordinary differential equations that satisfy a given set of
properties, thus dedicating itself to inverse problems of ordinary differential equations.
The Nambu bracket acts as the central tool to the authorsf approach. The book begins
with a characterization of ordinary differential equations in R^N which have a given set of
M*N partial and first integrals, before addressing planar polynomial differential systems
with a given set of polynomial partial integrals. The authors then go on to solve the
16th Hilbert problem (restricted to algebraic limit cycles) based on generic assumptions,
followed by a study of the inverse problem for constrained Lagrange mechanics and
Hamiltonian systems, as well as the issue of the integrability of a constrained rigid body.
The book concludes with an analysis of transpositional relations, a generalization of the
Hamiltonian principle, as well as the inverse problem in vakonomic mechanics.