Series: Springer Monographs in Mathematics
2009, XIV, 416 p., Hardcover
ISBN: 978-3-540-68346-9
Due: September 10, 2008
The classical books on interpolation address numerous negative results, i.e., results on divergent interpolation processes, usually constructed over some equidistant systems of nodes. The authors present, with complete proofs, recent results on convergent interpolation processes, for trigonometric and algebraic polynomials of one real variable, not yet published in other textbooks and monographs on approximation theory and numerical mathematics. In this special, but fundamental and important field of real analysis the authors present the state of art. Some 500 references are cited, including many new results of the authors. Basic tools in this field (orthogonal polynomials, moduli of smoothness, K-functionals, etc.) as well as some selected applications in numerical integration, integral equations, moment-preserving approximation and summation of slowly convergent series are also given. Beside the basic properties of the classical orthogonal polynomials the book provides new results on nonclassical orthogonal polynomials including methods for their numerical construction.
2009, Approx. 490 p., Softcover
ISBN: 978-3-7643-7479-2
Due: December 2008
Numerous examples, real calculations, a large number of exercises and many figures make this book a reliable escort for the whole course of studies
The third and last volume of this series deals with the theory of integration and the foundations of global analysis. Again a modern and clear construction is emphasized which not only provides a well-structured and beautiful theory, but also equips the reader with powerful tools for his further work in mathematics. On this account, for instance, the Bochner-Lebesgue integral is presented which is an indispensable resource for the modern theory of partial differential equations. Likewise a version of Stokefs theorem is proven that meets the practical needs of mathematics and theoretical physics as far as possible.
In the same way as in the previous volumes numerous prospects of continuative theories also will be given, and this will convey an impression of the importance and the strength of the presented theories to the reader. Additionally these parts will be used to practice and to deepen the provided material.
Numerous examples, real calculations, a large number of exercises and many figures make this book a reliable escort for the whole course of studies.
Preface.- IX. Elements of Measure Theory.- X. Theory of Integration.- XI. Manifolds and Differential Forms.- XII. Integration on Manifolds.- Bibliography.- Index.
Series: Undergraduate Texts in Mathematics
2009, Approx. 370 p. 40 illus., Hardcover
ISBN: 978-0-387-79147-0
Due: December 2008
Uses the "modified Moore method" approach in which examples and proof opportunities are worked into the text in order to encourage students to develop some of the content through their own examples and arguments while they are reading the text
Concentrates on the mathematics underlying
The material progresses at a gentle and inviting pace
Ample examples and exercises are included
This undergraduate textbook is written for a junior/senior level course on linear optimization. Unlike other texts, the treatment follows the "modified Moore method" approach in which examples and proof opportunities are worked into the text in order to encourage students to develop some of the content through their own experiments and arguments while they are reading the text. Additionally, the focus is on the mathematics underlying the ideas of optimizing linear functions under linear constraints and the algorithms used to solve them. In particular, the author uses the Simplex Algorithm to motivate these concepts. The text progresses at a gentle and inviting pace. The presentation is driven by examples and illustrations. Ample exercises are provided at the end of each chapter for mastering the material.
The instructor's version of the text contains solutions embedded within the text, rather than in an appendix. It also has extra material and suggestions for the teacherfs benefit. Junior/senior level undergraduate students will benefit from the book. Future secondary school mathematics teachers will also find this book useful.
Introduction.- The Simplex Algorithm.- Geometry.- The Duality Theorem.- Matrix Implementation.- General Form.- Unsolvable Systems.- Geometry Revisited.- Game Theory.- Network Implementation.- Combinatorics.- A Linear Algebra Overview.- B The Equivalence of the Auxiliary and Shortcut Methods.- C LOP Catalog.
Series: Applied Mathematical Sciences , Preliminary entry 167
Volume package An Introduction to the Mathematical Theory of the Navier-Stokes Equations
Originally published as volume 38 in series: Springer Tracts in Natural Philosophy
2009, XIII, 583 p. 1 illus., Hardcover
ISBN: 978-0-387-09619-3
Due: January 2009
This work is a systematic and up-to-date investigation of the fundamental properties of the Navier-Stokes equations, including existence, uniqueness, and regularity of solutions in bounded as well as unbounded domains. When the region of flow is unbounded, asymptotic behavior is also investigated. The problems are treated within the framework of Lebesgue spaces, such a general approach allowing for a comprehensive and unified treatment.
The subject is divided into two volumes, which deal with steady flow (boundary value problem). Each volume is self-contained. In both volumes, the nonlinear analysis is preceded and supported by a suitable linear analysis; however, the nonlinear analysis is treated to a large extent due to independent interest.
This volume examines linearised approximations of the steady-state Navier-Stokes problem ? specifically, the Stokes problem in bounded and exterior domains as well as in domains with noncompact boundaries. Moreover, Oseen equations and the associated boundary value problem are investigated in exterior domains.
This new edition has been revised and updated throughout to take into account the recent significant contributions to the field. A new chapter is dedicated to the motion of a rigid body in a fluid in the Stokes regime, which has found increased interest due to questions related to liquid-particle interactions.
The books are addressed to students (both graduate and advanced undergraduate) and to all mathematicians and applied mathematicians who wish to become acquainted with the subject.
Preface - Steady-State Solutions of the Navier-Stokes Equations: Statement of the Problem and Open Questions - Basic Function Spaces and Related Inequalities - The Function Spaces of Hydrodynamics - Steady Stokes Flow in Bounded Domains - Steady Stokes Flow in Exterior Domains - Steady Stokes Flow in Domains with Unbounded Boundaries - Steady Oseen Flow in Exterior Domains - Motion of a Rigid Body in a Fluid in the Stokes Regime - Bibliography