Pure and Applied Undergraduate Texts, Volume: 15
1998; 526 pp; hardcover
ISBN-13: 978-0-8218-6889-8
Expected publication date is August 19, 2011.
Building on the basic techniques of separation of variables and Fourier series, the book presents the solution of boundary-value problems for basic partial differential equations: the heat equation, wave equation, and Laplace equation, considered in various standard coordinate systems--rectangular, cylindrical, and spherical. Each of the equations is derived in the three-dimensional context; the solutions are organized according to the geometry of the coordinate system, which makes the mathematics especially transparent. Bessel and Legendre functions are studied and used whenever appropriate throughout the text. The notions of steady-state solution of closely related stationary solutions are developed for the heat equation; applications to the study of heat flow in the earth are presented. The problem of the vibrating string is studied in detail both in the Fourier transform setting and from the viewpoint of the explicit representation (d'Alembert formula). Additional chapters include the numerical analysis of solutions and the method of Green's functions for solutions of partial differential equations. The exposition also includes asymptotic methods (Laplace transform and stationary phase).
With more than 200 working examples and 700 exercises (more than 450 with answers), the book is suitable for an undergraduate course in partial differential equations.
Undergraduate students interested in PDE and applied PDE.
Preliminaries
Fourier series
Boundary-value problems in rectangular coordinates
Boundary-value problems in cylindrical coordinates
Boundary-value problems in spherical coordinates
Fourier transforms and applications
Asymptotic analysis
Numerical analysis
Green's functions
Appendixes
Answers to selected exercises
Index
Mathematical Surveys and Monographs, Volume: 176
2011; 264 pp; hardcover
ISBN-13: 978-0-8218-6871-3
Expected publication date is September 14, 2011.
The theory of nonautonomous dynamical systems in both of its formulations as processes and skew product flows is developed systematically in this book. The focus is on dissipative systems and nonautonomous attractors, in particular the recently introduced concept of pullback attractors. Linearization theory, invariant manifolds, Lyapunov functions, Morse decompositions and bifurcations for nonautonomous systems and set-valued generalizations are also considered as well as applications to numerical approximations, switching systems and synchronization. Parallels with corresponding theories of control and random dynamical systems are briefly sketched.
With its clear and systematic exposition, many examples and exercises, as well as its interesting applications, this book can serve as a text at the beginning graduate level. It is also useful for those who wish to begin their own independent research in this rapidly developing area.
Graduate students and research mathematicians interested in dynamical systems.
Autonomous dynamical systems
Nonautonomous dynamical systems
Attractors
Morse decompositions
Linear systems
Invariant manifolds
Lyapunov functions
Bifurcations
Set-valued nonautonomous dynamical systems
Nonautonomous semi-dynamical systems
Approximation and perturbation of attractors
Infinite-dimensional systems
Switching and control systems
Random dynamical systems
Synchronization
Appendix
Bibliography
Index
Contemporary Mathematics, Volume: 550
2011; 196 pp; softcover
ISBN-13: 978-0-8218-5257-6
Expected publication date is September 4, 2011.
This volume contains the proceedings of the Workshop on Geometric Analysis of Several Complex Variables and Related Topics, which was held from May 10-14, 2010, in Marrakesh, Morocco.
The articles in this volume present current research and future trends in the theory of several complex variables and PDE. Of note are two survey articles, the first presenting recent results on the solvability of complex vector fields with critical points while the second concerns the Lie group structure of the automorphism groups of CR manifolds. The other articles feature original research in major topics of analysis dealing with analytic and Gevrey regularity, existence of distributional traces, the barpartial-Neumann operator, automorphisms of hypersurfaces, holomorphic vector bundles, spaces of harmonic forms, and Gysin sequences.
Graduate students and research mathematicians interested in several complex variables, PDE, and CR geometry.
R. F. Barostichi, P. D. Cordaro, and G. Petronilho -- Analytic vectors in locally integrable structures
M. Derridj and B. Helffer -- Subellipticity and maximal hypoellipticity for two complex vector fields in (2+2)-variables
J. Hounie and E. R. da Silva -- Existence of trace for solutions of locally integrable systems of vector fields
M. Kola? and F. Meylan -- Chern-Moser operators and weighted jet determination problems
B. Lamel -- Jet embeddability of local automorhpism groups of real-analytic CR manifolds
J. Leiterer -- Splitting of holomorphic cocycles with estimates. Several variables
G. A. Mendoza -- A Gysin sequence for manifolds with mathbb{R}-action
S. ?ahuto?lu -- A potential theoretic characterization of compactness of the overline{partial}-Neumann problem
M.-C. Shaw -- Duality between harmonic and Bergman spaces
F. Treves -- On the solvability and hypoellipticity of complex vector fields
Contemporary Mathematics, Volume: 551
2011; 280 pp; softcover
ISBN-13: 978-0-8218-5291-0
Expected publication date is September 24, 2011.
This volume contains papers based on lectures given at the Eleventh International Conference on p-adic Functional Analysis, which was held from July 5-9, 2010, in Clermont-Ferrand, France.
The articles collected here feature recent developments in various areas of non-Archimedean analysis: Hilbert and Banach spaces, finite dimensional spaces, topological vector spaces and operator theory, strict topologies, spaces of continuous functions and of strictly differentiable functions, isomorphisms between Banach function spaces, and measure and integration.
Other topics discussed in this volume include p-adic differential and q-difference equations, rational and non-Archimedean analytic functions, the spectrum of some algebras of analytic functions, and maximal ideals of the ultrametric corona algebra.
Graduate students and research mathematicians interested in non-Archimedean analysis.
C. Perez-Garcia and W. H. Schikhof -- Remembering Nicole De Grande-De Kimpe (1936-2008)
V. Anashin, A. Khrennikov, and E. Yurova -- Using van der Put basis to determine if a 2-adic function is measure-preserving or ergodic w.r.t. Haar measure
N. Boudjerida, A. Boutabaa, and S. Medjerab -- q-difference equations in ultrametric fields
K. Boussaf, A. Escassut, and J. Ojeda -- Primitives of p-adic meromorphic functions
W. Cherry -- Existence of GCD's and factorization in rings of non-Archimedean entire functions
G. Christol -- The radius of convergence function for first order differential equations
B. Diarra -- The Lipschitz condition for rational functions on ultrametric valued fields
A. Escassut -- Differential and maximal ideals of the ultrametric Corona algebra
A. K. Katsaras -- Linear topologies on non-Archimedean function spaces
A. K. Katsaras, L. A. Khan, and A. R. Khan -- On maximal closed ideals in topological algebras of continuous vector-valued functions over non-Archimedean valued fields
H. A. Keller and H. Ochsenius -- Perturbations of bounded linear operators on orthomodular Hilbertian spaces
A. Kubzdela -- On some geometrical properties of linear subspaces of l^infty
M. L. Lapidus and L. Hung -- The geometry of p-adic fractal strings: A comparative survey
H. Maiga -- Identities and congruences for Genocchi numbers
H. M. Moreno -- Toward an ultrametric calculus in a field K with an infinite rank valuation
E. Olivos and W. H. Schikhof -- Extending the multiplication of a totally ordered group to its completion
S. Priess-Crampe -- Norm Hilbert spaces with uncountable orthogonal basis
K. Shamseddine -- Absolute and relative extrema, the mean value theorem and the inverse function theorem for analytic functions on a Levi-Civita field
F. Tangara -- Some p-adic q-difference equations on mathcal{C}(mathbb{Z}_p,K)
MSRI Mathematical Circles Library, Volume: 6
2011; approx. 346 pp; softcover
ISBN-13: 978-0-8218-5314-6
Expected publication date is October 13, 2011.
Functions and their properties have been part of the rigorous precollege curriculum for decades. And functional equations have been a favorite topic of the leading national and international mathematical competitions. Yet the subject has not received equal attention by authors at an introductory level. The majority of the books on the topic remain unreachable to the curious and intelligent precollege student. The present book is an attempt to eliminate this disparity.
The book opens with a review chapter on functions, which collects the relevant foundational information on functions, plus some material potentially new to the reader. The next chapter presents a working definition of functional equations and explains the difficulties in trying to systematize the theory. With each new chapter, the author presents methods for the solution of a particular group of equations. Each chapter is complemented with many solved examples, the majority of which are taken from mathematical competitions and professional journals. The book ends with a chapter of unsolved problems and some other auxiliary material.
The book is an invaluable resource for precollege and college students who want to deepen their knowledge of functions and their properties, for teachers and instructors who wish to enrich their curricula, and for any lover of mathematical problem-solving techniques.
Titles in this series are co-published with the Mathematical Sciences Research Institute (MSRI).
High school teachers and students, undergraduate students interested in functional equations; anyone interested in tips, tricks, and techniques for mathematical competitions and math circles.
Background
Functions
Basic equations
A primer on functional relations
Equations for arithmetic functions
Equations reducing to algebraic systems
Cauchy's equations
Cauchy's mathbb{NQR} method
Equations for trigonometric functions
Generalizations
The Pexider, Vincze and Wilson equations
Vector and matrix variables
Systems of equations
Changing the rules
Less than continuity
More than continuity
Functional equations for polynomials
Conditional functional equations
Functional inequalities
Equations with no parameters
Iterations
Solving by invariants and linearization
More on fixed points
Getting additional experience
Miscellaneous problems
Additional problems
Auxiliary material
Acronyms and abbreviations
Set conventions
Named equations
Bibliography
Index