Courant Lecture Notes, Volume: 1
2011; 147 pp; softcover
ISBN-13: 978-0-8218-5313-9
Expected publication date is April 6, 2011.
Elliptic Partial Differential Equations by Qing Han and FangHua Lin is one of the best textbooks I know. It is the perfect introduction to PDE. In 150 pages or so it covers an amazing amount of wonderful and extraordinary useful material. I have used it as a textbook at both graduate and undergraduate levels which is possible since it only requires very little background material yet it covers an enormous amount of material. In my opinion it is a must read for all interested in analysis and geometry, and for all of my own PhD students it is indeed just that. I cannot say enough good things about it--it is a wonderful book.
--Tobias Colding
This volume is based on PDE courses given by the authors at the Courant Institute and at the University of Notre Dame, Indiana. Presented are basic methods for obtaining various a priori estimates for second-order equations of elliptic type with particular emphasis on maximal principles, Harnack inequalities, and their applications. The equations considered in the book are linear; however, the presented methods also apply to nonlinear problems.
This second edition has been thoroughly revised and in a new chapter the authors discuss several methods for proving the existence of solutions of primarily the Dirichlet problem for various types of elliptic equations.
Graduate students and research mathematicians interested in elliptic PDEs.
DIMACS: Series in Discrete Mathematics and Theoretical Computer Science, Volume: 76
2011; 245 pp; hardcover
ISBN-13: 978-0-8218-4295-9
Expected publication date is April 27, 2011.
Even though contemporary biology and mathematics are inextricably linked, high school biology and mathematics courses have traditionally been taught in isolation. But this is beginning to change. This volume presents papers related to the integration of biology and mathematics in high school classes.
The first part of the book provides the rationale for integrating mathematics and biology in high school courses as well as opportunities for doing so. The second part explores the development and integration of curricular materials and includes responses from teachers.
Papers in the third part of the book explore the interconnections between biology and mathematics in light of new technologies in biology. The last paper in the book discusses what works and what doesn't and presents positive responses from students to the integration of mathematics and biology in their classes.
High school teachers, education specialists, graduate students, and research mathematicians interested in mathematics and biology education.
The rationale for high school BioMath
F. S. Roberts -- Why BioMath? Why now?
E. Jakobsson -- The interdisciplinary scientist of the 21st century
L. J. Heyer and A. M. Campbell -- Teaching bioinformatics and genomics: An interdisciplinary approach
N. H. Fefferman and L. M. Fefferman -- Mathematical macrobiology: An unexploited opportunity in high school education
A. Nkwanta, D. Hill, A. Swamy, and K. Peters -- Counting RNA patterns in the classroom: A link between molecular biology and enumerative combinatorics
Curriculum materials and teacher training/development
M. B. Cozzens -- New materials to integrate biology and mathematics in the high school curriculum
K. M. Gabric -- The awakening of a high school biology teacher to the BioMath connection
L. J. Morris, C. Long, and J. Kissler -- A beginning experience: Linking high school biology and mathematics
K. G. Herbert and J. H. Dyer -- Integrating interdisciplinary science into high school science modules through a preproinsulin example
M. C. Rogers and D. S. Yuster -- Insights from math-science collaboration at the high school level
Topics, course changes, and technology
H. Scheintaub, E. Klopfer, M. Scheintaub, and E. Rosenbaum -- Complexity and biology--bringing quantitative science to the life sciences classroom
J. Malkevitch -- Distance and trees in high school biology and mathematics classrooms
M. E. Martin -- Mathematical biology: Tools for inquiry on the Internet
E. S. Marland and M. E. Searcy -- The calculus cycle: Using biology to connect discrete and continuous modeling in calculus
C. Mullins and D. W. Cranston -- Research at ASMSA based on the DIMACS BioMath program
Evaluation of how integration of biology/mathematics works
A. E. Weinberg and L. Albright -- Integrating biology and mathematics in high school classrooms
AMS Chelsea Publishing, Volume: 373
2011; approx. 404 pp; hardcover
ISBN-13: 978-0-8218-5316-0
Expected publication date is April 29, 2011.
The spectral theory of Sturm-Liouville operators is a classical domain of analysis, comprising a wide variety of problems. Besides the basic results on the structure of the spectrum and the eigenfunction expansion of regular and singular Sturm-Liouville problems, it is in this domain that one-dimensional quantum scattering theory, inverse spectral problems, and the surprising connections of the theory with nonlinear evolution equations first become related. The main goal of this book is to show what can be achieved with the aid of transformation operators in spectral theory as well as in their applications. The main methods and results in this area (many of which are credited to the author) are for the first time examined from a unified point of view.
The direct and inverse problems of spectral analysis and the inverse scattering problem are solved with the help of the transformation operators in both self-adjoint and nonself-adjoint cases. The asymptotic formulae for spectral functions, trace formulae, and the exact relation (in both directions) between the smoothness of potential and the asymptotics of eigenvalues (or the lengths of gaps in the spectrum) are obtained. Also, the applications of transformation operators and their generalizations to soliton theory (i.e., solving nonlinear equations of Korteweg-de Vries type) are considered.
The new Chapter 5 is devoted to the stability of the inverse problem solutions. The estimation of the accuracy with which the potential of the Sturm-Liouville operator can be restored from the scattering data or the spectral function, if they are only known on a finite interval of a spectral parameter (i.e., on a finite interval of energy), is obtained.
Graduate students and research mathematicians interested in operator theory.
The Sturm-Liouville equation and transformation operators
The Sturm-Liouville boundary value problem on the half line
The boundary value problem of scattering theory
Nonlinear equations
Stability of inverse problems
References
Contemporary Mathematics, Volume: 539
2011; 465 pp; softcover
ISBN-13: 978-0-8218-5329-0
Expected publication date is May 7, 2011.
This book is based on the mini-workshop Renormalization, held in December 2006, and the conference Combinatorics and Physics, held in March 2007. Both meetings took place at the Max-Planck-Institut fur Mathematik in Bonn, Germany.
Research papers in the volume provide an overview of applications of combinatorics to various problems, such as applications to Hopf algebras, techniques to renormalization problems in quantum field theory, as well as combinatorial problems appearing in the context of the numerical integration of dynamical systems, in noncommutative geometry and in quantum gravity.
In addition, it contains several introductory notes on renormalization Hopf algebras, Wilsonian renormalization and motives.
Graduate students and research mathematicians interested in applications of combinatorics to physics.
C. Brouder and F. Patras -- One-particle irreducibility with initial correlations
F. Brown -- Multiple zeta values and periods: From moduli spaces to Feynman integrals
F. Chapoton and A. Frabetti -- From quantum electrodynamics to posets of planar binary trees
G. H. E. Duchamp and C. Tollu -- Sweedler's duals and Schutzenberger's calculus
L. Foissy -- Primitive elements of the Hopf algebra of free quasi-symmetric functions
R. Friedrich -- A Renormalisation Group approach to Stochastic L?wner Evolutions
J. M. Gracia-Bondia -- On the causal gauge principle
M. Gubinelli -- Abstract integration, combinatorics of trees and differential equations
R. Holtkamp -- Rooted trees appearing in products and co-products
A. Iserles -- Magnus expansions and beyond
T. Krajewski and P. Martinetti -- Wilsonian renormalization, differential equations and Hopf algebras
E. Kraus -- Algebraic analysis of non-renormalization theorems in supersymmetric field theories
D. Kreimer -- Not so non-renormalizable gravity
D. Manchon -- Renormalised multiple zeta values which respect quasi-shuffle relations
F. Menous -- Formulas for the Connes-Moscovici Hopf algebra
A. Mestre and R. Oeckl -- Hopf algebras and the combinatorics of connected graphs in quantum field theory
A. Lundervold and H. Munthe-Kaas -- Hopf algebras of formal diffeomorphisms and numerical integration on manifolds
D. Oriti -- A combinatorial and field theoretic path to quantum gravity: The new challenges of group field theory
S. Paycha -- Noncommutative formal Taylor expansions and second quantised regularised traces
A. Rej -- Motives: An introductory survey for physicists
W. van Suijlekom -- Combinatorics and Feynman graphs for gauge theories
F. Vignes-Tourneret -- Multi-scale analysis and non-commutative field theory
Contemporary Mathematics, Volume: 540
2011; 259 pp; softcover
ISBN-13: 978-0-8218-4907-1
Expected publication date is May 8, 2011.
This volume contains papers on semi-linear and quasi-linear elliptic equations from the workshop on Nonlinear Elliptic Partial Differential Equations, in honor of Jean-Pierre Gossez's 65th birthday, held September 2-4, 2009 at the Universite Libre de Bruxelles, Belgium.
The workshop reflected Gossez's contributions in nonlinear elliptic PDEs and provided an opening to new directions in this very active research area. Presentations covered recent progress in Gossez's favorite topics, namely various problems related to the p-Laplacian operator, the antimaximum principle, the Fu?ik Spectrum, and other related subjects. This volume will be of principle interest to researchers in nonlinear analysis, especially in partial differential equations of elliptic type.
Graduate students and research mathematicians interested in nonlinear partial differential equations.
J. Mawhin -- Partial differential equations also have principles: Maximum and antimaximum
B. Ruf -- On the Fu?ik spectrum for equations with symmetries
B. Kawohl -- Variations on the p-Laplacian
V. Bouchez and J. Van Schaftingen -- Extremal functions in Poincare-Sobolev inequalities for functions of bounded variation
P. Bousquet and P. Mironescu -- An elementary proof of an inequality of Maz'ya involving L^1 vector fields
D. G. Costa and C. Li -- Homoclinic type solutions for a class of differential equations with periodic coefficients
J. Giacomoni, J. Hernandez, and A. Moussaoui -- Quasilinear and singular systems: The cooperative case
P. Drabek, R. F. Manasevich, and P. Taka? -- Manifolds of critical points in a quasilinear model for phase transitions
L. Leadi and H. R. Quoirin -- Weighted asymmetric problems for an indefinite elliptic operator
F. Obersnel and P. Omari -- Multiple non-trivial solutions of the Dirichlet problem for the prescribed mean curvature equation
M. Perez-Llanos and J. D. Rossi -- Limits as p(x)toinfty of p(x)-harmonic
functions with non-homogeneous Neumann boundary conditions
C. A. Stuart -- Bifurcation and decay of solutions for a class of elliptic
equations on mathbb{R}^N
S. de Valeriola and M. Willem -- Existence of nodal solutions for some nonlinear elliptic problems
F. Robert -- Admissible Q-curvatures under isometries for the conformal GJMS operators