Publication planned for: December 2017
availability: Not yet published - available from December 2017
format: Hardback
isbn: 9781107163225
This introduction to finite difference and finite element methods is aimed at graduate students who need to solve differential equations. The prerequisites are few (basic calculus, linear algebra, and ODEs) and so the book will be accessible and useful to readers from a range of disciplines across science and engineering. Part I begins with finite difference methods. Finite element methods are then introduced in Part II. In each part, the authors begin with a comprehensive discussion of one-dimensional problems, before proceeding to consider two or higher dimensions. An emphasis is placed on numerical algorithms, related mathematical theory, and essential details in the implementation, while some useful packages are also introduced. The authors also provide well-tested MATLABR codes, all available online.
Offers a concise and practical introduction to finite difference and finite element methods
Well-tested MATLABR codes are free to download
Teaches students how to use computers to solve linear ODEs and PDEs in one and two dimensions
1. Introduction
Part I. Finite Difference Methods:
2. Finite difference methods for 1D boundary value problems
3. Finite difference methods for 2D elliptic PDEs
4. FD methods for parabolic PDEs
5. Finite difference methods for hyperbolic PDEs
Part II. Finite Element Methods:
6. Finite element methods for 1D boundary value problems
7. Theoretical foundations of the finite element method
8. Issues of the FE method in one space dimension
9. The finite element method for 2D elliptic PDEs
Appendix. Numerical solutions of initial value problems
References
Index.
Publication planned for: February 2018
format: Hardback
isbn: 9781108418812
While differentiating elementary functions is merely a skill, finding definite integrals is an art. This practical introduction to the art of integration gives readers the tools and confidence to tackle common and uncommon integrals. After a review of the basic properties of the Riemann integral, each chapter is devoted to a particular technique of elementary integration. Thorough explanations and plentiful worked examples prepare the reader for the extensive exercises at the end of each chapter. These exercises increase in difficulty from warm-up problems, through drill examples, to challenging extensions which illustrate such advanced topics as the irrationality of ƒÎ and e, the solution of the Basel problem, Leibniz's series and Wallis's product. The author's accessible and engaging manner will appeal to a wide audience, including students, teachers and self-learners. The book can serve as a complete introduction to finding elementary integrals, or as a supplementary text for any beginning course in calculus.
A systematic introduction to integration, containing many fully worked examples to demonstrate how the techniques are applied in practice
Contains more than 500 exercises ranging in difficulty, from warm-ups to challenging extensions
Accessible and engaging, this book will be of interest to students, teachers and self-learners
Part of Encyclopedia of Mathematics and its Applications
Publication planned for: December 2017
format: Hardback
isbn: 9780521869928
Quasicrystals are non-periodic solids that were discovered in 1982 by Dan Shechtman, Nobel Prize Laureate in Chemistry 2011. The mathematics that underlies this discovery or that proceeded from it, known as the theory of Aperiodic Order, is the subject of this comprehensive multi-volume series. This second volume begins to develop the theory in more depth. A collection of leading experts, among them Robert V. Moody, cover various aspects of crystallography, generalising appropriately from the classical case to the setting of aperiodically ordered structures. A strong focus is placed upon almost periodicity, a central concept of crystallography that captures the coherent repetition of local motifs or patterns, and its close links to Fourier analysis. The book ends with an epilogue on the emergence of quasicrystals from the perspective of physical sciences, written by Peter Kramer, one of the founders of the field on the side of theoretical and mathematical physics.
The second of a comprehensive multi-volume series covering aperiodic order and its applications
Builds on the first volume by developing the theory
Chapters are written by leading experts and founders of the field
Foreword Jeffrey C. Lagarias
Preface Michael Baake and Uwe Grimm
1. More Iinflation tilings Dirk Frettloh
2. Discrete tomography of model sets: reconstruction and uniqueness Uwe Grimm, Peter Gritzmann and Christian Huck
3. Geometric enumeration problems for lattices and embedded Z-modules Michael Baake and Peter Zeiner
4. Almost periodic measures and their fourier transforms Robert V. Moody and Nicolae Strungaru
5. Almost periodic pure point measures Nicolae Strungaru
6. Averaging almost periodic functions along exponential sequences Michael Baake, Alan Haynes and Daniel Lenz
Epilogue. Gateways towards quasicrystals Peter Kramer
Index.
Part of Cambridge Tracts in Mathematics
Publication planned for: January 2018
format: Hardback
isbn: 9781107095458
The arrangement of nonzero entries of a matrix, described by the graph of the matrix, limits the possible geometric multiplicities of the eigenvalues, which are far more limited by this information than algebraic multiplicities or the numerical values of the eigenvalues. This book gives a unified development of how the graph of a symmetric matrix influences the possible multiplicities of its eigenvalues. While the theory is richest in cases where the graph is a tree, work on eigenvalues, multiplicities and graphs has provided the opportunity to identify which ideas have analogs for non-trees, and those for which trees are essential. It gathers and organizes the fundamental ideas to allow students and researchers to easily access and investigate the many interesting questions in the subject.
Provides a unified development of theory of eigenvalues, multiplicities, and graphs
Includes new information, including non-trees and geometric multiplicities
Offers numerous examples to demonstrate applications of the theory
Background
1. Introduction
2. Parter-Wiener, etc. theory
3. Maximum multiplicity for trees, I
4. Multiple eigenvalues and structure
5. Maximum multiplicity, II
6. The minimum number of distinct eigenvalues
7. Construction techniques
8. Multiplicity lists for generalized stars
9. Double generalized stars
10. Linear trees
11. Non-trees
12. Geometric multiplicities for general matrices over a field.
Part of London Mathematical Society Lecture Note Series
Publication planned for: December 2017
format: Paperback
isbn: 9781108412308
The proceedings of the summer school held at the Universite Savoie Mont Blanc, France, 'Mathematics in Savoie 2015', whose theme was long time behavior and control of evolution equations. The event was attended by world-leading researchers from the community of control theory, as well as young researchers from around the globe. This volume contains surveys of active research topics, along with original research papers containing exciting new results on the behavior of evolution equations. It will therefore benefit both graduate students and researchers. Key topics include the recent view on the controllability of parabolic systems that permits the reader to overview the moment method for parabolic equations, as well as numerical stabilization and control of partial differential equations.
Discusses the state of the art in control theory and evolution equations
Accessible to researchers and graduate students
Authors include internationally renowned researchers in the area of control theory
Preface Kais Ammari and Stephane Gerbi
1. Controllability of parabolic systems ? the moment method Farid Ammar Khodja
2. Stabilization of semilinear PDEs, and uniform decay under discretization Emmanuel Trelat
3. A null controllability result for the linear system of Thermoelastic plates with a single control Carlos Castro and Luz de Teresa
4. Doubly connected V-states for the generalized surface Quasi-Geostrophic equations Francisco de la Hoz, Zineb Hassainia and Taoufik Hmidi
5. About least-squares type approach to address direct and controllability problems Arnaud Munch and Pablo Pedregal
6. A note on the asymptotic stability of wave-type equations with switching time-delay Serge Nicaise and Cristina Pignotti
7. Ill-posedness of coupled systems with delay Lisa Fischer and Reinhard Racke
8. Controllability of parabolic equations by the flatness approach Philippe Martin, Lionel Rosier and Pierre Rouchon
9. Mixing for the burgers equation driven by a localised two-dimensional stochastic forcing Armen Shirikyan.