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An Introduction to Computational Stochastic PDEs
This book offers a practical presentation of stochastic partial differential equations arising in physical applications and their numerical approximation.
Frontiers in Numerical Analysis
A set of detailed lecture notes on six topics at the forefront of current research in numerical analysis and applied mathematics. Each set of notes presents a self-contained guide to a current research area. Detailed proofs of key results are provided. The notes start from a level suitable for first year graduate students in applied mathematics, mathematical analysis or numerical analysis, and proceed to current research topics. Current (unsolved) problems are also described and directions for future research are given. This book is also suitable for professional mathematicians.
Singularities: Formation, Structure and Propagation
This book explores a wide range of singular phenomena, providing mathematical tools for understanding them and highlighting their common features.
Discrete Systems and Integrability
A first introduction to the theory of discrete integrable systems at a level suitable for students and non-experts.
Introduction to Magnetohydrodynamics
Comprehensive textbook prioritising physical ideas over mathematical detail. New material includes fusion plasma magnetohydrodynamics.
Geometric and Topological Inference
A rigorous introduction to geometric and topological inference, for anyone interested in a geometric approach to data science.
The Fluid Dynamics of Cell Motility
A pedagogical review of the mathematical modelling in fluid dynamics necessary to understand the motility of most microorganisms on Earth.
Dynamics of Algorithms
The articles collected in this volume represent the contributions presented at the IMA workshop on "Dynamics of Algorithms" which took place in November 1997. The workshop was an integral part of the 1997 -98 IMA program on "Emerging Applications of Dynamical Systems." The interaction between algorithms and dynamical systems is mutually beneficial since dynamical methods can be used to study algorithms that are applied repeatedly. Convergence, asymptotic rates are indeed dynamical properties. On the other hand, the study of dynamical systems benefits enormously from having efficient algorithms to compute dynamical objects.
Numerical Linear Algebra
This self-contained introduction to numerical linear algebra provides a comprehensive, yet concise, overview of the subject. It includes standard material such as direct methods for solving linear systems and least-squares problems, error, stability and conditioning, basic iterative methods and the calculation of eigenvalues. Later chapters cover more advanced material, such as Krylov subspace methods, multigrid methods, domain decomposition methods, multipole expansions, hierarchical matrices and compressed sensing. The book provides rigorous mathematical proofs throughout, and gives algorithms in general-purpose language-independent form. Requiring only a solid knowledge in linear algebra and basic analysis, this book will be useful for applied mathematicians, engineers, computer scientists, and all those interested in efficiently solving linear problems.
Numerical Methods: Think before You Compute
This guide to computational fluid mechanics introduces beginning graduate students to the subject's standard methods and common pitfalls.
