Author : Zhongying Chen
Publisher : Cambridge University Press
Page : 551 pages
File Size : 12,10 MB
Release : 2015-07-16
Category : Mathematics
ISBN : 1107103479
Presents the state of the art in the study of fast multiscale methods for solving these equations based on wavelets.
Author : Hermann Brunner
Publisher : Cambridge University Press
Page : 405 pages
File Size : 28,40 MB
Release : 2017-01-20
Category : Mathematics
ISBN : 1316982653
This book offers a comprehensive introduction to the theory of linear and nonlinear Volterra integral equations (VIEs), ranging from Volterra's fundamental contributions and the resulting classical theory to more recent developments that include Volterra functional integral equations with various kinds of delays, VIEs with highly oscillatory kernels, and VIEs with non-compact operators. It will act as a 'stepping stone' to the literature on the advanced theory of VIEs, bringing the reader to the current state of the art in the theory. Each chapter contains a large number of exercises, extending from routine problems illustrating or complementing the theory to challenging open research problems. The increasingly important role of VIEs in the mathematical modelling of phenomena where memory effects play a key role is illustrated with some 30 concrete examples, and the notes at the end of each chapter feature complementary references as a guide to further reading.
Author : Carola-Bibiane Schönlieb
Publisher : Cambridge University Press
Page : 265 pages
File Size : 39,26 MB
Release : 2015-10-26
Category : Mathematics
ISBN : 1316404587
This book is concerned with digital image processing techniques that use partial differential equations (PDEs) for the task of image 'inpainting', an artistic term for virtual image restoration or interpolation, whereby missing or occluded parts in images are completed based on information provided by intact parts. Computer graphic designers, artists and photographers have long used manual inpainting to restore damaged paintings or manipulate photographs. Today, mathematicians apply powerful methods based on PDEs to automate this task. This book introduces the mathematical concept of PDEs for virtual image restoration. It gives the full picture, from the first modelling steps originating in Gestalt theory and arts restoration to the analysis of resulting PDE models, numerical realisation and real-world application. This broad approach also gives insight into functional analysis, variational calculus, optimisation and numerical analysis and will appeal to researchers and graduate students in mathematics with an interest in image processing and mathematical analysis.
Author : Christian Düll
Publisher : Cambridge University Press
Page : 322 pages
File Size : 13,52 MB
Release : 2021-10-07
Category : Mathematics
ISBN : 1009020471
Structured population models are transport-type equations often applied to describe evolution of heterogeneous populations of biological cells, animals or humans, including phenomena such as crowd dynamics or pedestrian flows. This book introduces the mathematical underpinnings of these applications, providing a comprehensive analytical framework for structured population models in spaces of Radon measures. The unified approach allows for the study of transport processes on structures that are not vector spaces (such as traffic flow on graphs) and enables the analysis of the numerical algorithms used in applications. Presenting a coherent account of over a decade of research in the area, the text includes appendices outlining the necessary background material and discusses current trends in the theory, enabling graduate students to jump quickly into research.
Author : V. Temlyakov
Publisher : Cambridge University Press
Page : 551 pages
File Size : 31,49 MB
Release : 2018-07-19
Category : Computers
ISBN : 1108428754
Self-contained presentation of multivariate approximation from classical linear approximation to contemporary nonlinear approximation.
Author : Alfio Quarteroni
Publisher : Cambridge University Press
Page : 291 pages
File Size : 32,55 MB
Release : 2019-05-09
Category : Mathematics
ISBN : 1108570534
Mathematical and numerical modelling of the human cardiovascular system has attracted remarkable research interest due to its intrinsic mathematical difficulty and the increasing impact of cardiovascular diseases worldwide. This book addresses the two principal components of the cardiovascular system: arterial circulation and heart function. It systematically describes all aspects of the problem, stating the basic physical principles, analysing the associated mathematical models that comprise PDE and ODE systems, reviewing sound and efficient numerical methods for their approximation, and simulating both benchmark problems and clinically inspired problems. Mathematical modelling itself imposes tremendous challenges, due to the amazing complexity of the cardiovascular system and the need for computational methods that are stable, reliable and efficient. The final part is devoted to control and inverse problems, including parameter estimation, uncertainty quantification and the development of reduced-order models that are important when solving problems with high complexity, which would otherwise be out of reach.
Author : I︠U︡riĭ Aleksandrovich Kuznet︠s︡ov
Publisher : Cambridge University Press
Page : 423 pages
File Size : 38,51 MB
Release : 2019-03-28
Category : Mathematics
ISBN : 1108499678
Combines a systematic analysis of bifurcations of iterated maps with concrete MATLAB® implementations and applications.
Author : Thomas J. Bridges
Publisher : Cambridge University Press
Page : 240 pages
File Size : 31,83 MB
Release : 2017-07-03
Category : Science
ISBN : 1108101321
Nonlinear waves are pervasive in nature, but are often elusive when they are modelled and analysed. This book develops a natural approach to the problem based on phase modulation. It is both an elaboration of the use of phase modulation for the study of nonlinear waves and a compendium of background results in mathematics, such as Hamiltonian systems, symplectic geometry, conservation laws, Noether theory, Lagrangian field theory and analysis, all of which combine to generate the new theory of phase modulation. While the build-up of theory can be intensive, the resulting emergent partial differential equations are relatively simple. A key outcome of the theory is that the coefficients in the emergent modulation equations are universal and easy to calculate. This book gives several examples of the implications in the theory of fluid mechanics and points to a wide range of new applications.
Author : Houman Owhadi
Publisher : Cambridge University Press
Page : 491 pages
File Size : 10,48 MB
Release : 2019-10-24
Category : Mathematics
ISBN : 1108588042
Although numerical approximation and statistical inference are traditionally covered as entirely separate subjects, they are intimately connected through the common purpose of making estimations with partial information. This book explores these connections from a game and decision theoretic perspective, showing how they constitute a pathway to developing simple and general methods for solving fundamental problems in both areas. It illustrates these interplays by addressing problems related to numerical homogenization, operator adapted wavelets, fast solvers, and Gaussian processes. This perspective reveals much of their essential anatomy and greatly facilitates advances in these areas, thereby appearing to establish a general principle for guiding the process of scientific discovery. This book is designed for graduate students, researchers, and engineers in mathematics, applied mathematics, and computer science, and particularly researchers interested in drawing on and developing this interface between approximation, inference, and learning.
Author : David Colton
Publisher : SIAM
Page : 286 pages
File Size : 23,83 MB
Release : 2013-11-15
Category : Mathematics
ISBN : 1611973155
This classic book provides a rigorous treatment of the Riesz?Fredholm theory of compact operators in dual systems, followed by a derivation of the jump relations and mapping properties of scalar and vector potentials in spaces of continuous and H?lder continuous functions. These results are then used to study scattering problems for the Helmholtz and Maxwell equations. Readers will benefit from a full discussion of the mapping properties of scalar and vector potentials in spaces of continuous and H?lder continuous functions, an in-depth treatment of the use of boundary integral equations to solve scattering problems for acoustic and electromagnetic waves, and an introduction to inverse scattering theory with an emphasis on the ill-posedness and nonlinearity of the inverse scattering problem.
