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A Practical Guide to the Invariant Calculus
This book explains recent results in the theory of moving frames that concern the symbolic manipulation of invariants of Lie group actions. In particular, theorems concerning the calculation of generators of algebras of differential invariants, and the relations they satisfy, are discussed in detail. The author demonstrates how new ideas lead to significant progress in two main applications: the solution of invariant ordinary differential equations and the structure of Euler-Lagrange equations and conservation laws of variational problems. The expository language used here is primarily that of undergraduate calculus rather than differential geometry, making the topic more accessible to a student audience. More sophisticated ideas from differential topology and Lie theory are explained from scratch using illustrative examples and exercises. This book is ideal for graduate students and researchers working in differential equations, symbolic computation, applications of Lie groups and, to a lesser extent, differential geometry.
Partial Differential Equation Methods for Image Inpainting
This book introduces the mathematical concept of partial differential equations (PDE) for virtual image restoration. It provides insight in mathematical modelling, partial differential equations, functional analysis, variational calculus, optimisation and numerical analysis. It is addressed towards generally informed mathematicians and graduate students in mathematics with an interest in image processing and mathematical analysis.
Numerical Bifurcation Analysis of Maps
Combines a systematic analysis of bifurcations of iterated maps with concrete MATLAB® implementations and applications.
Discrete Variational Problems with Interfaces
A systematic presentation of discrete-to-continuum results and methods, offering new perspectives on intrinsically discrete problems.
Quasi-Interpolation
Delve into an in-depth description and analysis of quasi-interpolation, starting from various areas of approximation theory.
Difference Equations by Differential Equation Methods
Straightforward introduction for non-specialists and experts alike. Explains how to derive solutions, first integrals and conservation laws of difference equations.
Spaces of Measures and their Applications to Structured Population Models
Presents a comprehensive analytical framework for structured population models in spaces of Radon measures and their numerical approximation.
Mathematical Modelling of the Human Cardiovascular System
Addresses the mathematical and numerical modelling of the human cardiovascular system, from patient data to clinical applications.
The Christoffel–Darboux Kernel for Data Analysis
This accessible overview introduces the Christoffel-Darboux kernel as a novel, simple and efficient tool in statistical data analysis.
Multiscale Methods for Fredholm Integral Equations
Presents the state of the art in the study of fast multiscale methods for solving these equations based on wavelets.
