Differential calculus and equations

This volume contains two of the three lectures that were given at the 33rd Probability Summer School in Saint-Flour (July 6-23, 2003).

Nonlinear analysis has developed rapidly in the last three decades.

Author's Note: The material of this book has been reworked and expanded with a lot more detail and published in the author's 2014 book "e;Upper and Lower Bounds for Stochastic Processes"e; (Ergebnisse Vol.

The NLAGA's Biennial International Research Symposium (NLAGA-BIRS) is intended to gather African expertises in Nonlinear Analysis, Geometry and their Applications with their international partners in a four days conference where new mathematical results are presented and discussed.

This textbook is a comprehensive overview of the construction, implementation, and application of important numerical methods for the solution of Initial Value Problems (IVPs).

Linear switched systems are a fascinating field of research, with many theoretical questions arising from applications which require sophisticated mathematical tools for their resolution.

The theory of mean periodic functions is a subject which goes back to works of Littlewood, Delsarte, John and that has undergone a vigorous development in recent years.

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Periodic Systems gives a comprehensive treatment of the theory of periodic systems, including the problems of filtering and control.

Aimed at graduate and postgraduate students and researchers in mathematics and the applied sciences, this book provides an introductory account of scattering phenomena and a guide to the technical requirements for investigating wave scattering problems.

Developed from a course taught to senior undergraduates, this book provides a unified introduction to Fourier analysis and special functions based on the Sturm-Liouville theory in L2.

This monograph presents the existence and properties of both weak and strong solutions to the problems of the flow of a compressible fluid in a domain whose motion is prescribed.

Defined as solutions of linear differential or difference equations with polynomial coefficients, D-finite functions play an important role in various areas of mathematics.

This book introduces a unified implementation of bond- and state-based peridynamic theory (PD) within a commercial finite element framework, Ansys, utilizing its native elements.

This book provides an introduction to methods for practically solving mathematical problems, such as solving systems of linear equations, determining eigenvalues, approximating and integrating functions, solving nonlinear equations, and the approximate solution of ordinary differential equations.

This monograph introduces a new mathematical model in population dynamics that describes two species sharing the same environmental resources in a situation of open hostility.

Spectral properties for Schrodinger operators are a major concern in quantum mechanics both in physics and in mathematics.

This textbook provides an introduction to the mathematical methods used to analyse deterministic models in life sciences, including population dynamics, epidemiology and ecology.

This book provides a complete round-up of developments concerned with the application of partial moments in system identification and data-driven modelling; it captures the essence of work carried out at the Laboratoire d'Informatique et d'Automatique pour les Systemes for more than 40 years.

This book focuses on the foundations of compressible flow, illustrating the use of principles of thermodynamics and fluid dynamics in the development of compressible flow equations.

This textbook presents a concise and comprehensive treatment of the theory of elasticity.

This textbook presents a concise and comprehensive treatment of the theory of elasticity.

This book presents selected, peer-reviewed contributions from the International Symposium on Mathematical Analysis of Fractals and Dynamical Systems-2023 (ISMAFDS - 2023), held at the Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Tamil Nadu in India during August 24-25, 2023.

In this monograph, the authors present their recently developed theory of electromagnetic interactions.

Potential Theory presents a clear path from calculus to classical potential theory and beyond, with the aim of moving the reader into the area of mathematical research as quickly as possible.

The book comprises a rigorous and self-contained treatment of initial-value problems for ordinary differential equations.

Mathematical models can be used to meet many of the challenges and opportunities offered by modern biology.

This monograph is concerned with the mathematical analysis of patterns which are encountered in biological systems.

This book develops a systematic and rigorous mathematical theory of finite difference methods for linear elliptic, parabolic and hyperbolic partial differential equations with nonsmooth solutions.

Modern algorithmic techniques for summation, most of which were introduced in the 1990s, are developed here and carefully implemented in the computer algebra system Maple(TM).

The featured review of the AMS describes the author's earlier work in the field of approach spaces as, 'A landmark in the history of general topology'.

Stochastic instantaneous volatility models such as Heston, SABR or SV-LMM have mostly been developed to control the shape and joint dynamics of the implied volatility surface.

The theory of dynamical systems is a broad and active research subject with connections to most parts of mathematics.

Dynamical system theory has developed rapidly over the past fifty years.

Many phenomena in the physical and biological sciences involve the collective behaviour of (very large) numbers of individual objects.

The principal aim of the volume is gathering all the contributions given by the speakers (mini courses) and some of the participants (short talks) of the summer school "e;Modern Problems in PDEs and Applications"e; held at the Ghent Analysis and PDE Center from 23 August to 2 September 2023.

This book studies the theoretical aspects for a variety of coupled fractional differential systems involving Riemann-Liouville, Caputo, ?

The principal aim of the volume is gathering all the contributions given by the speakers (mini courses) and some of the participants (short talks) of the summer school "e;Modern Problems in PDEs and Applications"e; held at the Ghent Analysis and PDE Center from 23 August to 2 September 2023.

This textbook provides an introduction to the mathematical methods used to analyse deterministic models in life sciences, including population dynamics, epidemiology and ecology.

This book is devoted to the least gradient problem and its variants.

This volume presents a timely overview of control theory and related topics, such as the reconstruction problem, the stability of PDEs, and the Calderon problem.

This book is devoted to the least gradient problem and its variants.

The content of the book collects some contributions related to the talks presented during the INdAM Workshop "e;Fractional Differential Equations: Modelling, Discretization, and Numerical Solvers"e;, held in Rome, Italy, on July 12-14, 2021.