Differential calculus and equations

This book contains the written versions of lectures delivered since 1997 in the well-known weekly seminar on Applied Mathematics at the College de France in Paris, directed by Jacques-Louis Lions.

This monograph provides a comprehensive treatment of expansion theorems for regular systems of first order differential equations and n-th order ordinary differential equations.

Solving nonlinear problems is inherently difficult, and the stronger the nonlinearity, the more intractable solutions become.

This latest volume in the Wavelets Analysis and Its Applications Series provides significant and up-to-date insights into recent developments in the field of wavelet constructions in connection with partial differential equations.

The objective of Volume II is to show how asymptotic methods, with the thickness as the small parameter, indeed provide a powerful means of justifying two-dimensional plate theories.

The Handbook of Mathematical Fluid Dynamics is a compendium of essays that provides a survey of the major topics in the subject.

Volumes 1A and 1B.

Handbook of Analysis and Its Foundations is a self-contained and unified handbook on mathematical analysis and its foundations.

This handbook is volume II in a series collecting mathematical state-of-the-art surveys in the field of dynamical systems.

The book contains seven survey papers about ordinary differential equations.

This book is a landmark title in the continuous move from integer to non-integer in mathematics: from integer numbers to real numbers, from factorials to the gamma function, from integer-order models to models of an arbitrary order.

This volume in the Elsevier Series in Electromagnetism presents a detailed, in-depth and self-contained treatment of the Fast Multipole Method and its applications to the solution of the Helmholtz equation in three dimensions.

This book deals with numerical methods for solving large sparse linear systems of equations, particularly those arising from the discretization of partial differential equations.

Banach Spaces

This book has evolved from the lecture course on Functional Analysis I had given several times at the ETH.

General Theory of C*-Algebras

The book contains a unitary and systematic presentation of both classical and very recent parts of a fundamental branch of functional analysis: linear semigroup theory with main emphasis on examples and applications.

Functional analysis is a powerful tool when applied to mathematical problems arising from physical situations.

This book is a compilation of several works from well-recognized figures in the field of Representation Theory.

Multivariate polysplines are a new mathematical technique that has arisen from a synthesis of approximation theory and the theory of partial differential equations.

A collection of self contained state-of-the art surveys.

This book contains several introductory texts concerning the main directions in the theory of evolutionary partial differential equations.

This book gathers peer-reviewed, selected contributions from participants of the 6th International Workshop on Nonlinear and Modern Mathematical Physics (NMMP-2022), hosted virtually from June 17-19, 2022.

Intended for a serious first course or a second course, this textbook will carry students beyond eigenvalues and eigenvectors to the classification of bilinear forms, to normal matrices, to spectral decompositions, and to the Jordan form.

Modeling has become an essential tool for the groundwater hydrologist.

The book could be a good companion for any graduate student in partial differential equations or in applied mathematics.

This book offers an in-depth verification of numerical solutions for differential equations modeling heat transfer phenomena, where the smoothed particle hydrodynamics (SPH) method is used to discretize the mathematical models.

This book convenes and deepens generic results about spectral measures, many of them available so far in scattered literature.

Perturbed functional iterations (PFI) is a large scale nonlinear system solver.

The present book develops the mathematical and numerical analysis of linear, elliptic and parabolic partial differential equations (PDEs) with coefficients whose logarithms are modelled as Gaussian random fields (GRFs), in polygonal and polyhedral physical domains.

Multigrid presents both an elementary introduction to multigrid methods for solving partial differential equations and a contemporary survey of advanced multigrid techniques and real-life applications.

This second half of Volume 1 of this Handbook follows Volume 1A, which was published in 2002.

This book convenes and deepens generic results about spectral measures, many of them available so far in scattered literature.

The Finite Element Method (FEM) has become an indispensable technology for the modelling and simulation of engineering systems.

Boundary Value Problems, Fifth Edition, is the leading text on boundary value problems and Fourier series.

Current and historical research methods in approximation theory are presented in this book beginning with the 1800s and following the evolution of approximation theory via the refinement and extension of classical methods and ending with recent techniques and methodologies.

The material collected in this volume reflects the active present of this area of mathematics, ranging from the abstract theory of gradient flows to stochastic representations of non-linear parabolic PDE's.

Employ the essential and hands-on tools and functions of MATLAB's ordinary differential equation (ODE) and partial differential equation (PDE) packages, which are explained and demonstrated via interactive examples and case studies.

This handbook is volume III in a series devoted to stationary partial differential quations.

This handbook is the third volume in a series of volumes devoted to self contained and up-to-date surveys in the tehory of ordinary differential equations, written by leading researchers in the area.

This book introduces the method of lower and upper solutions for ordinary differential equations.

This volume introduces a unified, self-contained study of linear discrete parabolic problems through reducing the starting discrete problem to the Cauchy problem for an evolution equation in discrete time.

The book contains a systematic treatment of the qualitative theory of elliptic boundary value problems for linear and quasilinear second order equations in non-smooth domains.

The aim of this Handbook is to acquaint the reader with the current status of the theory of evolutionary partial differential equations, and with some of its applications.

The book presents a systematic and compact treatment of the qualitative theory of half-lineardifferential equations.

This handbook is the second volume in a series devoted to self contained and up-to-date surveys in the theory of ordinary differential equations, writtenby leading researchers in the area.

A collection of self contained, state-of-the-art surveys.

This advanced textbook introduces the main concepts and advances in systems and control theory, and highlights the importance of geometric ideas in the context of possible extensions to the more recent developments in nonlinear systems theory.

This volume offers a collection of carefully selected, peer-reviewed papers presented at the BIOMAT 2018 International Symposium, which was held at the University Hassan II, Morocco, from October 29th to November 2nd, 2018.