Calculus and mathematical analysis

To tailor time series models to a particular physical problem and to follow the working of various techniques for processing and analyzing data, one must understand the basic theory of spectral (frequency domain) analysis of time series.

Sobolev Spaces presents an introduction to the theory of Sobolev Spaces and other related spaces of function, also to the imbedding characteristics of these spaces.

This volume explains how the recent advances in wavelet analysis provide new means for multiresolution analysis and describes its wide array of powerful tools.

This monograph explores the design of controllers that suppress oscillations and instabilities in congested traffic flow using PDE backstepping methods.

Recent decades have seen a very rapid success in developing numerical methods based on explicit control over approximation errors.

Real Analysis with an Introduction to Wavelets and Applications is an in-depth look at real analysis and its applications, including an introduction to wavelet analysis, a popular topic in "e;applied real analysis"e;.

Projects for Calculus is designed to add depth and meaning to any calculus course.

The geometry of power exponents includes the Newton polyhedron, normal cones of its faces, power and logarithmic transformations.

The book is devoted to the perturbation analysis of matrix equations.

In the last decade parallel computing has been put forward as the only computational answer to the increasing computational needs arising from very large and complex fluid dynamic problems.

This volume contains the papers presented at the Parallel Computing Fluid Dynamics '93 Conference, Paris, 1993.

This book contains the papers presented at the Parallel Computational Fluid Dynamics 1998 Conference.

Contributed presentations were given by over 50 researchers representing the state of parallel CFD art and architecture from Asia, Europe, and North America.

In accordance with the developments in computation, theoretical studies on numerical schemes are now fruitful and highly needed.

Since their introduction in the 1980's, wavelets have become a powerful tool in mathematical analysis, with applications such as image compression, statistical estimation and numerical simulation of partial differential equations.

Nonlinear Diffusion of Electromagnetic Fields covers applications of the phenomena of non-linear diffusion of electromagnetic fields, such as magnetic recording, electromagnetic shielding and non-destructive testing, development of CAD software, and the design of magnetic components in electrical machinery.

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 book is intended for people (graduates, researchers, but also undergraduates with a good mathematical background) involved in the study of (static) optimization problems (in finite-dimensional spaces).

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.

This book includes a collection of extended papers based on presentations given during the SimHydro 2023 conference, held in EDF Lab Chatou, France, with the support of  Societe Hydrotechnique de France (SHF), the Association Francaise de Mecanique (AFM), the Environmental and Water Resources Institute (EWRI), and the International Association for Hydro-Environment Engineering and Research (IAHR).

The Lyapunov and Riccati equations are two of the fundamental equations of control and system theory, having special relevance for system identification, optimization, boundary value problems, power systems, signal processing, and communications.

Inequalities for Differential and Integral Equations has long been needed; it contains material which is hard to find in other books.

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

Handbook of the Geometry of Banach Spaces

Volumes 1A and 1B.

The main goal of this Handbook isto survey measure theory with its many different branches and itsrelations with other areas of mathematics.

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.

Geometric Function Theory is a central part of Complex Analysis (one complex variable).

This text is an introduction to harmonic analysis on symmetric spaces, focusing on advanced topics such as higher rank spaces, positive definite matrix space and generalizations.

Fuzzy Mathematics, Graphs, and Similarity Measures provides a solid foundation in core analytical tracks of mathematics of uncertainty, from fuzzy mathematics to graphs and similarity measures with applications in a range of timely cases studies and world challenges.

In this book, the functional inequalities are introduced to describe:(i) the spectrum of the generator: the essential and discrete spectrums, high order eigenvalues, the principle eigenvalue, and the spectral gap;(ii) the semigroup properties: the uniform intergrability, the compactness, the convergence rate, and the existence of density;(iii) the reference measure and the intrinsic metric: the concentration, the isoperimetic inequality, and the transportation cost inequality.

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.

Fourier Analysis and Boundary Value Problems provides a thorough examination of both the theory and applications of partial differential equations and the Fourier and Laplace methods for their solutions.

ACMES (Algorithms and Complexity in Mathematics, Epistemology, and Science) is a multidisciplinary conference series that focuses on epistemological and mathematical issues relating to computation in modern science.

All the existing books in Infinite Dimensional Complex Analysis focus on the problems of locally convex spaces.

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.

Two distinct systems of hypercomplex numbers in n dimensions are introduced in this book, for which the multiplication is associative and commutative, and which are rich enough in properties such that exponential and trigonometric forms exist and the concepts of analytic n-complex function, contour integration and residue can be defined.

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

This book is intended to introduce researchers and graduate students to the concepts of causal symmetric spaces.

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 first edition of this highly successful book appeared in 1975 and evolved from lecture notes for classes in physical optics, diffraction physics and electron microscopy given to advanced undergraduate and graduate students.

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.

Working through this student-centred text readers will be brought up to speed with the modelling of control systems using Laplace, and given a solid grounding of the pivotal role of control systems across the spectrum of modern engineering.