Calculus and mathematical analysis Books

This book deals with the efficient numerical solution of challenging nonlinear problems in science and engineering, both in finite and in infinite dimension. Its focus is on local and global Newton methods for direct problems...

1. 1. Overview of Numerical Quadrature The numerical evaluation of integrals is one of the oldest problems in mathematics. One can trace its roots back at least to Archimedes. The task is to compute the value of the definite...

These notes are, for the most part, the result of a course I taught at the University of Arizona during the Spring of 1977. Their main purpose is to inves­ tigate the effect that delays (of Volterra integral type) have when...

This book contains tables of integrals of the Mellin transform type z-l J (a) 1> (z) q,(x)x dx o t Since the substitution x = e- transforms (a) into (b) 1> (z) the Mellin transform is sometimes referred to as the two sided...

This material represents a collection of integrals of the Laplace- and inverse Laplace Transform type. The usef- ness of this kind of information as a tool in various branches of Mathematics is firmly established. Previous...

Unique book on Reaction-Advection-Diffusion problems

The main theme is the integration of the theory of linear PDE and the theory of finite difference and finite element methods. For each type of PDE, elliptic, parabolic, and hyperbolic, the text contains one chapter on the...

It has been 15 years since the first edition of Stochastic Integration and Differential Equations, A New Approach appeared, and in those years many other texts on the same subject have been published, often with connections to...

Graphs drawn on two-dimensional surfaces have always attracted researchers by their beauty and by the variety of difficult questions to which they give rise. The theory of such embedded graphs, which long seemed rather...

This volume is dedicated to the eminent Georgian mathematician Roland Duduchava on the occasion of his 70th birthday. It presents recent results on Toeplitz, Wiener-Hopf, and pseudodifferential operators, boundary value problems, operator theory,...

The book is devoted to dynamic inequalities of Hardy type and extensions and generalizations via convexity on a time scale T. In particular, the book contains the time scale versions of classical Hardy type inequalities, Hardy and...

This book contains the most recent progress in data assimilation in meteorology, oceanography and hydrology including land surface. It spans both theoretical and applicative aspects with various methodologies such as variational, Kalman filter, ensemble,...

Broadly organized around the applications of Fourier analysis, "Methods of Applied Mathematics with a MATLAB Overview" covers both classical applications in partial differential equations and boundary value problems, as well as the concepts and...

This book is a comprehensive, unifying introduction to the field of mathematical analysis and the mathematics of computing. It develops the relevant theory at a modern level and it directly relates modern mathematical ideas to their diverse applications...

Featuring the work of twenty-three internationally-recognized experts, this volume explores the trace formula, spectra of locally symmetric spaces, p-adic families, and other recent techniques from harmonic analysis and representation theory...

This book develops the foundations of "summability calculus", which is a comprehensive theory of fractional finite sums. It fills an important gap in the literature by unifying and extending disparate historical results. It also presents new material...

This book is devoted to boundary value problems of the Laplace equation on bounded and unbounded Lipschitz domains. It studies the Dirichlet problem, the Neumann problem, the Robin problem, the derivative oblique problem, the transmission...

Introduction.- Analytic preliminaries.- The de Branges spaces B(E) and H(A).- Three extension problems.- Spectral functions for ci problems.- Inverse spectral problems.- Generalizations.- Real and symmetric constraints...

This second volume of Analysis in Banach Spaces, Probabilistic Methods and Operator Theory, is the successor to Volume I, Martingales and Littlewood-Paley Theory. It presents a thorough study of the fundamental randomisation techniques and the...

Focused on the logistics and transportation operations within a supply chain, this book brings together the latest models, algorithms, and optimization possibilities. Logistics and transportation problems are examined within a sustainability perspective...

Part I - Biographical material.- List of publications of Heinz Langer.- Program of the Laudatio ceremony and photos.- Heinz Langer Laudatio.- Part II - Papers.- The inverse monodromy problem.- The bitangential matrix Nevanlinna-Pick interpolation problem...

The volume is a follow-up to the INdAM meeting "Special metrics and quaternionic geometry" held in Rome in November 2015. It offers a panoramic view of a selection of cutting-edge topics in differential geometry, including 4-manifolds, quaternionic and...

This book explores recent advances in uncertainty quantification for hyperbolic, kinetic, and related problems. The contributions address a range of different aspects, including: polynomial chaos expansions, perturbation methods, multi-level Monte Carlo...

This book provides an overview of different topics related to the theory of partial differential equations. Selected exercises are included at the end of each chapter to prepare readers for the "research project for beginners" proposed at the end of the...

This book features a selection of high-quality papers chosen from the best presentations at the International Conference on Spectral and High-Order Methods (2016), offering an overview of the depth and breadth of the activities within this important...

This book provides a unique survey displaying the power of Riccati equations to describe reversible and irreversible processes in physics and, in particular, quantum physics. Quantum mechanics is supposedly linear, invariant under time-reversal,...

This book includes a review of mathematical tools like modelling, analysis of stochastic processes, calculus of variations and stochastic differential equations which are applied to solve financial problems like modern portfolio theory and option pricing...

This book addresses mathematics in a wide variety of applications, ranging from problems in electronics, energy and the environment, to mechanics and mechatronics. Using the classification system defined in the EU Framework Programme for Research and...

This is an collection of some easily-formulated problems that remain open in the study of the geometry and analysis of Banach spaces. Assuming the reader has a working familiarity with the basic results of Banach space theory, the authors focus on...

This monograph presents the newly developed method of rigged Hilbert spaces as a modern approach in singular perturbation theory. A key notion of this approach is the Lax-Berezansky triple of Hilbert spaces embedded one into another, which specifies the...

This edited volume offers a state of the art overview of fast and robust solvers for the Helmholtz equation. The book consists of three parts:new developments and analysis in Helmholtz solvers, practical methods and implementations of Helmholtz solvers,...

This book provides the mathematical foundations for Feynman's operator calculus and for the Feynman path integral formulation of quantum mechanics as a natural extension of analysis and functional analysis to the infinite-dimensional setting.  ...

Are you looking for new lectures for your course on algorithms, combinatorial optimization, or algorithmic game theory?  Maybe you need a convenient source of relevant, current topics for a graduate student or advanced undergraduate student...

This volume presents some of the research topics discussed at the 2014-2015 Annual Thematic Program Discrete Structures: Analysis and Applications at the Institute for Mathematics and its Applications during Fall 2014, when combinatorics was the focus...

Written by a team of leading experts in the field, this volume presents a self-contained account of the theory, techniques and results in metric type spaces (in particular in G-metric spaces); that is, the text approaches this important area of fixed...

These are the proceedings of the "AstroNet-II International Final Conference". This conference was one of the last milestones of the Marie-Curie Research Training Network on Astrodynamics "AstroNet-II", that has been funded by the European Commission...

This monograph provides a self-contained introduction to symmetric functions and their use in enumerative combinatorics.  It is the first book to explore many of the methods and results that the authors present. Numerous exercises are included...

This book addresses the modelling of mechanical waves by asking the right questions about them and trying to find suitable answers. The questions follow the analytical sequence from elementary understandings to complicated cases, following a step-by-step...

This textbook presents the physical principles pertinent to the mathematical modeling of soft materials used in engineering practice, including both man-made materials and biological tissues. It is intended for seniors and...