This contributed volume contains a collection of articles on state-of-the-art developments on the construction of theoretical integral techniques and their application to specific problems in science and engineering. Written by internationally recognized researchers, the chapters in this book are based on talks given at the Thirteenth International Conference on Integral Methods in Science and Engineering, held July 21–25, 2014, in Karlsruhe, Germany. A broad range of topics is addressed, ...

This graduate-level textbook introduces the reader to the area of inverse problems, vital to many fields including geophysical exploration, system identification, nondestructive testing, and ultrasonic tomography. It aims to expose the basic notions and difficulties encountered with ill-posed problems, analyzing basic properties of regularization methods for ill-posed problems via several simple analytical and numerical examples. The book also presents three special nonlinear inverse probl...

This book introduces the reader to the area of inverse problems. The study of inverse problems is of vital interest to many areas of science and technology such as geophysical exploration, system identification, nondestructive testing and ultrasonic tomography.The aim of this book is twofold: in the first part, the reader is exposed to the basic notions and difficulties encountered with ill-posed problems. Basic properties of regularization methods for linear ill-posed problems are ...

This book gives a concise introduction to the basic techniques needed for the theoretical analysis of the Maxwell Equations, and filters in an elegant way the essential parts, e.g., concerning the various function spaces needed to rigorously investigate the boundary integral equations and variational equations. The book arose from lectures taught by the authors over many years and can be helpful in designing graduate courses for mathematically orientated students on electromagnetic wave pr...

Tough Test Questions? Missed Lectures? Not Enough Time? Textbook too Pricey?Fortunately, there's Schaum's. This all-in-one-package includes more than 600 fully-solved problems, examples, and practice exercises to sharpen your problem-solving skills. Plus, you will have access to 25 detailed videos featuring math instructors who explain how to solve the most commonly tested problems--it's just like having your own virtual tutor! You'll find everything you need to bu...

This book provides a comprehensive and unified introduction to stochastic differential equations and related optimal control problems. The material is new and the presentation is reader-friendly. A major contribution of the book is the development of generalized Malliavin calculus in the framework of white noise analysis, based on chaos expansion representation of stochastic processes and its application for solving several classes of stochastic differential equations with singular data in...

This first volume, a three-part introduction to the subject, is intended for students with a beginning knowledge of mathematical analysis who are motivated to discover the ideas that shape Fourier analysis. It begins with the simple conviction that Fourier arrived at in the early nineteenth century when studying problems in the physical sciences--that an arbitrary function can be written as an infinite sum of the most basic trigonometric functions.The first part implements this ide...

Linear Algebra is intended for a one-term course at the junior or senior level. It begins with an exposition of the basic theory of vector spaces and proceeds to explain the fundamental structure theorems for linear maps, including eigenvectors and eigenvalues, quadric and hermitian forms, diagonalization of symmetric, hermitian, and unitary linear maps and matrices, triangulation, and Jordan canonical form. The book also includes a useful chapter on convex sets and the finite-dimensional ...

These notes provide an introduction to the theory of spherical harmonics in an arbitrary dimension as well as an overview of classical and recent results on some aspects of the approximation of functions by spherical polynomials and numerical integration over the unit sphere. The notes are intended for graduate students in the mathematical sciences and researchers who are interested in solving problems involving partial differential and integral equations on the unit sphere, especially on ...

This work describes the propagation properties of the so-called symmetric interior penalty discontinuous Galerkin (SIPG) approximations of the 1-d wave equation. This is done by means of linear approximations on uniform meshes. First, a careful Fourier analysis is constructed, highlighting the coexistence of two Fourier spectral branches or spectral diagrams (physical and spurious) related to the two components of the numerical solution (averages and jumps). Efficient filtering mechanisms ...

This textbook on linear algebra includes the key topics of the subject that most advanced undergraduates need to learn before entering graduate school. All the usual topics, such as complex vector spaces, complex inner products, the Spectral theorem for normal operators, dual spaces, the minimal polynomial, the Jordan canonical form, and the rational canonical form, are covered, along with a chapter on determinants at the end of the book. In addition, there is material throughout the text ...

This book offers an essential introduction to the mathematical theory of compressible viscous fluids. The main goal is to present analytical methods from the perspective of their numerical applications. Accordingly, we introduce the principal theoretical tools needed to handle well-posedness of the underlying Navier-Stokes system, study the problems of sequential stability, and, lastly, construct solutions by means of an implicit numerical scheme. Offering a unique contribution – by explor...