This second edition provides an enhanced exposition of the long-overlooked Hadamard semidifferential calculus, first introduced in the 1920s by mathematicians Jacques Hadamard and Maurice Rene Frechet. Hadamard semidifferential calculus is possibly the largest family of nondifferentiable functions that retains all the features of classical ......
Compressed sensing is a relatively recent area of research that refers to the recovery of high-dimensional but low-complexity objects from a limited number of measurements. The topic has applications to signal/image processing and computer algorithms, and it draws from a variety of mathematical techniques such as graph theory, probability theory, ......
Due to its ubiquity across a variety of fields in science and engineering, fractional calculus has gained momentum in industry and academia. While a number of books and papers introduce either fractional calculus or numerical approximations, no current literature provides a comprehensive collection of both topics. This monograph introduces ......
Fast solvers for elliptic PDEs form a pillar of scientific computing. They enable detailed and accurate simulations of electromagnetic fields, fluid flows, biochemical processes, and much more. This textbook provides an introduction to fast solvers from the point of view of integral equation formulations, which lead to unparalleled accuracy and ......
This book develops the theory of probability and mathematical statistics with the goal of analyzing real-world data. Throughout the text, the R package is used to compute probabilities, check analytically computed answers, simulate probability distributions, illustrate answers with appropriate graphics, and help students develop intuition ......
Based on first principle quantum mechanics, electronic structure theory is widely used in physics, chemistry, materials science, and related fields and has recently received increasing research attention in applied and computational mathematics. This book provides a self-contained, mathematically oriented introduction to the subject and its ......
A compendium of the authors' recently published results, this book discusses sliding mode control of uncertain nonlinear systems, with a particular emphasis on advanced and optimization based algorithms. The authors survey classical sliding mode control theory and introduce four new methods of advanced sliding mode control. They analyze classical ......
A resurgence of interest in network synthesis in the last decade, motivated in part by the introduction of the inerter, has led to the need for a better understanding of the most economical way to realize a given passive impedance. This monograph outlines the main contributions to the field of passive network synthesis and presents new research ......
This textbook develops the fundamental skills of numerical analysis: designing numerical methods, implementing them in computer code, and analyzing their accuracy and efficiency. A number of mathematical problems-interpolation, integration, linear systems, zero finding, and differential equations-are considered, and some of the most important ......
