Divided into two self-contained parts, this textbook is an introduction to modern real analysis. More than 350 exercises and 100 examples are integrated into the text to help clarify the theoretical considerations and the practical applications to differential geometry, Fourier series, differential equations, and other subjects. The first ......
In this textbook on calculus of one variable, applications to the natural sciences play a central role. Examples from biology, chemistry, and physics are discussed in detail without compromising the discussion of the mathematics essential to differential and integral calculus. Calculus for the Natural Sciences distinguishes itself from others on ......
In just over 100 pages, this book provides basic, essential knowledge of some of the tools of real analysis: the Hardy-Littlewood maximal operator, the Calderon-Zygmund theory, the Littlewood-Paley theory, interpolation of spaces and operators, and the basics of H1 and BMO spaces. This concise text offers brief proofs and exercises of various ......
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 ......
The shape of the Earth was a significant scientific question in the eighteenth century. When it was discovered that the Earth was flattened at the poles, scientists sought to understand the cause, leading to the study of the gravitational attraction of celestial spheroids. The solution drew upon Newton's law of universal gravitation, which used ......
And Related Problems of Mathematical Physics, Engineering, and Life Sciences
This book is the first to offer a systematic methodology for solving nonlinear ordinary differential equations (ODEs) using power series, specifically those arising in mathematical physics. It provides tools to eliminate the tedious manipulation of infinite series, enabling recursive computation of all terms. The authors also present a structured ......
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 ......
From the Preface: 'The aim of this book is to offer a discussion of the fundamental concepts in the theory of differential and integral equations, with a view toward preparing the reader for graduate-level courses on advanced topics. This book can also serve a graduate-level course for non-mathematics majors. Students of various disciplines have ......
