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 ......
Differential equations are the basis for models of any physical systems that exhibit smooth change. This book combines much of the material found in a traditional course on ordinary differential equations with an introduction to the more modern theory of dynamical systems. Applications of this theory to physics, biology, chemistry, and engineering ......
Using material from many different sources in a systematic and unified way, this self-contained book provides both rigorous mathematical theory and practical numerical insights while developing a framework for determining the convergence rate of discrete approximations to optimal control problems. Elements of the framework include the reference ......
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 ......
This book provides an overview of global sensitivity analysis methods and algorithms, including their theoretical basis and mathematical properties. The authors use a practical point of view and real case studies as well as numerous examples, and applications of the different approaches are illustrated throughout using R code to explain their ......
Applied Numerical Linear Algebra introduces students to numerical issues that arise in linear algebra and its applications. A wide range of techniques are touched on, including direct to iterative methods, orthogonal factorizations, least squares, eigenproblems, and nonlinear equations. Inside Applied Numerical Linear Algebra, readers will find: ......
Research on the Anderson Acceleration (AA) has exploded in the last 15 years. This book brings together these recent fundamental results applied to nonlinear solvers for PDEs, which are ubiquitous across mathematics, science, engineering, and economics as predictive models for a vast quantity of important phenomena. Coverage includes: AA ......
From Magnetic Fields to Symmetries and Optimization
This self-contained book is the first to provide readers with an introduction to mathematical foundations and modeling of stellarator design. It covers the fundamental theoretical building blocks of magnetic fields modeling, some of the associated challenges, and the main concepts behind optimization for the design of stellarators. The book is ......
