Applied mathematics Books

The second edition of Matrix Analysis and Applied Linear Algebra has been almost completely rewritten to create a textbook designed to provide flexibility for nearly any desired degree of rigor and depth of coverage. Throughout, there are carefully...

Symbolic dynamics is essential in the study of dynamical systems of various types and is connected to many other fields such as stochastic processes, ergodic theory, representation of numbers, information and coding, etc. This graduate text introduces...

An abelian network is a collection of communicating automata whose state transitions and message passing each satisfy a local commutativity condition. This paper is a continuation of the abelian networks series of Bond and Levine (2016), for which we...

Systems of polynomial equations can be used to model an astonishing variety of phenomena. This book explores the geometry and algebra of such systems and includes numerous applications. The book begins with elimination theory from Newton to the...

Can we coexist with the other life forms that have evolved on this planet? Are there realistic alternatives to fossil fuels that would sustainably provide for human society's energy needs and have fewer harmful effects? How do we deal with threats such...

Algebraic Geometry Codes: Advanced Chapters is devoted to the theory of algebraic geometry codes, a subject related to several domains of mathematics. On one hand, it involves such classical areas as algebraic geometry and number theory; on the other, it...

This book contains the proceedings of the AMS Special Session on Topology of Biopolymers, held from April 21-22, 2018, at Northeastern University, Boston, MA. The papers cover recent results on the topology and geometry of DNA and protein knotting using...

This paper is a corrigendum and improvements to Carleman Estimates, Observability Inequalities and Null Controllability for Interior Degenerate Nonsmooth Parabolic Equations and its consequences. We give here the corrected proofs of the concerned...

This volume contains the proceedings of the AMS Special Session on Topological Phases of Matter and Quantum Computation, held from September 24-25, 2016, at Bowdoin College, Brunswick, Maine. Topological quantum computing has exploded in popularity in...

This book introduces students with diverse backgrounds to various types of mathematical analysis that are commonly needed in scientific computing. The subject of numerical analysis is treated from a mathematical point of view, offering a complete...

Mathematical modelling is a subject without boundaries. It is the means by which mathematics becomes useful to virtually any subject. Moreover, modelling has been and continues to be a driving force for the development of mathematics itself. This book...

Emphasizing conceptual understanding over mathematics, this user-friendly text introduces linear regression analysis to students and researchers across the social, behavioral, consumer, and health sciences. Coverage includes model construction and...

Once upon a time in America, few knew or cared about math. In Republic of Numbers, David Lindsay Roberts tells the story of how all that changed, as America transformed into a powerhouse of mathematical thinkers. Covering more than 200 years of American...

This book discusses the foundations of the mathematical theory of finite element methods. The focus is on the concept of discrete stability and the exact sequence conforming elements and covers both coercive and non-coercive problems. Following a...

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...

Among the many branches of applied mathematics, options pricing theory occupies a unique position: it utilizes a wide range of advanced mathematical concepts, making it appealing to mathematicians, and it is regularly applied at financial institutions,...

This text presents a unique treatment of network control systems. Drawing from fundamental principles of dynamical systems theory and dynamical thermodynamics, the authors develop a continuous-time, discrete-time, and hybrid dynamical system and control...

Rounding Errors in Algebraic Processes was the first book to give systematic analyses of the effects of rounding errors on a variety of key computations involving polynomials and matrices. A detailed analysis is given of the rounding errors made in the...

Reduced order modeling is an important, growing field in computational science and engineering, and this is the first book to address the subject in relation to computational fluid dynamics. It focuses on complex parametrization of shapes for their...

Fit for students just starting to build a background in mathematics, this textbook provides an introduction to numerical methods for linear algebra problems. Introduction to Numerical Linear Algebra is ideal for a flipped classroom, as it provides...

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,...

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...

Numerical Linear Algebra with Julia provides in-depth coverage of fundamental topics in numerical linear algebra, including how to solve dense and sparse linear systems, compute QR factorizations, compute the eigendecomposition of a matrix, and solve...

Numerical Linear Algebra with Julia provides in-depth coverage of fundamental topics in numerical linear algebra, including how to solve dense and sparse linear systems, compute QR factorizations, compute the eigendecomposition of a matrix, and solve...

Dynamical systems are a principal tool in the modeling, prediction, and control of a wide range of complex phenomena. As the need for improved accuracy leads to larger and more complex dynamical systems, direct simulation often becomes the only available...

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...

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...

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...

Computational methods to approximate the solution of differential equations play a crucial role in science, engineering, mathematics, and technology. The key processes that govern the physical world-wave propagation, thermodynamics, fluid flow, solid...

Computational methods to approximate the solution of differential equations play a crucial role in science, engineering, mathematics, and technology. The key processes that govern the physical world-wave propagation, thermodynamics, fluid flow, solid...

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...

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...

This book differs from traditional numerical analysis texts in that it focuses on the motivation and ideas behind the algorithms presented rather than on detailed analyses of them. It presents a broad overview of methods and software for solving...

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...

In many dynamical systems, time delays arise because of the time it takes to measure system states, perceive and evaluate events, formulate decisions, and act on those decisions. The presence of delays may lead to undesirable outcomes; without an...

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...

Web-like waves, often observed on the surface of shallow water, are examples of nonlinear waves. They are generated by nonlinear interactions among several obliquely propagating solitary waves, also known as solitons. In this book, modern mathematical...

This book is about making decisions driven by experience. In this context, a scenario is an observation that comes from the environment, and scenario optimization refers to optimizing decisions over a set of available scenarios. Scenario optimization can...

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...

This book presents new computational tools for the H? control of distributed parameter systems in which transfer functions are considered as input-output descriptions for the plants to be controlled. The emphasis is on the computation of the controller...

As one of the classical statistical regression techniques, and often the first to be taught to new students, least squares fitting can be a very effective tool in data analysis. Given measured data, we establish a relationship between independent and...

Elementary Mathematical Models offers instructors an alternative to standard college algebra, quantitative literacy, and liberal arts mathematics courses. Presuming only a background of exposure to high school algebra, the text introduces students to the...

Elementary Mathematical Models offers instructors an alternative to standard college algebra, quantitative literacy, and liberal arts mathematics courses. Presuming only a background of exposure to high school algebra, the text introduces students to the...

Discrete Painleve equations are nonlinear difference equations, which arise from translations on crystallographic lattices. The deceptive simplicity of this statement hides immensely rich mathematical properties, connecting dynamical systems, algebraic...

This book introduces game theory and its applications from an applied mathematician's perspective, systematically developing tools and concepts for game-theoretic modelling in the life and social sciences. Filled with down-to-earth examples of strategic...

This volume is based on lectures delivered at the 2019 AMS Short Course ""Sum of Squares: Theory and Applications'', held January 14-15, 2019, in Baltimore, Maryland. This book provides a concise state-of-the-art overview of the theory and applications...