Computational Applied Mathematics and Operations Research: Fundamental Texts

Intermediate-level guide to integer programming, providing readers with clear, up-to-date explanations on why some problems are difficult to solve, how techniques can be reformulated to give better results, and how mixed integer programming systems can be used more effectively.

A practical, accessible guide to optimization problems with discrete or integer variables.

An elegant and rigorous presentation of integer programming, exposing the subject's mathematical depth and broad applicability. Special attention is given to the theory behind the algorithms used in state-of-the-art solvers. An abundance of concrete examples and exercises of both theoretical and real-world interest.

A modern treatment of linear optimization. Includes theory and practice of linear programming, network flow problems, and discrete optimization.

Includes clear and comprehensive coverage of the fundamentals of operations research, an extensive set of interesting problems and cases, and state-of-the-practice operations research software used in conjunction with examples from the text.

Presents a carefully selected group of methods for unconstrained and bound constrained optimization problems and analyzes them in depth both theoretically and algorithmically. It focuses on clarity in algorithmic description and analysis rather than generality, and while it provides pointers to the literature for the most general theoretical results and robust software, the author thinks it is more important that readers have a complete understanding of special cases that convey essential ideas.

This book has become the standard for a complete, state-of-the-art description of the methods for unconstrained optimization and systems of nonlinear equations. Provides information needed to understand both the theory and the practice of these methods and provides pseudocode for the problems.

This natural and reasonable approach to mathematical programming covers numerical methods for finite-dimensional optimization problems. It begins with very simple ideas progressing through more complicated concepts, concentrating on methods for both unconstrained and constrained optimization.

This book is a comprehensive survey of the mathematical concepts and principles of industrial mathematics. Its purpose is to provide students and professionals with an understanding of the fundamental mathematical principles used in Industrial Mathematics/OR in modeling problems and application solutions.

Describes the theory of linear and integer programming and surveys the algorithms for linear and integer programming problems, focusing on complexity analysis. Applications to combinatorial optimization are given. The book is intended for graduate students and researchers in operations research, mathematics and computer science.

Designed for use by first-year graduate students from a variety of engineering and scientific disciplines, this comprehensive textbook covers the solution of linear systems, least squares problems, eigenvalue problems, and the singular value decomposition.

Renowned applied mathematician Gilbert Strang teaches applied mathematics with the clear explanations, examples and insights of an experienced teacher. This book progresses steadily through a range of topics from symmetric linear systems to differential equations to least squares and Kalman filtering and optimization. It clearly demonstrates the power of matrix algebra in engineering problem solving.

Based on a successful course at Oxford University, this book covers a wide range of problems ranging from the approximation of functions and integrals to the approximate solution of algebraic, transcendental, differential and integral equations.

Gives a modern view of iterative methods for solving linear and nonlinear equations, which are the basis for many, if not most, of the models of phenomena in science and engineering; their efficient numerical solution is critical to progress in these areas.

Provides an in-depth, up-to-date view of practical algorithms for solving large-scale linear systems of equations. These equations can number in the millions and are sparse in the sense that each involves only a small number of unknowns. The methods described are iterative, i.e., they provide sequences of approximations that will converge to the solution.

With a highly applied and computational focus, this book combines the important underlying theory with examples from electrical engineering, computer science, physics, biology and economics.

An overview of linear algebra and the foundations of deep learning.

An essential reference for computational scientists and engineers in addition to researchers in the numerical linear algebra community. Anyone whose work requires the solution to a matrix problem and an appreciation of its mathematical properties will find this book to be an indispensable tool.

This well-respected book introduces readers to the theory and application of modern numerical approximation techniques. Providing an accessible treatment that requires only a calculus prerequisite, the authors explain how, why, and when approximation techniques can be expected to work-and why, in some situations, they fail. A wealth of examples and exercises develop readers' intuition, and demonstrate the subject's practical applications to important everyday problems in math, computing, engineering, and physical science disciplines.

A rigorous treatment of approximation, nonlinear equations, numerical differentiation and integration, and ordinary differential equations. Each chapter concludes with a substantial set of exercises covering all the chapter's topics.

Designed for use as a stand-alone textbook in a one-semester, graduate-level course in the topic.

Partial differential equations (PDEs) are essential for modeling many physical phenomena. This undergraduate textbook introduces students to the topic with a unique approach that emphasizes the modern finite element method alongside the classical method of Fourier analysis.