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Publishing May 2025

This self-contained textbook provides the foundations of linear optimization, covering topics in both continuous and discrete linear optimization. It gradually builds the connection between theory, algorithms, and applications so that readers gain a theoretical and algorithmic foundation, familiarity with a variety of applications, and the ability to apply the theory and algorithms to actual problems.

To deepen the reader's understanding, the authors provide

• many applications from diverse areas of applied sciences, such as resource allocation, line fitting, graph coloring, the traveling salesman problem, game theory, and network flows;

• more than 180 exercises, most of them with partial answers and about 70 with complete solutions; and

• a continuous illustration of the theory through examples and exercises.

A First Course in Linear Optimization is intended to be read cover to cover and requires only a first course in linear algebra as a prerequisite. Its 13 chapters can be used as lecture notes for a first course in linear optimization.

Publishing May 2025

“George Haller provides a substantial literature overview which, in combination with his many contributions, results in the first book on spectral model reduction techniques. He covers basic theory for both linear and nonlinear problems and model- and data-driven techniques, and he demonstrates the method's excellent behavior on nontrivial problems.”

— Jan S. Hesthaven, Karlsruhe Institute of Technology (KIT)

“This is an exciting topic and a powerful method that already has and will continue to have an impact on any field where model reduction is a key ingredient or a central concern. The content is presented in a logical order, from the equation-based to the data-driven version of the method to applications that progressively increase in complexity.”

— Peter Schmid, KAUST

This concise text presents an introduction to the emerging area of reducing complex nonlinear differential equations or time-resolved data sets to spectral submanifolds (SSMs). SSMs are ubiquitous low-dimensional attracting invariant manifolds that can be constructed systematically, building on the spectral properties of the linear part of a nonlinear system. The internal dynamics within SSMs then serve as exact, low-dimensional models with which the full system evolution synchronizes exponentially fast.

SSM-based model reduction has a solid mathematical foundation and hence is guaranteed to deliver accurate and predictive reduced-order models under a precise set of assumptions. This book:

• introduces the foundations of SSM theory to the novice reader;

• reviews recent extensions of classic SSM results for the advanced reader; and

• illustrates the power of SSM reduction on a large collection of equation- and data-driven applications in fluid mechanics, solid mechanics, and control.

Get 10% off by pre-ordering this book.

This item has not yet published. Pre-order now and we will ship and process payment when the book becomes available.

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215-382-9800 (outside US & Canada)

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Print Prices: List $77.40 / Member $61.20

Publishing May 2025

This comprehensive textbook focuses on numerical methods for approximating solutions to partial differential equations (PDEs). The authors present a broad survey of these methods, introducing readers to the central concepts of various families of discretizations and solution algorithms and laying the foundation needed to understand more advanced material. The authors include over 100 well-established definitions, theorems, corollaries, and lemmas and summaries of and references to in-depth treatments of more advanced mathematics when needed.

Numerical Partial Differential Equations is divided into four parts:

• Part I covers basic background on PDEs and numerical methods.

• Part II introduces the three main classes of numerical methods for PDEs that are the book's focus (finite-difference, finite-element, and finite-volume methods).

• Part III discusses linear solvers and finite-element and finite-volume methods at a more advanced level.

• Part IV presents further high-level topics on discretizations and solvers.