Boundary Value Problems for Systems of Differential, Difference and Fractional Equations: Positive Solutions discusses the concept of a differential equation that brings together a set of additional constraints called the boundary conditions. As boundary value problems arise in several branches of math given the fact that any physical differential equation will have them, this book will provide a timely presentation on the topic. Problems involving the wave equation, such as the determination of normal modes, are often stated as boundary value problems. To be useful in applications, a boundary value problem should be well posed. This means that given the input to the problem there exists a unique solution, which depends continuously on the input. Much theoretical work in the field of partial differential equations is devoted to proving that boundary value problems arising from scientific and engineering applications are in fact well-posed.

Combinatorial optimization is a multidisciplinary scientific area, lying in the interface of three major scientific domains: mathematics, theoretical computer science and management. The three volumes of the Combinatorial Optimization series aim to cover a wide range of topics in this area. These topics also deal with fundamental notions and approaches as with several classical applications of combinatorial optimization. Concepts of Combinatorial Optimization, is divided into three parts: - On the complexity of combinatorial optimization problems, presenting basics about worst-case and randomized complexity; - Classical solution methods, presenting the two most-known methods for solving hard combinatorial optimization problems, that are Branch-and-Bound and Dynamic Programming; - Elements from mathematical programming, presenting fundamentals from mathematical programming based methods that are in the heart of Operations Research since the origins of this field.

Developed for the new International A Level specification, these new resources are specifically designed for international students, with a strong focus on progression, recognition and transferable skills, allowing learning in a local context to a global standard. Recognised by universities worldwide and fully comparable to UK reformed GCE A levels. Supports a modular approach, in line with the specification. Appropriate international content puts learning in a real-world context, to a global standard, making it engaging and relevant for all learners. Reviewed by a language specialist to ensure materials are written in a clear and accessible style. The embedded transferable skills, needed for progression to higher education and employment, are signposted so students understand what skills they are developing and therefore go on to use these skills more effectively in the future. Exam practice provides opportunities to assess understanding and progress, so students can make the best progress they can.

Containing selected papers on the fundamentals and applications of Complexity Science, this multi-disciplinary book presents new approaches for resolving complex issues that cannot be resolved using conventional mathematical or software models. Complex Systems problems can occur in a variety of areas such as physical sciences and engineering, the economy, the environment, humanities and social and political sciences. Complexity Science problems, the science of open systems consisting of large numbers of diverse components engaged in rich interaction, can occur in a variety of areas such as physical sciences and engineering, the economy, the environment, humanities and social and political sciences. The global behaviour of these systems emerges from the interaction of constituent components and is unpredictable but not random. The key attribute of Complex Systems is the ability to self-organise and adapt to unpredictable changes in their environment. Renown complexity thinkers and practitioners as well as those who are new to the area of complexity will find interest in this book.

Mathematics Applications and Interpretation for the IB Diploma Higher Level provides comprehensive coverage of the new curriculum, developed for first examinations in 2021. Written by a highly experienced IB author team, this book includes the following features: integrated GeoGebra applets created specifically for the course, worked examples to help you tackle questions and apply concepts and skills, practice questions to help you prepare for the exam, a rich and wide-ranging Theory of Knowledge chapter, and guidance on the Internal Assessment.

Containing case studies and examples, the book aims to cover extensive research particularly on surface stress and topics related to the variational approach to the subject, and non-standard topics such as the rigorous treatment of constraints and a full discussion of algebraic inequalities associated with realistic material behaviour, and their implications. Serving as an introduction to the basic elements of Finite Elasticity, this textbook is the cornerstone for any graduate-level on the topic, while also providing a template for a host of theories in Solid Mechanics.