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The volume presents a selection of in-depth studies and state-of-the-art surveys of several challenging topics that are at the forefront of modern applied mathematics, mathematical modeling, and computational science. These three areas represent the foundation upon which the methodology of mathematical modeling and computational experiment is built as a ubiquitous tool in all areas of mathematical applications. This book covers both fundamental and applied research, ranging from studies of elliptic curves over finite fields with their applications to cryptography, to dynamic blocking problems, to random matrix theory with its innovative applications. The book provides the reader with state-of-the-art achievements in the development and application of new theories at the interface of applied mathematics, modeling, and computational science. This book aims at fostering interdisciplinary collaborations required to meet the modern challenges of applied mathematics, modeling, and computational science. At the same time, the contributions combine rigorous mathematical and computational procedures and examples from applications ranging from engineering to life sciences, providing a rich ground for graduate student projects.

Advances in Applied Mechanics

This textbook is a comprehensive introduction to computational mathematics and scientific computing suitable for undergraduate and postgraduate courses. It presents both practical and theoretical aspects of the subject, as well as advantages and pitfalls of classical numerical methods alongside with computer code and experiments in Python. Each chapter closes with modern applications in physics, engineering, and computer science. Features: No previous experience in Python is required. Includes simplified computer code for fast-paced learning and transferable skills development. Includes practical problems ideal for project assignments and distance learning. Presents both intuitive and rigorous faces of modern scientific computing. Provides an introduction to neural networks and machine learning.

Quantum Computation presents the mathematics of quantum computation. The purpose is to introduce the topic of quantum computing to students in computer science, physics and mathematics who have no prior knowledge of this field. The book is written in two parts. The primary mathematical topics required for an initial understanding of quantum computation are dealt with in Part I: sets, functions, complex numbers and other relevant mathematical structures from linear and abstract algebra. Topics are illustrated with examples focussing on the quantum computational aspects which will follow in more detail in Part II. Part II discusses quantum information, quantum measurement and quantum algorithms. These topics provide foundations upon which more advanced topics may be approached with confidence. Features A more accessible approach than most competitor texts, which move into advanced, research-level topics too quickly for today's students. Part I is comprehensive in providing all necessary mathematical underpinning, particularly for those who need more opportunity to develop their mathematical competence. More confident students may move directly to Part II and dip back into Part I as a reference. Ideal for use as an introductory text for courses in quantum computing. Fully worked examples illustrate the application of mathematical techniques. Exercises throughout develop concepts and enhance understanding. End-of-chapter exercises offer more practice in developing a secure foundation.

This multi-author contributed proceedings volume contains recent advances in several areas of Computational and Applied Mathematics. Each review is written by well known leaders of Computational and Applied Mathematics. The book gives a comprehensive account of a variety of topics including – Efficient Global Methods for the Numerical Solution of Nonlinear Systems of Two point Boundary Value Problems; Advances on collocation based numerical methods for Ordinary Differential Equations and Volterra Integral Equations; Basic Methods for Computing Special Functions, Melt Spinning: Optimal Control and Stability Issues; Brief survey on the CP methods for the Schrödinger equation; Symplectic Partitioned Runge-Kutta methods for the numerical integration of periodic and oscillatory problems. Recent Advances in Computational and Applied Mathematics is aimed at advanced undergraduates and researchers who are working in these fast moving fields.

This book “Advanced Applications of Computational Mathematics” covers multidisciplinary studies containing advanced research in the field of computational and applied mathematics. The book includes research methodology, techniques, applications, and algorithms. The book will be very useful to advanced students, researchers and practitioners who are involved in the areas of computational and applied mathematics and engineering.

This volume is an excellent resource for professionals in various areas of applications of mathematics, modeling, and computational science. It focuses on recent progress and modern challenges in these areas. The volume provides a balance between fundamental theoretical and applied developments, emphasizing the interdisciplinary nature of modern trends and detailing state-of-the-art achievements in Applied Mathematics, Modeling, and Computational Science. The chapters have been authored by international experts in their respective fields, making this book ideal for researchers in academia, practitioners, and graduate students. It can also serve as a reference in the diverse selected areas of applied mathematics, modelling, and computational sciences, and is ideal for interdisciplinary collaborations.