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A. Ted Watson: Foundations of
Mathematical Modeling and Analysis in E

Foundations of Mathematical Modeling and Analysis in Engineering

1. Introduction 2. Mathematical representations of physical phenomena 3. Solving linear algebraic equations 4. Vector spaces and their representations 5. Linear transformations and representations 6. Inner product spaces 7. Operators and matrix representations 8. Ordinary differential equations 9. Function representation and transforms 10. Partial differential equations 11. System and parameter identification

Extended Hypergeometric Functions and Orthogonal Polynomials

De Gruyter Series in Applied and Numerical Mathematics

Advanced Computational Approaches for Rarefied Flows

Beyond Navier-Stokes

Mathematics and Biomedical Engineering in Medicine, Physiology and Health Sciences is a visionary book, whose purpose is to demonstrate how fundamental mathematics and biomedical engineering can be incorporated into physiology, medicine, and health sciences teaching, research, and clinical practice to make these disciplines more quantitative and computational, and hence more explanatory and informative. The book also provides more quantitative formulation of medical procedures, towards supporting the growing field of precision medicine.

Mathematics and Biomedical Engineering in Medicine, Physiology and Health Sciences

Data Science and Interactive Visualization Tools for the Analysis of Qualitative Evidence empowers qualitative and mixed methods researchers in the data science movement by offering no-code, cost-free software access so that they can apply cutting-edge and innovative methods to synthetize qualitative data. The book builds on the idea that qualitative and mixed methods researchers should not have to learn to code to benefit from rigorous open-source, cost-free software that uses artificial intelligence, machine learning, and data visualization tools-just as people do not need to know C++ or TypeScript to benefit from Microsoft Word. The real barrier is the hundreds of R code lines required to apply these concepts to their databases. By removing the coding proficiency hurdle, this book will empower their research endeavors and help them become active members of and contributors to the applied data science community. The book offers a comprehensive explanation of data science and machine learning methodologies, along with access to software application tools to implement these techniques without any coding proficiency. The book addresses the need for innovative tools that enable researchers to tap into the insights that come out of cutting-edge data science tools with absolutely no computer language literacy requirements.

Data Science and Interactive Visualization Tools for the Analysis of Qualitative Evidence

This text focuses on the parts of stochastic theory that are particularly relevant to applications. It begins with a description of Brownian motion and the associated stochastic calculus, including the relationship to partial differential equations. It then solves stochastic differential equations by a variety of methods. The author also studies in detail the one-dimensional case. The book concludes with a treatment of semigroups and generators, applying the theory of Harris chains to diffusions as well as weak convergence of Markov chains to diffusions.

This text focuses on the parts of stochastic theory that are particularly relevant to applications. It begins with a description of Brownian motion and the associated stochastic calculus, including the relationship to partial differential equations. It then solves stochastic differential equations by a variety of methods. The author also studies in detail the one-dimensional case. The book concludes with a treatment of semigroups and generators, applying the theory of Harris chains to diffusions as well as weak convergence of Markov chains to diffusions.

An Elementary Introduction Emphasizing Applications

Stochastic Calculus

This book is the first one that shows how to accurately and efficiently solve time-varying problems in real-time or online using continuous- or discrete-time zeroing dynamics. The authors provide a comprehensive treatment of the theory of both static and dynamic neural networks. They develop, analyze, model, simulate, and compare zeroing dynamics models for the online solution of numerous time-varying problems, such as root finding, nonlinear equation solving, matrix inversion, matrix square root finding, quadratic optimization, and inequality solving.

Neural networks and neural dynamics are powerful approaches for the online solution of mathematical problems arising in many areas of science, engineering, and business. Compared with conventional gradient neural networks that only deal with static problems of constant coefficient matrices and vectors, the authors’ new method called zeroing dynamics solves time-varying problems. Zeroing Dynamics, Gradient Dynamics, and Newton Iterations is the first book that shows how to accurately and efficiently solve time-varying problems in real-time or online using continuous- or discrete-time zeroing dynamics. The book brings together research in the developing fields of neural networks, neural dynamics, computer mathematics, numerical algorithms, time-varying computation and optimization, simulation and modeling, analog and digital hardware, and fractals.The authors provide a comprehensive treatment of the theory of both static and dynamic neural networks. Readers will discover how novel theoretical results have been successfully applied to many practical problems. The authors develop, analyze, model, simulate, and compare zeroing dynamics models for the online solution of numerous time-varying problems, such as root finding, nonlinear equation solving, matrix inversion, matrix square root finding, quadratic optimization, and inequality solving.

Zeroing Dynamics, Gradient Dynamics, and Newton Iterations

Genetics and Society

This book provides a timely analysis of the past, present and future of the stem cell. It uncovers an intriguing and paradoxical story of scientific setbacks and advance, medical breakthroughs and technical innovation amid ongoing uncertainty about the nature of the stem cell.

This book provides a timely analysis of the past, present and future of the stem cell. It uncovers an intriguing and paradoxical story of scientific setbacks and advance, medical breakthroughs and technical innovation amid ongoing uncertainty about the nature of the stem cell.

From Radiobiology to Regenerative Medicine

The Scientific, Clinical and Commercial Development of the Stem Cell

This book is designed as an introductory course in Quantum Field Theory (QFT) for students who have completed two full graduate-level courses in Quantum Mechanics (QM). Quantum Field Theory is the framework that combines quantum mechanics with special relativity, providing a comprehensive description of fundamental forces and particles. It is a crucial part of modern theoretical physics and essential for understanding the behaviour of elementary particles, the dynamics of fields, and the interactions that govern the universe at the smallest scales. This book is structured to gradually introduce the key concepts and mathematical tools necessary for mastering QFT. Each chapter builds on the knowledge acquired in previous sections, ensuring a coherent and comprehensive understanding of the subject. The material presented here helps doctoral students bridge the gap between the traditional quantum mechanics taught at the graduate level and the more advanced concepts and techniques used in quantum field theory. Key Features:<ul> <li>Specifically designed to connect traditional quantum mechanics knowledge with quantum field theory.</li> <li>Presents a coherent learning path, including end-of-chapter trivia questions and problems, that gradually introduces the concepts and skills needed for grasping QFT.</li> <li>Tailored for doctoral-level physics students, ensuring appropriate depth and complexity.</li> </ul>

For Doctoral Level Physics

A First Graduate Course in Quantum Field Theory

Series on Concrete & Applicable Mathematics

Rainbow And Properly Colored Subgraphs

This book embarks on an in-depth exploration of Problem-Based Learning (PBL) in the context of engineering education. Its overarching goal is to provide a comprehensive understanding of the genesis, potential, challenges, contemporary relevance and methodological approaches of PBL. The impetus behind this undertaking arises from the acknowledged challenges within engineering education, necessitating a fundamental paradigm shift. The study's justification lies in the imperative adoption of innovative teaching methodologies for student performance improvement and fostering competency among engineering graduates.The narrative unfolds across four distinct sections: Background and Theoretical Perspectives, Methodological Aspects of PBL, Implications of PBL in Engineering Education and Case Studies, Plausible Examples and Reflections and Future Direction.Section one establishes a robust foundation by defining PBL, tracing its historical roots, and weighing its potential against challenges. A critical examination of PBL's relevance underscores the urgent need for a paradigm shift in engineering education. The section weaves a "golden thread" that permeates subsequent explorations. A theoretical perspective of PBL follows, exploring its underpinnings and theoretical frameworks. This is complemented by a comparative analysis, offering insights into PBL's efficacy compared to traditional learning methods.The second section examines the alignment of PBL with Outcomes-Based Education and lays the groundwork for a coherent and practical integration of these educational approaches within the Engineering curriculum, and also offers methodological approaches to deliver and practice PBL.The third section explores PBL's application for reinforcing engineering education, emphasising its tangible impact. It probes into PBL as a means to instil entrepreneurial attributes in students and further expands to encompass the decolonisation and internationalisation of engineering education through PBL.The final section provides case studies, offer plausible examples, reflect on the lessons learned and draw insightful conclusions, synthesising the findings into a cohesive whole.Overall, this book seeks to make a substantial contribution to the ongoing discourse on innovative teaching methodologies, particularly within the context of engineering education. Through a meticulous examination of theoretical foundations, comparative analyses, and the provision of practical methodologies, it aims to serve as a valuable resource for educators, researchers, and policymakers who seek to enhance the effectiveness and relevance of engineering education in our ever-evolving world.

Foundations of Mathematical Modeling and Analysis in Engineering

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