Extreme-Scale Computing
Scientific computing is essential for tackling complex problems across many domains--but how can scientists develop high-performance and high-quality software that scales efficiently? This book serves as an accessible introduction to extreme-scale computing, specifically designed for domain scientists who may not have formal computer science training but need to harness the power of C++ and parallel computing for large-scale applications. The book begins by covering the fundamentals of scientific computing software management, including essential tools like Linux, Git, and CMake, before diving into a detailed exploration of C++ for extreme-scale computing. Readers familiar with languages like Python will gain the necessary skills to transition to C++ and build scalable, efficient software. Beyond basic programming, this book delves into hardware-aware computing, teaching readers how to optimize software performance by understanding the underlying architecture of modern computational systems. It then introduces parallel computing techniques, covering MPI for distributed memory parallelism, shared memory parallelism, CUDA for GPU programming, and Kokkos for performance portability. Further chapters focus on efficient I/O, debugging, and profiling, which all address aspects of the critical challenge of performance optimization in extreme-scale computing. The book concludes with an overview of popular libraries for extreme-scale computing, equipping readers with the tools they need to solve real-world computational problems. With a balance of theory, practical applications, and illustrative case studies, this book provides domain scientists with a comprehensive roadmap to mastering extreme-scale computing and developing highly parallel and performant software.
Exact Methods for Nonlinear Pdes
Exact Methods for Nonlinear PDEs describes effective analytical methods for finding exact solutions to nonlinear differential equations of mathematical physics and other partial differential equations and also demonstrates the practical applications of these methods. It covers the methods of generalized separation of variables, methods of functional separation of variables, the classical method of symmetry reductions, the direct method of symmetry reductions, the method of weak symmetry reductions, and the method of differential constraints. The book presents several simple methods for finding exact solutions to nonlinear partial differential equations (PDEs). These methods do not require specialized knowledge and aim to minimize intermediate calculations. For the first time, it discusses the application of nonrigorous, intuitive reasoning in deriving exact solutions to nonlinear PDEs.Each section provides numerous examples, problems, and exercises to help readers develop practical skills in applying the methods. The material is illustrated with equations of mass and heat transfer, hydrodynamics, wave theory, nonlinear optics, and other nonlinear equations of mathematical physics. The key points that distinguish this book from others in the field include: - it presents many methods in a simpler and more visual format; - it describes a number of simple methods for constructing exact solutions to nonlinear PDEs and delay PDEs;- it emphasizes and details the practical use of non-rigorous reasoning to derive exact solutions for nonlinear PDEs. The book is intended for a diverse audience, including researchers, university professors, engineers, postgraduates, and students specializing in applied mathematics, theoretical physics, and engineering sciences.
Asclepius of Tralles
This is a print on demand edition of an important, hard-to-find publication.
Elements of Geometry and Trigonometry From the Works of A. M. Legendre
Mathematical Programming Model for Fighter Training Squadron Pilot Scheduling
An Investigation of the Effects of Correlation, Autocorrelation, and Sample Size in Classifier Fusion
Updating Optimal Decisions Using Game Theory and Exploring Risk Behavior Through Response Surface Methodology
The Application of Category Theory and Analysis of Receiver Operating Characteristics to Information Fusion
A Group Theoretic Tabu Search Methodology for Solving the Theater Distribution Vehicle Routing and Scheduling Problem
The Application of Category Theory and Analysis of Receiver Operating Characteristics to Information Fusion
Updating Optimal Decisions Using Game Theory and Exploring Risk Behavior Through Response Surface Methodology
A Group Theoretic Tabu Search Methodology for Solving the Theater Distribution Vehicle Routing and Scheduling Problem
An Investigation of the Effects of Correlation, Autocorrelation, and Sample Size in Classifier Fusion
Traveling Salesman Problem for Surveillance Mission Using Particle Swarm Optimization
Error Functions - Approximations and Implementations with modern FORTRAN. Volume I
Number Systems
Number Systems: A Path into Rigorous Mathematics aims to introduce number systems to an undergraduate audience in a way that emphasises the importance of rigour, and with a focus on providing detailed but accessible explanations of theorems and their proofs.The book continually seeks to build upon students' intuitive ideas of how numbers and arithmetic work, and to guide them towards the means to embed this natural understanding into a more structured framework of understanding. The author's motivation for writing this book is that most previous texts, which have complete coverage of the subject, have not provided the level of explanation needed for first-year students. On the other hand, those that do give good explanations tend to focus broadly on Foundations or Analysis and provide incomplete coverage of Number Systems.Features- Approachable for first year undergraduates, but still of interest to more advanced students and postgraduates- Does not merely present definitions, theorems and proofs, but also motivates them in terms of intuitive knowledge and discusses methods of proof- Draws attention to connections with other areas of mathematics- Plenty of exercises for students, both straightforward problems and more in-depth investigations- Introduces many concepts that are required in more advanced topics in mathematicsNew to the second edition- Complete solutions to all exercises, and hints for the in-depth investigations- Extensive changes to chapters 4 and 5, including defining integral domains as distinct from commutative rings, a more complete discussion of irreducibles, primes and unique factorisation, and more topics in elementary number theory- A completely revised chapter 8, giving a more coherent account of quadratic rings and their unique (or non-unique) factorisation properties- A thorough correction of typos and errors across all chapters- Updates to the bibliography
Models Demystified
In this comprehensive guide, we delve into the world of data science, machine learning, and AI modeling, providing readers with a robust foundation and practical skills to tackle real-world problems. From basic modeling techniques to advanced machine learning algorithms, this book covers a wide range of topics, ensuring that readers at all levels can benefit from its content. Each chapter is meticulously crafted to offer clear explanations, hands-on examples, and code snippets in both Python and R, making complex concepts accessible and actionable. Additional focus is placed on model interpretation and estimation, common data issues, modeling pitfalls to avoid, and best practices for modeling in general.
Number Systems
Number Systems: A Path into Rigorous Mathematics aims to introduce number systems to an undergraduate audience in a way that emphasises the importance of rigour, and with a focus on providing detailed but accessible explanations of theorems and their proofs.The book continually seeks to build upon students' intuitive ideas of how numbers and arithmetic work, and to guide them towards the means to embed this natural understanding into a more structured framework of understanding. The author's motivation for writing this book is that most previous texts, which have complete coverage of the subject, have not provided the level of explanation needed for first-year students. On the other hand, those that do give good explanations tend to focus broadly on Foundations or Analysis and provide incomplete coverage of Number Systems.Features- Approachable for first year undergraduates, but still of interest to more advanced students and postgraduates- Does not merely present definitions, theorems and proofs, but also motivates them in terms of intuitive knowledge and discusses methods of proof- Draws attention to connections with other areas of mathematics- Plenty of exercises for students, both straightforward problems and more in-depth investigations- Introduces many concepts that are required in more advanced topics in mathematicsNew to the second edition- Complete solutions to all exercises, and hints for the in-depth investigations- Extensive changes to chapters 4 and 5, including defining integral domains as distinct from commutative rings, a more complete discussion of irreducibles, primes and unique factorisation, and more topics in elementary number theory- A completely revised chapter 8, giving a more coherent account of quadratic rings and their unique (or non-unique) factorisation properties- A thorough correction of typos and errors across all chapters- Updates to the bibliography
Advanced Engineering Mathematics with Matlab(r)
In the five previous editions of Advanced Engineering Mathematics with MATLAB(R), the author presented a text firmly grounded in mathematics that engineers and scientists must understand and know how to use. Tapping into decades of teaching at the US Navy Academy and the US Military Academy and serving for twenty-five years at (NASA) Goddard Space Flight, he combines teaching and practical experience that is rare among authors of advanced engineering mathematics books.This edition continues to refine a smaller, easier to read, and useful version of this classic textbook. While competing textbooks continue to grow, the book presents a slimmer, more practical option to align with the expectations of today's students.The new edition of the author's classic textbook continues on a path to creating the best possible learning resource for instructors and students alike. Through extensive class testing over five previous editions, including the author's current course at the US Naval Academy, the book has been steadily improved.The primary mission of this edition is to dramatically increase the quality and quantity of examples and problems, especially in the chapters on differential equations and Laplace transforms. The chapters on differential equations, linear algebra, Fourier series, and Laplace transforms have seen the greatest changes. Of course, this edition continues to offer a wealth of examples and applications from scientific and engineering literature, a highlight of previous editions.MATLAB(R) remains central to the presentation and is employed to reinforce the concepts that are taught. Worked solutions are given in the back of the book. An Instructor's Solutions Manual is also available.
The Fundamentals of Fractional Calculus
Fractional calculus is one of the most important divisions of theoretical and applied mathematics. This new book presents a wide variety of interesting technologies and practices used in fractional calculus, providing detailed insight into recent developments and the latest research in the field of science, engineering, etc., using fractional calculus.The result of the teaching experiences of the editors and authors to engineering and science students, the volume discusses fractional calculus via generalized functions and integral transforms of pathway type; Laplace transformation of fractional integrals and derivatives; estimating the order of derivation in a fractional differential equation; a new class of integro-differential equations with non-singular differential operators; various uses of the Caputo approach; a gingerbread-man discrete system; etc. The various applications of fractional calculus are shown with examples such as for creating and/or solving epidemic models, alcoholism models, model for divorce dynamics, and more.Giving a rigorous and thorough analysis of various aspects of fractional calculus, this volume helps scientific readers as well as researchers working in the area of fractional calculus to establish the key steps followed in the research methodology and concept development.
Statistical Methods and Applications in Systems Assurance and Quality
In the era of big data and real-time monitoring, vast amounts of information are generated every second through sensors and advanced tracking systems. The information contained in the data needs to be carefully analyzed and accurate results must be delivered to the users as soon as possible. This book explores the critical role of statistics in modern technologies and applied sciences such as health, informatics, and production systems.Statistical Methods and Applications in Systems Assurance and Quality provides a comprehensive overview of statistical methods for ensuring system quality and reliability. It discusses best practices for improving the quality of manufacturing products by using proper statistical methods. The book covers the current state of statistical methods used for system quality and conveys the importance of healthcare systems and employing statistics in the detection of epidemic outbreaks.Designed for researchers, industry professionals, and academics, this reference is ideal for those working in manufacturing, healthcare, computer engineering, statistical process control, and machine learning applications. It serves as a valuable resource for anyone seeking to enhance system performance through data-driven insights.
A Study Of Matrices, Elementary Divisors, And The Classification Of Collineations
The Perpetual Time Calculator, For Ascertaining The Number Of Days From Any Given Day To Any Other Within The Year
