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Elsevier

Books in Mathematics

The Mathematics collection presents a range of foundational and advanced research content across applied and discrete mathematics, including fields such as Computational Mathematics; Differential Equations; Linear Algebra; Modelling & Simulation; Numerical Analysis; Probability & Statistics.

  • Artificial Intelligence Modeling for Dynamical Problems

    • 1st Edition
    • Snehashish Chakraverty + 2 more
    • English
    Artificial Intelligence Modeling for Dynamical Problems provides a comprehensive exploration of AI-driven methodologies tailored to address the intricate challenges posed by dynamical systems. The chapters in this book delve into cutting-edge techniques, including scientific machine learning, operator learning, fuzzy logic, and optimization algorithms, highlighting their applications in structural dynamics, fluid dynamics, robotics, and wave dynamics. Readers will gain insights into innovative state-of-the-art approaches such as Physics-Informed Neural Networks (PINNs) for precise navigation and control in autonomous vehicles, convolutional neural networks (CNNs) for frequency dynamics recognition, and data-driven models for market sentiment analysis. Additionally, the book explores the role of uncertainty modeling, statistical inference, and hybrid AI techniques, such as Type-2 fuzzy fractional modeling, in advancing the field of dynamical system analysis. Each chapter combines foundational principles with practical applications, including recent investigations, making it a valuable resource for researchers, practitioners, students of STEM seeking to apply theoretical AI models to real-world dynamical problems.

  • Ensuring AI-enabled Zero Trust Security for Smart City and Healthcare Applications Part A

    • 1st Edition
    • Volume 146
    • English
    Ensuring AI-enabled Zero Trust Security for Smart City and Healthcare Applications Part A, published as Volume 146 of the serial Advances in Computers, provides a comprehensive examination of the convergence of artificial intelligence, Zero Trust security frameworks, smart city infrastructures, and healthcare technologies. The volume explores how AI-driven security architectures can safeguard increasingly interconnected urban and healthcare ecosystems, addressing challenges associated with IoT networks, autonomous vehicles, wearable devices, telemedicine platforms, medical imaging systems, and healthcare data interoperability. It highlights emerging approaches that integrate AI, blockchain, edge computing, digital twins, federated learning, threat intelligence, and quantum computing to strengthen cyber resilience, privacy protection, and trust management across critical applications. By combining foundational concepts with practical implementations and future-oriented perspectives, this volume serves as an authoritative resource for researchers, cybersecurity professionals, healthcare technologists, and smart city stakeholders seeking to develop secure, adaptive, and resilient digital environments.

  • Doing Bayesian Data Analysis

    A Tutorial With R, Stan, brms, and the tidyverse
    • 3rd Edition
    • John K. Kruschke + 1 more
    • English
    Doing Bayesian Data Analysis: A Tutorial with R, Stan, brms, and the tidyverse, Third Edition, provides a carefully scaffolded tutorial from beginning concepts to advanced, realistic data analyses. The book uses a proven sequence of topics unique to Doing Bayesian Data Analysis. The first part covers foundational concepts of statistical models, probability, Bayesian reasoning, and computer programming in R and the tidyverse. The second part introduces all the concepts and methods of Bayesian data analysis, including the Stan modeling language, by using the simplest possible data structures and statistical models. The third part covers the generalized linear model, including multilevel (a.k.a. hierarchical) versions of regression and analysis of variance, for a variety of data types (metric, ordinal, nominal, dichotomous, count), using the convenient computer package called brms. Every concept and case is illustrated with detailed examples, and all computer code is available at the book’s website. This book is intended for self-learners or classroom learning, for first-year graduate students, advanced undergraduates, and professionals. The methods apply to any field, including social sciences, biological sciences, and physical sciences, for any setting, including academia, government, business, and industry.

  • Theory of Probability and Statistics

    Solved Problems and Exercises
    • 1st Edition
    • Humbat Aliyev + 2 more
    • English
    Theory of Probability and Statistics: Solved Problems and Exercises is a comprehensive and practice-oriented textbook designed for undergraduate and graduate students seeking a clear, rigorous, and intuitive understanding of probability and statistical inference. Unlike many existing titles that either lean too heavily on theory or focus mostly on computations, this book bridges the gap by integrating conceptual foundations with problem-solving techniques and real-world applications. Each chapter progresses from essential theory to fully-worked examples, followed by a rich set of exercises that reinforce learning and promote mastery.Theory of Probability and Statistics: Solved Problems and Exercises offers significant benefits to its readers: streamlined explanations of fundamental concepts, step-by-step derivations, visual interpretations where helpful, and numerous solved problems that demonstrate how abstract principles translate into practical statistical tools. Topics span classical probability, random variables, distributions, limit theorems, estimation, hypothesis testing, regression, non-parametric methods, and modern extensions relevant to data science. This book provides a fresh, accessible approach that maintains mathematical rigor while remaining student-friendly, making it ideal for university courses, self-study, and exam preparation. By blending theory with extensive solved exercises, it fills a growing demand for a unified, application-driven text tailored to contemporary learners.

  • Discrete Choices

    A Comprehensive Guide to Distributions and Inference for Categorical Data
    • 1st Edition
    • Jiju Gillariose + 2 more
    • English
    Discrete Choices: A Comprehensive Guide to Distributions and Inference for Categorical Data provides a unified and modern treatment of probability, inference, and modeling for categorical and discrete data. Although categorical outcomes are ubiquitous across statistics, data science, economics, epidemiology, and the social sciences, existing resources often treat these topics in fragmented ways, separating probability theory, inference, diagnostics, and applications into distinct texts. This book addresses that gap by presenting a coherent framework that begins with probability foundations and sampling theory, develops classical and hierarchical discrete distributions, and advances to modern likelihood-based and Bayesian inference. Core topics include Bernoulli, Binomial, Multinomial, and Poisson models; compound distributions such as the Beta–Binomial and Dirichlet–Multinomia... resampling methods; model diagnostics; and principled model selection. Advanced chapters extend this framework to high-dimensional categorical data, compositional data, network and relational structures, causal inference with multi-valued treatments, and fairness and bias diagnostics in categorical prediction. Extensive case studies and interactive hands-on data labs illustrate real-world applications in health, the social sciences, marketing, and text analytics, emphasizing reproducible and applied workflows.Balancing theoretical rigor with practical relevance, Discrete Choices: A Comprehensive Guide to Distributions and Inference for Categorical Data is suitable both as a graduate-level textbook and as a professional reference for researchers and practitioners working with discrete data.

  • Physiology, Medicine, and Health Sciences

    Catalyzed by Biomedical Engineering Modeling
    • 1st Edition
    • Dhanjoo N. Ghista + 1 more
    • English
    Physiology, Medicine, and Health Sciences: Catalyzed by Biomedical Engineering Modeling is a quantitative handbook for mathematical and quantitative analysis of anatomical structures, physiological and organ systems, medical tests and surgical procedures. This book’s purpose is to demonstrate how fundamental mathematical modeling can be incorporated into physiology, medicine, and health sciences research, application, and clinical practice to make these disciplines more quantitative and computational, and hence more explanatory and informative. The book also provides quantitative formulation of medical procedures, towards supporting the growing field of precision medicine. Each chapter includes a robust introduction to the BME and mathematical concepts necessary to understand their application to the indicated medical and biological systems, beginning with Intrinsic Anatomy, showing how anatomical structures are intrinsically optimally designed for their functional performance, such as the intrinsic hyperboloid shape of the spinal vertebral body (as a lightweight, high-strength structure), and the ellipsoidal shape of the left ventricle that enables it to contract efficiently. Other BME and modelling concepts covered include: Physiological Engineering, in quantifying physiological systems and developing indices for assessing their function and dysfunction leading to medical diagnostics; Precision Medicine, by developing biomedical engineering formulation of medical diagnostic and assessment methods and indices, including the new concept of non-dimensional indices in medical assessment, such as cardiac contractility index for risk of heart failure and diabetes index for accurate diagnosis of diabetes; and, Computational Surgery, involving surgical design of prosthetic devices based on the intrinsic design of the fractured structure, such as the design of the spinal vertebral body cage for fractured vertebral body to preserve its intrinsic hyperboloid shape. Each chapter provides in-depth guidance on the engineering and mathematical concepts, methodology, and procedures for applying the formulas and equations to the appropriate biomedical and physiological systems, as well as step-by-step procedures for creating models for a wealth of specific applications.

  • Quantum Computing for Internet of Things

    • 1st Edition
    • Volume 145
    • English
    Quantum Computing for Internet of Things, published as Volume 147 of the serial Advances in Computers, provides a comprehensive examination of the convergence of quantum computing and the Internet of Things (IoT). The volume introduces the fundamental principles of quantum computing, including qubits and quantum mechanics, and explores the architectures, enabling technologies, and intelligent applications that underpin modern IoT ecosystems. It highlights how quantum technologies can enhance IoT performance, security, optimisation, and data processing capabilities across diverse application domains.The volume presents emerging advances in quantum-enabled IoT systems, including distributed quantum computing frameworks, quantum machine learning approaches, quantum simulation tools, and novel optimisation techniques tailored to IoT environments. Case studies and application-focused chapters demonstrate the use of quantum methods in military systems, climate change analysis, and healthcare analytics. The volume concludes by addressing key research challenges, implementation barriers, and future directions, making it a valuable resource for researchers and practitioners working at the intersection of quantum technologies and connected intelligent systems.

  • Mathematical Foundations of Physiology, Medicine, and Health Sciences

    • 1st Edition
    • Dhanjoo N. Ghista + 3 more
    • English
    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.

  • Digital Signal Processing with MATLAB®

    From Fundamentals to AI Applications
    • 1st Edition
    • Samir I. Abood + 1 more
    • English
    Digital Signal Processing with MATLAB®: From Fundamentals to AI Applications provides coverage of discrete-time signals and systems, and lays out the mathematical fundamentals of digital signal processing (DSP) systems. The book contains a solution to large-scale signal processing problems, namely the development of methods and algorithms that increase (a) operational efficiency under different uncertainty conditions and (b) system stability rate. It offers an algebraic approach to digital signal processing, including algorithms related to digital systems, the setting of parameters, plus operational estimation, detection, classification, resolution, and reliability. Digital Signal Processing with MATLAB®: From Fundamentals to AI Applications begins with a thorough explanation of MATLAB® in recognition of the Accreditation Board for Engineering and Technology (ABET) requirements for integrating computer tools into DSP. The principles of DSP are presented using a step-by-step approach; each chapter starts with an introduction that states the chapter objectives, and ends with a discussion of practical applications of DSP, including providing problems that help the reader understand how the concepts are used in real-life situations. Sometimes, problems are solved in two or three ways to facilitate a deeper understanding and comparison of different approaches. Digital Signal Processing with MATLAB®: From Fundamentals to AI Applications teaches the fundamental principles of digital signal processing, and explains how MATLAB® can be used in the development of methods and algorithms for DSP.

  • Advances in Machine Learning for Engineering Applications and Sustainable Development

    • 1st Edition
    • Volume 145
    • English
    Advances in Machine Learning for Engineering Applications and Sustainable Development, published as Volume 145 of the serial Advances in Computers, provides a comprehensive and timely exploration of how artificial intelligence (AI) and machine learning (ML) are transforming engineering practice and advancing sustainability goals. The volume brings together contributions from leading researchers to examine the integration of data-driven methods in concrete technology, digital fabrication, structural health monitoring, materials engineering, and industrial process optimisation. It highlights emerging paradigms such as AI-driven 3D printing, predictive analytics for failure detection, lifecycle and environmental impact assessment, and circular economy strategies.Spanning foundational methods and real-world implementations, the volume emphasises sustainable materials, eco-efficient construction processes, and intelligent system design. It pays particular attention to the use of ML in improving resource efficiency, enabling recycling of industrial by-products, and enhancing the performance of green materials such as biochar-based composites. By combining theoretical insights, mathematical modelling, and application-oriented case studies, this volume serves as a critical reference for advancing resilient, efficient, and environmentally responsible engineering systems.

  • Handbook of MRI Pulse Sequences

    • 2nd Edition
    • Xiaohong Joe Zhou + 4 more
    • English
    Handbook of MRI Pulse Sequences, Second Edition includes 92 self-contained sections, with each section focusing on a single subject. A new section on detailing the advanced pulse sequence techniques covers a variety of basic and advanced image reconstruction methods. The extensive topic coverage and cross-referencing makes this book ideal for beginners learning the building blocks of MRI pulse sequence design, as well as for experienced professionals who are seeking deeper knowledge of a particular technique.This book is among the most important medical imaging techniques available today. Each of these scanners is capable of running many different "pulse sequences." These sequences are governed by physics and engineering principles and implemented by software programs that control the MRI hardware.

  • Essential Statistics, Regression, and Econometrics

    • 3rd Edition
    • Gary Smith
    • English
    Essential Statistics, Regression, and Econometrics, Third Edition will helps students in introductory statistics courses develop statistical reasoning and critical thinking skills. The book demonstrates the power, elegance, and beauty of statistical reasoning, providing hundreds of new and updated examples and discussing the uses and potential abuses of statistics. Examples are drawn from real, contemporary areas to showcase that statistical reasoning is not an irrelevant abstraction, but instead an important part of everyday life. This updated resource highlights recent, exciting discoveries and provides a thorough foundation for students, instructors, and researchers alike, all of which are approaching the field from different backgrounds.Innovati... in its extended emphasis on statistical reasoning, real data, pitfalls in statistical analysis, the perils of p-hacking and data mining, and modeling issues, including functional forms and causality, the book includes extensive word problems that emphasize intuition, understanding, and practical applications.

  • An Introduction to Applied Sport Analytics

    • 1st Edition
    • Jon Nachtigal + 1 more
    • English
    An Introduction to Applied Sport Analytics offers a step-by-step path for applying data-driven methods in sports. The book begins with the evolution of sport analytics and foundational concepts like the Pythagorean theorem, correlation, and regression, then moves into hands-on instruction with industry tools such as Excel, SQL, R, Python, and Power BI. Readers learn how to explore data, evaluate performance, and make informed decisions across team operations, player valuation, and sport business strategy. The book features real-world examples, chapter exercises, and review questions and a dedicated section on data visualization walks readers through designing reports and dashboards using Power BI and Tableau.The book also introduces the growing role of artificial intelligence in sport, showing how tools like machine learning and coding assistants can enhance analysis. A robust ancillary program also provides support to students with additional practice opportunities. With its practical focus and clear structure, this book is ideal for undergraduate and graduate courses in sport management, analytics, and business, as well as for professionals seeking to build essential skills in a data-driven sport industry.

  • Mathematical Statistics with Applications in R

    • 4th Edition
    • Kandethody M. Ramachandran + 1 more
    • English
    Mathematical Statistics with Applications in R, Fourth Edition offers a modern calculus-based theoretical introduction to mathematical statistics and applications that spans numerous foundational and essential concepts in the field. The book covers many modern statistical computational and simulation concepts, including Exploratory Data Analysis, the Jackknife, bootstrap methods, the EM algorithms, and Markov chain Monte Carlo (MCMC) methods such as the Metropolis algorithm, Metropolis-Hastings algorithm and the Gibbs sampler. The final chapter of the book provides a step-by-step approach to modelling, analysis, and interpretation data from real-world applications, from the environment and cyber security to health and finance.By combining discussion on the theory of statistics with a wealth of engaging, real-world applications, this book helps students approach statistical problem-solving in a logical manner with accessible, step-by-step procedures on relatable topics. Computational aspects are covered through R and SAS examples.

  • Mathematical Modeling

    Process and Presentation
    • 1st Edition
    • Eric Marland + 3 more
    • English
    Mathematical Modeling: Process and Presentation offers a comprehensive introduction to the art of mathematical modeling, engaging students through thought-provoking questions and interactive content. Each chapter presents a different canonical modeling type, guiding readers through the essential components of the modeling process, from problem posing and assumptions to reflection and purpose definition. With relatable examples, such as estimating efforts in balloon filling or developing metrics for college roommate matching, students are encouraged to explore and expand on the models presented. This text stands out by revisiting the modeling process throughout, rather than focusing solely on examples, fostering a deeper understanding of the methodology. Accessible to a broad audience, it invites readers to apply their mathematical tools at varying levels of sophistication, ensuring that the focus remains on the core process, which remains relevant as their knowledge grows. Mathematical Modeling: Process and Presentation is an invaluable resource for undergraduate students and early graduate-level mathematics learners seeking to enhance their modeling skills and engage with real-world applications.

  • Machine Learning Solutions for Inverse Problems: Part B

    • 1st Edition
    • Volume 27
    • English
    Machine Learning Solutions for Inverse Problems: Part B, Volume 27 in the Handbook of Numerical Analysis, continues the exploration of emerging approaches at the intersection of machine learning and inverse problem theory. This volume presents a collection of chapters addressing a wide range of contemporary topics, including deep image prior methods for computed tomography, data-consistent learning strategies, and unified frameworks for training and inversion in machine learning-based reconstruction methods. Additional chapters examine learned regularization techniques, generative models for inverse problems, and the integration of deep learning with traditional computational frameworks such as full waveform inversion and PDE-based inverse modeling.The volume also discusses advances in self-supervised learning, data selection strategies, plug-and-play denoising methods, and diffusion models for solving imaging inverse problems. Further contributions explore neural network representations, operator learning, and learned iterative schemes, along with theoretical perspectives on stability, approximation hardness, hallucinations, and trustworthiness in AI-driven inverse problem methodologies.

  • Neural Networks

    • 1st Edition
    • Volume 55
    • English
    Neural Networks, Volume 55 delves into the world of deep learning machines, defining neural networks and covering their central role in the development of modern language models, machine‑learning‑bas... decision‑making systems, and many other advances in artificial intelligence. Chapters in this new release include Neural networks with random weights, Bayesian Neural Networks for Official Statistics: Modeling High-Dimensional Structure in Complex Surveys and Administrative Records, Weakly supervised learning for neural networks, How to test a neural network as a null hypothesis, Test-Time Adaptation with Neural Networks: Approaches and Advances in Image Classification, and much more.Additional sections cover Semantics and Verification of Neural Network Components in Robotic Control Software, Artificial Neural Network Procedures for the Nonlinear Dynamical Plankton System, Neural Networks from Statistical Perspective, Neural Network applications in Assistive and Collaborative Robotics, Neural Network applications in Assistive and Collaborative Robotics, and Neural Networks using SPDEs.

  • Graph Theory

    Fundamentals and Applications
    • 1st Edition
    • Sovan Samanta + 1 more
    • English
    Graph theory is a rapidly evolving and expanding mathematical discipline, with new discoveries, challenges, and techniques emerging every year. Graph Theory: Fundamentals and Applications provides a fully up-to-date and accessible introduction to graph theory, covering both the classical and the modern topics, as well as algorithms and evolving challenges addressed by discipline. Based on the latest syllabi and research trends worldwide, this book includes practical, solved problems that are user friendly to undergraduate, postgraduate, and PhD students, and acts as a key aid in learning the fundamentals and the frontiers of graph theory, as well as developing independent problem-solving and critical thinking skills. This book includes clear instruction in graph representation, basic graph operations, graph connectivity, trees and forests, matching theory, planar graphs and graph drawing, algebraic graph theory, graph traversals, network flows, topological graph theory, and cryptography, among other topics. Each chapter features key term definitions, proofs and algorithms, summary points, and unique exercises to reinforce learning, as well as open problems and research challenges that present unsolved or conjectural problems in graph theory for discussion. Supporting student and instructor sites offer additional exercises, solutions, examples, and case studies in graph theory applications.

  • Introductory Statistics

    • 5th Edition
    • Sheldon M. Ross
    • English
    Introductory Statistics, Fifth Edition, reviews statistical concepts and techniques in a way that teaches students not only how and when to utilize the statistical procedures developed, but also how to understand why these procedures should be used. The text's main merits are the clarity of presentation, contemporary examples, applications from diverse areas, an explanation of intuition, and the ideas behind the statistical methods. Concepts are motivated, illustrated, and explained in a way that attempts to increase intuition. Applications and examples refer to real-world issues, such as gun control, stock price models, vaccines and other health issues, driving age limits, and many others.To quote from the preface, it is only when a student develops a feel or intuition for statistics that they are really on the path toward making sense of data. Ross achieves this goal through a coherent mix of mathematical analysis, intuitive discussions, and examples.

  • Multidimensional Signal Processing

    • 1st Edition
    • Volume 54
    • English
    Multidimensional Signal Processing, Volume 54 in the Handbook of Statistics series is dedicated to presenting the latest developments and methodologies in multidimensional signal processing. The book aims to provide a comprehensive overview of the theories, models, and methods that form the foundation of this field. Chapters in this new release include Robust Parameter Estimation of Two Dimensional Chirp Model, Computability Theory for Multidimensional Signal Processing, Tensor signal processing, Spectral compressed sensing by structured matrix optimization methods, Space-time imaging, Hypercomplex Widely Linear Processing, and much more. The book's chapters are meticulously curated to offer detailed, educational content rather than conventional journal-style articles.Other chapters cover Hypercomplex phase retrieval, Hypercomplex widely linear estimation, MIMO radar signal processing, Computational lidar, Signal processing applications of higher-dimensional graphs, Space-Time Radio Signal Processing by Photonic Upconversion, Computational imaging, and Topology identification and learning over graphs using multi-dimensional data.

  • Functional Analysis

    Theory and Applications
    • 1st Edition
    • Anita Tomar + 2 more
    • English
    An applied understanding of functional analysis is essential for students pursuing research or careers in pure mathematics, applied mathematics, mathematical physics, and engineering, among other disciplines.Function... Analysis: Theory and Applications offers a comprehensive exploration of functional analysis. Authored by esteemed mathematicians with extensive expertise in the field, this book thoroughly introduces fundamental concepts in functional analysis, including Banach spaces, Hilbert spaces, operator theory, nonlinear analysis, linear operators, and normed spaces, and implements these in real-world problems across various scientific and engineering disciplines.The book's rigorous mathematical treatment is combined with worked examples, exercises and solutions, visual aids, application case studies, and future directions across all chapters to reinforce learning, while appendices offer supplementary materials, proofs of theorems, and tables of important results, among other resources.

  • Lebesgue Measure and Integration Theory

    Foundations and Solved Exercises
    • 1st Edition
    • Alberto Cabada + 1 more
    • English
    Lebesgue Measure and Integration Theory: Foundations and Solved Exercises offers a thorough, engaging introduction to Lebesgue measure and the theory of integration for students of mathematics and physics. This book provides the complete theoretical underpinnings of this theory, with the corresponding proofs, adapted to the level of advanced undergraduate and graduate students in these disciplines. Beginning with a fundamental discussion of measure spaces, the book moves onto measurable and non-measurable sets, approximation of measurable sets, measurable functions, the Lebesgue integral, the relationship between differentiation and integration on R, and product measures, among other topics. Examples and solved exercises are included across chapters to reinforce understanding and application.

  • Introduction to Fuzzy Mathematics

    With Applications to Global Problems
    • 1st Edition
    • John Mordeson + 2 more
    • English
    Delve into the intricate landscape of fuzzy mathematics, where the boundaries of traditional mathematical disciplines— analysis, abstract algebra, geometry, topology, and graph theory—are blurred to address pressing global issues. Through a rigorous examination of fuzzy sets and similarity measures, An Introduction to Fuzzy Mathematics: With Applications to Global Problems lays the groundwork for innovative solutions to complex problems, from medical diagnostics to sustainability, refugee crises, and the fight against human trafficking. Meanwhile, research projects and exercises integrated across chapters reinforce learning and apply fuzzy mathematics to real-world scenarios. Chapters are meticulously organized to guide readers through foundational concepts, including fuzzy sets, evidence theory, and implication operators, before advancing to applications in sustainability and climate change. Further, the book examines refugee dynamics and public health models, culminating in a thorough exploration of fuzzy algebraic structures, geometry, topology, and graph theory. This comprehensive resource not only enhances understanding of fuzzy mathematics but also equips readers—researchers, practitioners, and policymakers alike—with the tools to tackle critical global issues. By integrating mathematical rigor with real-life applications, the book serves as a vital reference for anyone seeking to navigate the complexities of our world through the lens of fuzzy mathematics.

  • Quantitative Biology

    Mathematical Modeling and Computation
    • 1st Edition
    • Alonso Ogueda-Oliva + 1 more
    • English
    Quantitative Biology provides quantitative and data-driven approaches for analyzing biological and bio-inspired systems, covering the foundations of mathematical modeling, analysis, and computation. The book presents a practical mix of both theory and computation for a variety of biological applications, with tied-in, engaging project activities, instruction, programming language, and technological tools. Modeling approaches combine mathematical foundations, statistical reasoning, and computational thinking, with applications in compartmental, agent-based, bio image, biological interaction, and neural network modeling, as well as machine learning, parameter identification, and applications across societal challenges.Each chapter includes exposure to models and modeling, a foundational instructional framework, benchmark applications, and numerical simulations with a literate programming guided style that helps readers go beyond replication models and into prediction and data-driven discovery. A companion website also features interactive code to accompany projects across each chapter.

  • Implementing R for Statistics

    • 1st Edition
    • Muhammad Imran + 3 more
    • English
    Implementing R for Statistics provides comprehensive coverage of basic statistical concepts using this important open-source programming language tool, from installing R and RStudio, to exploring its basic structure and uses, to extending some core functions such as vectors, basic mathematical operations, and data frames. The book will help readers understand the latest advances in the R programming language, as R allows for sophisticated and elegant data visualization. Illustrated examples are an integral part of the text, carefully designed to apply the core principles illustrated in the text to emerging topics in the field.The text also focuses on exploiting the flexible and user-friendly nature of R. Basic concepts and recent advances in the field, including understanding the R basics, as well as implementing and practicing them in statistics, are also covered. This first edition is an essential text for students, lecturers, data scientists, and applied researchers in all areas of statistics, as well as in related fields such as biostatistics, health care, finance, risk management, social sciences, market research, and environmental and climate research.

  • An Introduction to Writing Mathematical Proofs

    Shifting Gears from Calculus to Advanced Mathematics
    • 1st Edition
    • Thomas Bieske
    • English
    An Introduction to Writing Mathematical Proofs: Shifting Gears from Calculus to Advanced Mathematics addresses a critical gap in mathematics education, particularly for students transitioning from calculus to more advanced coursework. It provides a structured and supportive approach, guiding students through the intricacies of writing proofs while building a solid foundation in essential mathematical concepts. Sections introduce elementary proof methods, beginning with fundamental topics such as sets and mathematical logic, systematically develop the properties of real numbers and geometry from a proof-writing perspective, and delve into advanced proof methods, introducing quantifiers and techniques such as proof by induction, counterexamples, contraposition, and contradiction. Finally, the book applies these techniques to a variety of mathematical topics, including functions, equivalence relations, countability, and a variety of algebraic activities, allowing students to synthesize their learning in meaningful ways. It not only equips students with essential proof-writing skills but also fosters a deeper understanding of mathematical reasoning. Each chapter features clearly defined objectives, fully worked examples, and a diverse array of exercises designed to encourage exploration and independent learning. Supplemented by an Instructors' Resources guide hosted online, this text is an invaluable companion for undergraduate students eager to master the art of writing mathematical proofs.

  • Boundary Value Problems and Partial Differential Equations

    • 7th Edition
    • David L. Powers + 3 more
    • English
    For over fifty years, Boundary Value Problems and Partial Differential Equations, Seventh Edition has provided advanced students an accessible and practical introduction to deriving, solving, and interpreting explicit solutions involving partial differential equations with boundary and initial conditions. Fully revised and now in its Seventh Edition, this valued text aims to be comprehensive without affecting the accessibility and convenience of the original. The resource’s main tool is Fourier analysis, but the work covers other techniques, including Laplace transform, Fourier transform, numerical methods, characteristics, and separation of variables, as well, to provide well-rounded coverage. Mathematical modeling techniques are illustrated in derivations, which are widely used in engineering and science. In particular, this includes the modeling of heat distribution, a vibrating string or beam under various boundary conditions and constraints. New to this edition, the text also now uniquely discusses the beam equation. Throughout the text, examples and exercises have been included, pulled from the literature based on popular problems from engineering and science. These include some "outside-the-box" exercises at the end of each chapter, which provide challenging and thought-provoking practice that can also be used to promote classroom discussion. Chapters also include Projects, problems that synthesize or dig more deeply into the material that are slightly more involved than standard book exercises, and which are intended to support team solutions. Additional materials, exercises, animations, and more are also accessible to students via links and in-text QR codes to support practice and subject mastery.

  • Measure and Integration

    Concepts, Examples, and Applications
    • 1st Edition
    • Ahmed Ghatasheh + 2 more
    • English
    Measure and Integration: Examples, Concepts, and Applications instructs on core proofs, theorems, and approaches of real analysis as illustrated via compelling exercises and carefully crafted, practical examples. Following early chapters on core concepts and approaches of real analysis, the authors apply real analysis across integration on product spaces, radon functionals, bounded variation and lebesgue-stieltjes measures, convolutions, probability, and differential equations, among other topics. From chapter one onward, students are asked to apply concepts to reinforce understanding and gain applied experience in real analysis. In particular, exercises challenge students to use key proofs of major real analysis theorems to encourage independent thinking, problem-solving, and new areas of research powered by real analysis.

  • An Introduction to Point-Set Topology

    A Hybrid Texas Style Approach
    • 1st Edition
    • Shelby J. Kilmer
    • English
    An Introduction to Point-Set Topology is intended for use in a beginning topology course for undergraduates or as an elective course for graduate students. The book’s style can be thought of as a hybrid between the Texas style (Moore method) of teaching topology and the more traditional styles. In the Texas style the students are given the definitions and the statements of the theorems and then they present their proofs to the class. This type of participation builds students’ confidence and provides them with a deeper understanding of the subject that they will retain longer. This text offers some of the theorems with their proofs and leaves others for the students to prove and present. Those theorems chosen to have their proofs presented in the text keep the course moving forward under the instructors’ guidance and increase student comprehension. An Introduction to Point-Set Topology covers a broad range of topological concepts, including but not limited to, metric spaces, topological spaces, homeomorphisms, connected sets, compact sets, product spaces, Hausdorff spaces, sequences, limits, weak topologies, the axiom of choice, Zorn’s lemma, and Nets. Incorporating both historical references and color graphics, the material keeps readers engaged. The book’s goals include increasing student participation, thus promoting a deeper knowledge through an intuitive understanding of how and why topology was developed in the way that it was. This “instructor-friendly... accessible text is also accompanied by a detailed solutions manual to support both experienced topologists and other mathematicians who would like to teach topology.

  • Machine Learning Solutions for Inverse Problems: Part A

    • 1st Edition
    • Volume 26
    • English
    Machine Learning Solutions for Inverse Problems: Part A, Volume 26 in the Handbook of Numerical Analysis, highlights new advances in the field, with this new volume presenting interesting chapters on a variety of timely topics, including Data-Driven Approaches for Generalized Lasso Problems, Implicit Regularization of the Deep Inverse Prior via (Inertial) Gradient Flow, Generalized Hardness of Approximation, Hallucinations, and Trustworthiness in Machine Learning for Inverse Problems, Energy-Based Models for Inverse Imaging Problems, Regularization Theory of Stochastic Iterative Methods for Solving Inverse Problems, and more.Other sections cover Advances in Identifying Differential Equations from Noisy Data Observations, The Complete Electrode Model for Electrical Impedance Tomography: A Comparative Study of Deep Learning and Analytical Methods, Learned Iterative Schemes: Neural Network Architectures for Operator Learning, Jacobian-Free Backpropagation for Unfolded Schemes with Convergence Guarantees, and Operator Learning Meets Inverse Problems: A Probabilistic Perspective

  • An Introduction to Stochastic Modeling

    • 5th Edition
    • Gabriel Lord + 1 more
    • English
    An Introduction to Stochastic Modeling, Fifth Edition bridges the gap between basic probability and an intermediate level course in stochastic processes, serving as the foundation for either a one-semester or two-semester course in stochastic processes for students familiar with elementary probability theory and calculus. The objectives are to introduce students to the standard concepts and methods of stochastic modeling, to illustrate the rich diversity of applications of stochastic processes in the applied sciences, and to provide an integrated treatment of theory, applications and practical implementation. A well-regarded resource for many years, the text is an ideal foundation for a broad range of students.

  • Recent Developments in Theory and Applications of Fractional Order Systems

    • 1st Edition
    • Mehmet Yavuz + 2 more
    • English
    Recent Developments in Theory and Applications of Fractional Order Systems presents a rigorous and thorough analysis of various aspects of Fractional Calculus. The book provides readers with a thorough understanding of fundamental concepts and methods of applied mathematics utilized in a variety of scientific and engineering disciplines. The authors present each computational modeling concept with a definition, methods, theorems, and observations followed by typical application problems and step-by-step solutions. Each topic is covered in detail, followed typically by several meticulously worked out examples and a problem set containing many additional related problems.In addition, the book discusses recent developments and the latest research on Fractional Calculus and its applications, demonstrating important applications in Engineering, Computer Science, Management, Social Science, and the Humanities.

  • Statistics in Industry and Government

    • 1st Edition
    • Volume 53
    • English
    Statistics in Industry and Government covers industrial quality control and high-class quality maintenance in products. The book aims to cover as many applications that use statistics as an underlying tool in bringing the best quality products and industrial designs. Chapters in this new release include Analysis of Official Time Series with Ecce Signum, an R Package for Multivariate Signal Extraction and Forecasting, The Maturity Structure of Public Debt: A Granular Approach Using Indian Data, Harnessing the power of spherical intersection: A less arbitrary unsupervised learning method applied to pattern recognition within financial data, and much more.Other chapters in this release include The Use of Causal Inference with Structural Models in Industry, MSME Statistics in India, The Importance of Accurate, Timely, Credible Crime Data to Inform Crime and Justice Policy, Combining Information from Multiple Sources in Official Statistics, Active Learning of Computer Experiment with both Quantitative and Qualitative Inputs, On the use of machine learning methods for missing data problems, Optimal Experimental Planning for Experiments Based on Coherent Systems with Industrial Applications, and more.

  • Numerical Linear Algebra with Applications

    Using MATLAB and Octave
    • 2nd Edition
    • William Ford + 1 more
    • English
    Numerical Linear Algebra with Applications: Using MATLAB and Octave, Second Edition provides practical knowledge on modern computational techniques for the numerical solution of linear algebra problems. The book offers a unified presentation of computation, basic algorithm analysis, and numerical methods to compute solutions. Useful to readers regardless of background, the text begins with six introductory courses to provide background for those who haven’t taken applied or theoretical linear algebra. This approach offers a thorough explanation of the issues and methods for practical computing using MATLAB as the vehicle for computation.Appropri... for advanced undergraduate and early graduate courses on numerical linear algebra, this useful textbook explores numerous applications to engineering and science.

  • Stochastic Theory of Service Systems

    • 1st Edition
    • L. Kosten
    • I. N. Sneddon + 1 more
    • English
    International Series of Monographs in Pure and Applied Mathematics, Volume 103: Stochastic Theory of Service Systems focuses on the principles, methodologies, and approaches involved in the stochastic theory of service systems. The publication first examines the general description of service systems, characteristics of the arrival process, standard cases, and the distribution of waiting-times in the system M/M/c-delay. Discussions focus on "random" condition, probability of delay and average waiting-time for the system M/M/c-delay, Engset formula, and probability of blocking for the system M/M/c-blocking. The text then examines general holding-time assumption, non-stationary behavior, and priority. Topics include pre-emptive priority, transient behavior of the system M/G/1-delay, Markov process with a finite number of states, and hyperexponential distributions. The manuscript takes a look at simulation, arrival and service in batches, and restricted availability, including approximate determination of probabilities of blocking, "unscheduled ferry problem", principles of roulette simulation, and implementation of randomness. The publication is a dependable source material for researchers interested in the stochastic theory of service systems.

  • An Introduction to Discrete Mathematics

    • 1st Edition
    • Vidyadhar Kulkarni
    • English
    An Introduction to Discrete Mathematics offers an engaging and accessible introduction to discrete mathematics for beginning undergraduate students across a wide range of application areas, from mathematics to statistics, operations research, business, engineering, and the sciences. It provides solid foundation in precise proof writing methods, with early chapters introducing set theory and logic that are followed by deductive and inductive proof techniques, number theory, counting principles, permutations and combinations, probability of events, random variables, graphs, and weighted graphs.The book illustrates fundamental concepts in discrete mathematics with clear and precise definitions that are paired with examples and counter-examples as applied in combinatorics, discrete probability, and graph theory. Chapters include student exercises to enhance learning, and a solutions manual and example questions are available for instructors on a companion website.

  • Markov Chains: Theory and Applications

    • 1st Edition
    • Volume 52
    • English
    Markov Chains: Theory and Applications, Volume 52 in the Handbook of Statistics series, highlights new advances in the field, with this new volume presenting interesting chapters on topics such as Markov Chain Estimation, Approximation, and Aggregation for Average Reward Markov Decision Processes and Reinforcement Learning, Ladder processes: symmetric functions and semigroups, Continuous-time Markov Chains and Models: Study via Forward Kolmogorov System, Analysis of Data Following Finite-State Continuous-Time Markov Chains, Computational applications of poverty measurement through Markov model for income classes, and more.Other sections cover Estimation and calibration of continuous time Markov chains, Additive High-Order Markov Chains, The role of the random-product technique in the theory of Markov chains on a countable state space., On estimation problems based on type I Longla copulas, and Long time behavior of continuous time Markov chains.

  • Mathematical Modeling in Bioscience

    Theory and Applications
    • 1st Edition
    • Hemen Dutta
    • English
    Mathematical Modeling in Bioscience: Theory and Applications provides readers with tools and techniques for mathematical modeling in bioscience through a wide range of novel and intriguing topics. The book concentrates on larger elements of mathematical modeling in bioscience, including topics such as modeling of the Topp--Leone new power generalized Weibull-G distribution family, vector-borne disease modeling, transmission modeling of SARS-COV-2 among other infectious diseases, pattern formulation models, compartmental models for HIV/AIDS transmission, population models, irrigation scheduling models, and predator--prey models. The readers will discover a variety of new methods, approaches, and techniques, as well as a wide range of applications demonstrating key concepts in bioscience modeling. This book provides a leading-edge resource for researchers in a variety of scientific fields who are interested in mathematical modeling, including mathematics, statistics, biology, biomedical engineering, computer science, and applied sciences.

  • Generalized Quantum Calculus with Applications

    • 1st Edition
    • Svetlin G. Georgiev + 1 more
    • English
    Generalized Quantum Calculus with Applications is devoted to the qualitative theory of general quantum calculus and its applications to general quantum differential equations and inequalities. The book is aimed at upper-level undergraduate students and beginning graduate students in a range of interdisciplinary courses including physical sciences and engineering, from quantum mechanics to differential equations, with pedagogically organized chapters that each concludes with a section of practical problems. Generalized quantum calculus includes a generalization of the q-quantum calculus and the time scale calculus. There are many open problems and difficulties in q-quantum calculus and time-scale calculus, and this book explores how to use the generalized quantum operators to solve difficulties arising in q-quantum calculus and time-scale calculus, including but not limited to generalized quantum integration, generalized quantum chain rules, and generalized quantum Taylor formula.Since generalized quantum calculus includes the q-quantum and time-scale calculus, this book can be utilized by a wide audience of researchers and students. This text is one of few foundational books on generalized quantum calculus and can be used for future discoveries in the area of integral transforms, variational calculus, integral equations, and inequalities in the language of generalized quantum calculus. This book also offers detailed proofs, exercises, and examples to aid instructors, researchers, and users in their studies.

  • Approximation Theory and Applications

    Piecewise Linear and Generalized Functions
    • 1st Edition
    • Sergei Aliukov
    • English
    Approximation Theory and Applications: Piecewise Linear and Generalized Functions presents the main provisions of approximation theory, and considers existing and new methods for approximating piecewise linear and generalized functions, widely used to solve problems related to mathematical modeling of systems, processes, and phenomena in fields ranging from engineering to economics. The widespread use of piecewise linear and generalized functions is explained by the simplicity of their structure. However, challenges often arise when constructing solutions over the entire domain of these functions, requiring the use special mathematical methods to put theory into practice. This book first offers a first full foundation in approximation theory as it relates to piecewise linear and generalized functions, followed by staged methods to resolve common problems in practice, with applications examined across structural mechanics, medicine, quantum theory, signal theory, semiconductor theory, mechanical engineering, heat engineering, and other fields. Later chapters consider numerical verification of approximation methods, and approximation theory as the basis for new macroeconomic theory with impulse and jump characteristics. Each chapter includes questions for review and sample problems, accompanied by a separate Solutions Manual hosted for instructor access.

  • Irreducible Tensorial Sets

    • 1st Edition
    • U. Fano + 1 more
    • H. S. W. Massey + 1 more
    • English
    Irreducible Tensorial Sets discusses mathematical methods originating from the theory of coupling and recoupling of angular momenta in atomic physics that constitute an extension of vector and tensor algebra. The book presents a unified treatment with a compact system of notations from different approaches, such as group theory, algebra, and quantum mechanical transformation theory. It discusses irreducible tensorial sets that cover different sets of quantities such as tensor components and states of atomic systems. It also explains quantum mechanical applications, coupling and recoupling of atomic and nuclear states, the Wigner-Eckart theorem, and the products of tensorial sets of operators. The text shows how to calculate the interaction energy between atomic systems couple with one another with a constant total angular momentum. The book also explains the correlations which are functions of the Euler angles between the frame of reference in which a radiation is observed and a frame of reference attached to the orienting radiation or field. It then cites sample problems related to the angular distribution of radiations. The book will prove useful for physicists, for mathematicians, or for readers with some knowledge in theoretical physics, particularly on theory of groups and quantum mechanics.

  • Mathematical Methods in Medical and Biological Sciences

    • 1st Edition
    • Harendra Singh + 1 more
    • English
    Mathematical Methods in Medical and Biological Sciences presents mathematical methods for computational models arising in the medical and biological sciences. The book presents several real-life medical and biological models, such as infectious and non-infectious diseases that can be modeled mathematically to accomplish　profound research in virtual environments when the cost of laboratory expenses is relatively high. It focuses on mathematical techniques that provide global solutions for models arising in medical and biological sciences by considering their long-term benefits.In addition, the book provides leading-edge developments and insights for a range of applications, including epidemiological modeling of pandemic dynamics, viral infection developments, cancer developments, blood oxygen dynamics, HIV infection spread, reaction-diffusion models, polio infection spread, and chaos modeling with fractional order derivatives.

  • Encyclopedia of Mathematical Physics

    • 2nd Edition
    • Richard Szabo + 1 more
    • English
    Encyclopedia of Mathematical Physics, Second Edition provides a complete resource for researchers, students, and lecturers with an interest in mathematical physics. The book enables readers to access basic information on topics peripheral to their own areas by providing a repository of core information that can be used to refresh even the experienced researcher’s memory and aid teachers in directing students to entries relevant to their course-work. The impressive amount of information in this work - approximately 270 chapters - has been distilled, organized into 10 distinct sections and presented as a complete reference tool to the userThe book is a stimulus for new researchers working in mathematical physics—or in areas using the methods originating from work in mathematical physics—providing them with focused, high-quality background information.

  • Fuzzy Mathematics, Graphs, and Similarity Measures

    Analysis and Application Across Global Challenges
    • 1st Edition
    • John Mordeson + 1 more
    • English
    Fuzzy Mathematics, Graphs, and Similarity Measures provides a solid foundation in core analytical tracks of mathematics of uncertainty, from fuzzy mathematics to graphs and similarity measures with applications in a range of timely cases studies and world challenges. Following a full grounding in fuzzy graph indices, connectivity in fuzzy graph structures, lattice isomorphisms, and similarity measures, the book applies these models in analyzing world challenges, from human trafficking to modern slavery, global poverty, global hunger, homelessness, biodiversity, extinction, terrorism and bioterrorism, pandemics, and climate change.Connections and constructive steps forward are tied throughout to UN Sustainable Development Goals (SDGs). The authors demonstrate and instruct readers in applying techniques from mathematics of uncertainty in examining issues where accurate data is impossible to obtain. In addition to a diverse range of cases studies, exercises reinforce key concepts in each chapter, and an online instructor’s manual supports teaching across a range of course contexts.

  • Probability Models

    • 1st Edition
    • Volume 51
    • English
    Probability Models, Volume 51 in the Handbook of Statistics series, highlights new advances in the field, with this new volume presenting interesting chapters on Stein’s methods, Probabilities and thermodynamics third law, Random Matrix Theory, General tools for understanding fluctuations of random variables, An approximation scheme to compute the Fisher-Rao distance between multivariate normal distributions, Probability Models Applied to Reliability and Availability Engineering, Backward stochastic differential equation– Stochastic optimization theory and viscous solution of HJB equation, and much more.Additional chapters cover Probability Models in Machine Learning, The recursive stochastic algorithm, randomized urn models and response-adaptive randomization in clinical trials, Random matrix theory: local laws and applications, KOO methods and their high-dimensional consistencies in some multivariate models, Fourteen Lectures on Inference for Stochastic Processes, and A multivariate cumulative damage model and some applications.

  • Handbook of Statistical Analysis

    AI and ML Applications
    • 3rd Edition
    • Robert Nisbet + 2 more
    • English
    Handbook of Statistical Analysis: AI and ML Applications, third edition, is a comprehensive introduction to all stages of data analysis, data preparation, model building, and model evaluation. This valuable resource is useful to students and professionals across a variety of fields and settings: business analysts, scientists, engineers, and researchers in academia and industry. General descriptions of algorithms together with case studies help readers understand technical and business problems, weigh the strengths and weaknesses of modern data analysis algorithms, and employ the right analytical methods for practical application. This resource is an ideal guide for users who want to address massive and complex datasets with many standard analytical approaches and be able to evaluate analyses and solutions objectively. It includes clear, intuitive explanations of the principles and tools for solving problems using modern analytic techniques; offers accessible tutorials; and discusses their application to real-world problems.

  • Computer and Information Security Handbook (2-Volume Set)

    • 4th Edition
    • John Vacca
    • English
    Computer and Information Security Handbook, Fourth Edition offers deep coverage of an extremely wide range of issues in computer and cybersecurity theory, along with applications and best practices, offering the latest insights into established and emerging technologies and advancements. With new parts devoted to such current topics as Cyber Security for the Smart City and Smart Homes, Cyber Security of Connected and Automated Vehicles, and Future Cyber Security Trends and Directions, the book now has 104 chapters in 2 Volumes written by leading experts in their fields, as well as 8 updated appendices and an expanded glossary.Chapters new to this edition include such timely topics as Threat Landscape and Good Practices for Internet Infrastructure, Cyber Attacks Against the Grid Infrastructure, Threat Landscape and Good Practices for the Smart Grid Infrastructure, Energy Infrastructure Cyber Security, Smart Cities Cyber Security Concerns, Community Preparedness Action Groups for Smart City Cyber Security, Smart City Disaster Preparedness and Resilience, Cyber Security in Smart Homes, Threat Landscape and Good Practices for Smart Homes and Converged Media, Future Trends for Cyber Security for Smart Cities and Smart Homes, Cyber Attacks and Defenses on Intelligent Connected Vehicles, Cyber Security Issues in VANETs, Use of AI in Cyber Security, New Cyber Security Vulnerabilities and Trends Facing Aerospace and Defense Systems, and much more.

  • Mechanism Design, Behavioral Science and Artificial Intelligence in International Relations

    • 1st Edition
    • Tshilidzi Marwala
    • English
    Recent advances in AI and Mechanism Design provide a vital tool for solving collective action problems, common in international relations. By using AI to optimize mechanisms for cooperation and coordination, we can better address issues such as climate change, trade, and security. Mechanism Design, Behavioral Science and Artificial Intelligence in International Relations shows readers how the intersection of Mechanism Design and Artificial Intelligence is revolutionizing the way we approach international relations. By using AI to optimize mechanisms, we can design better institutions, policies, and agreements that are more effective and efficient. Dr. Tshilidzi Marwala, United Nations University Rector and UN Under-Secretary General, presents the essential technologies used in Game Theory, Mechanism Design and AI and applies these to significant global issues such as interstate conflict, cybersecurity, and energy. International relations are a complex field, with many different actors and interests in play. By incorporating AI into our analysis and decision-making processes, we can better understand and predict the behavior of multiple actors and design mechanisms that take these behaviors into account, thereby producing more desirable and creative interdisciplinary approaches. The book presents real-world applications of these rapidly evolving technologies in crucial research fields such as Interstate Conflict, International Trade, Climate Change, Water management, Energy, cybersecurity, and global finance.

  • Information Modeling and Relational Databases

    • 3rd Edition
    • Terry Halpin + 1 more
    • English
    Information Modeling and Relational Databases, Third Edition, provides thorough coverage of information modeling approaches, including object-role modeling (ORM), entity-relationship (ER) modeling, and the unified modeling language (UML). It shows how to map models developed with those approaches to a variety of relational and nonrelational database systems, including document databases, column-oriented databases, graph databases, and deductive databases. Process and state modeling, ontological modeling, and metamodeling are also covered. For this new edition, the coverage of ORM, ER, UML, SQL, OWL, and BPMN has been thoroughly updated to include their latest versions. A significant amount of new material has been added. Various data file formats such as CSV, XML, JSON, YAML, and some other markup languages are now covered, and a more thorough treatment is provided for nonrelational databases, especially NoSQL. One of the major features of the book is its large number of exercises, which have been thoroughly class-tested. This book is intended for anyone with a stake in the accuracy and efficacy of databases such as systems analysts, information modelers, database designers and administrators, and programmers.

  • Fractional Calculus

    Bridging Theory with Computational and Contemporary Advances
    • 1st Edition
    • Behzad Ghanbari
    • English
    Fractional Calculus: Bridging Theory with Computational and Contemporary Advances is an authoritative and comprehensive guide that delves into the world of fractional calculus, offering a unique blend of theoretical foundations, numerical algorithms, practical applications, and innovative perspectives. This book explores the mathematical framework of fractional calculus and its relevance across various disciplines, providing readers with a deep understanding of this rapidly growing field. The author presents a rigorous yet accessible approach to fractional calculus, making it suitable for mathematicians, researchers, academics, graduate students, and professionals in engineering and applied sciences. The book covers a wide range of topics, including numerical methods for fractional calculus equations, fractional differential equations, fractal dynamics, and fractional control systems. It also explores applications in areas such as physics, engineering, signal processing, and data analysis. Fractional Calculus: Bridging Theory with Computational and Contemporary Advances equips readers with the necessary tools to tackle challenging problems involving fractional calculus, empowering them to apply these techniques in their research, professional work, or academic pursuits. The book provides a comprehensive introduction to the fundamentals of fractional calculus, explaining the theoretical concepts and key definitions in a clear and accessible manner. This helps readers build a strong foundation in the subject. The book then covers a range of numerical algorithms specifically designed for fractional calculus problems, explaining the underlying principles, step-by-step implementation, and computational aspects of these algorithms. This enables readers to apply numerical techniques to solve fractional calculus problems effectively. The book also provides examples that illustrate how fractional calculus is applied to solve real-world problems, providing readers with insights into the wide-ranging applications of the subject.

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