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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.

BooksJournals

    • Recent Developments in Theory and Applications of Fractional Order Systems

      • 1st Edition
      • September 1, 2025
      • Mehmet Yavuz + 2 more
      • English
      • Paperback
        9 7 8 0 4 4 3 2 3 9 5 2 6
      • eBook
        9 7 8 0 4 4 3 2 3 9 5 3 3
      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.

    • Methods of Mathematical Modeling

      • 1st Edition
      • July 18, 2025
      • Hemen Dutta
      • English
      • Paperback
        9 7 8 0 4 4 3 1 3 3 1 7 6
      • eBook
        9 7 8 0 4 4 3 1 3 3 1 6 9
      Methods of Mathematical Modeling: Advances and Applications delves into recent progress in this field, highlighting innovative methods and their uses in different domains. This book covers convergence analysis involving nonlinear integral equations and boundary value problems, Navier-Stokes equations in Sobolev-Gevrey spaces, magneto-hydrodynamic... of ternary nanofluids with heat transfer effects, vortex nerve complexes in video frame shape approximation, hybrid schemes for computing hyperbolic conservation laws, and solutions to new fractional differential equations. Additionally, the book examines dynamics of Leslie-Gower type predator-prey models and models for the dynamics of generic crop and water availability.Readers will find diverse approaches, techniques, and applications needed for modeling various physical and natural systems. Each chapter is self-contained, encouraging independent study and application of the modeling examples to individual research projects. This book serves as a valuable resource for researchers, students, educators, scientists, and practitioners involved in different aspects of modeling.

    • Quaternion Generalized Inverses

      • 1st Edition
      • July 9, 2025
      • Ivan I. Kyrchei
      • English
      • Paperback
        9 7 8 0 4 4 3 3 4 1 4 5 8
      • eBook
        9 7 8 0 4 4 3 3 4 1 4 6 5
      A cornerstone of linear algebra, the determinant's utility in real and complex fields is undeniable, though traditionally limited to invertibility, rank, and solving linear systems. Quaternion Generalized Inverses: Foundations, Theory, Problems, and Solutions ventures into uncharted territory: extending these concepts to linear algebra over the noncommutative quaternion skew field. The author's groundbreaking theory of "noncommutative" row–column determinants is central to this exploration, a significant advancement beyond the Moore determinant. This seven-chapter work thoroughly introduces the history of noncommutative determinants before delving into the author's theory and its application to inverse matrix computation and Cramer's rule for quaternion systems. The main portion of this work is dedicated to a comprehensive examination of quaternion generalized inverses, spanning the well-established Moore–Penrose and Drazin inverses to more recent developments such as core-EP and composite inverses. The book provides their definitions, properties, and, uniquely, their determinantal representations based on the author's noncommutative determinants. It culminates in demonstrating their powerful applications in solving a wide range of quaternion matrix equations, including Sylvester-type and constrained equations, as well as differential matrix equations.

    • Information Modeling and Relational Databases

      • 3rd Edition
      • July 9, 2024
      • Terry Halpin + 1 more
      • English
      • Hardback
        9 7 8 0 4 4 3 2 3 7 9 0 4
      • eBook
        9 7 8 0 4 4 3 2 3 7 9 1 1
      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.

    • Advanced Calculus for Mathematical Modeling in Engineering and Physics

      • 1st Edition
      • June 14, 2024
      • David Stapleton
      • English
      • Paperback
        9 7 8 0 4 4 3 2 2 2 8 9 4
      • eBook
        9 7 8 0 4 4 3 2 2 2 8 8 7
      Advanced Calculus for Mathematical Modeling in Engineering and Physics: With Discrete and Numerical Analogies introduces the principles and methods of advanced calculus for mathematical modeling through a balance of theory and application using a state space approach with elementary functional analysis. This framework facilitates a deeper understanding of the nature of mathematical models, and of the behavior of their solutions. The work provides a variety of advanced calculus models for mathematical, physical science, and engineering audiences, with discussions on how calculus-based models and their discrete analogies are generated. This valuable textbook offers scientific computations driven by Octave/MATLAB script.

    • Difference Equations and Applications

      • 1st Edition
      • October 24, 2024
      • Youssef N. Raffoul
      • English
      • Paperback
        9 7 8 0 4 4 3 3 1 4 9 2 6
      • eBook
        9 7 8 0 4 4 3 3 1 4 9 3 3
      Difference Equations and Applications provides unique coverage of high-level topics in the application of difference equations and dynamical systems. The book begins with extensive coverage of the calculus of difference equations, including contemporary topics on l_p stability, exponential stability, and parameters that can be used to qualitatively study solutions to non-linear difference equations, including variations of parameters and equations with constant coefficients, before moving on to the Z-Transform and its various functions, scalings, and applications. It covers systems, Lyapunov functions, and stability, a subject rarely covered in competitor titles, before concluding with a comprehensive section on new variations of parameters.Exercises are provided after each section, ranging from an easy to medium level of difficulty. When finished, students are set up to conduct meaningful research in discrete dynamical systems. In summary, this book is a comprehensive resource that delves into the mathematical theory of difference equations while highlighting their practical applications in various dynamic systems. It is highly likely to be of interest to students, researchers, and professionals in fields where discrete modeling and analysis are essential.

    • An Introduction to Probability and Statistical Inference

      • 3rd Edition
      • May 16, 2024
      • George G. Roussas
      • English
      • Paperback
        9 7 8 0 4 4 3 1 8 7 2 0 9
      • eBook
        9 7 8 0 4 4 3 1 8 7 2 1 6
      An Introduction to Probability and Statistical Inference, Third Edition guides the reader through probability models and statistical methods to develop critical-thinking skills. Written by award-winning author George Roussas, this valuable text introduces a thinking process to help users obtain the best solution to a posed question or situation and provides a plethora of examples and exercises to illustrate applying statistical methods to different situations.

    • Fractional Differential Equations

      • 1st Edition
      • April 29, 2024
      • Praveen Agarwal + 2 more
      • English
      • Paperback
        9 7 8 0 4 4 3 1 5 4 2 3 2
      • eBook
        9 7 8 0 4 4 3 1 5 4 2 4 9
      Fractional Differential Equations: Theoretical Aspects and Applications presents the latest mathematical and conceptual developments in the field of Fractional Calculus and explores the scope of applications in research science and computational modeling. The book delves into these methods and applied computational modelling techniques, including analysis of equations involving fractional derivatives, fractional derivatives and the wave equation, analysis of FDE on groups, direct and inverse problems, functional inequalities, and computational methods for FDEs in physics and engineering. Other modeling techniques and applications explored include general fractional derivatives involving the special functions in analysis and fractional derivatives with respect to other functions. Fractional Calculus, the field of mathematics dealing with operators of differentiation and integration of arbitrary real or even complex order, extends many of the modelling capabilities of conventional calculus and integer-order differential equations and finds its application in various scientific areas, such as physics, mechanics, engineering, economics, finance, biology, and chemistry, among others.

    • Visualizing More Quaternions

      • 1st Edition
      • July 1, 2024
      • Andrew J. Hanson
      • English
      • Hardback
        9 7 8 0 3 2 3 9 9 2 0 2 2
      • eBook
        9 7 8 0 3 2 3 9 9 3 9 0 6
      Visualizing More Quaternions is a sequel to Dr. Andrew J. Hanson’s first book, Visualizing Quaternions, which appeared in 2006. This new volume develops and extends concepts that have attracted the author’s attention in the intervening 18 years, providing new insights into existing scholarship, and detailing results from Dr. Hanson’s own published and unpublished investigations relating to quaternion applications. Among the topics covered are the introduction of new approaches to depicting quaternions and their properties, applications of quaternion methods to cloud matching, including both orthographic and perspective projection problems, and orientation feature analysis for proteomics and bioinformatics. The quaternion adjugate variables are introduced to embody the nontrivial quaternion topology on the three-sphere and incorporate it into machine learning tasks. Other subjects include quaternion applications to a wide variety of problems in physics, including quantum computing, complexified quaternions in special relativity, and a detailed study of the Kleinian “ADE”discrete groups of the ordinary two-sphere. Quaternion geometry is also incorporated into the isometric embedding of the Eguchi–Hanson gravitational instanton corresponding to the k = 1 Kleinian cyclic group. Visualizing More Quaternions endeavors to explore novel ways of thinking about challenging problems that are relevant to a broad audience involved in a wide variety of scientific disciplines.

    • Computation and Modeling for Fractional Order Systems

      • 1st Edition
      • February 20, 2024
      • Snehashish Chakraverty + 1 more
      • English
      • Paperback
        9 7 8 0 4 4 3 1 5 4 0 4 1
      • eBook
        9 7 8 0 4 4 3 1 5 4 0 5 8
      Computation and Modeling for Fractional Order Systems provides readers with problem-solving techniques for obtaining exact and/or approximate solutions of governing equations arising in fractional dynamical systems presented using various analytical, semi-analytical, and numerical methods. Various analytical/semi-anal... methods are applied for solving real-life fractional order problems. The comprehensive descriptions of different recently developed fractional singular, non-singular, fractal-fractional, and discrete fractional operators, along with computationally efficient methods, are included for the reader to understand how these may be applied to real-world systems, and a wide variety of dynamical systems such as deterministic, stochastic, continuous, and discrete are addressed.Fractional calculus has gained increasing popularity and relevance over the last few decades, due to its well-established applications in various fields of science and engineering. It deals with the differential and integral operators with non-integral powers. Fractional differential equations are the pillar of various systems occurring in a wide range of science and engineering disciplines, namely physics, chemical engineering, mathematical biology, financial mathematics, structural mechanics, control theory, circuit analysis, and biomechanics, among others.

Related subjects

Mathematics and applied mathematics

Statistics and probability