Books in Applied mathematics

Extended Hypergeometric Functions and Orthogonal Polynomials

1st Edition
February 1, 2026
Praveen Agarwal + 1 more
English

Extended Hypergeometric Functions and Orthogonal Polynomials presents a comprehensive and accessible resource for researchers and graduate students interested in exploring the rich connections between extended hypergeometric functions, orthogonal polynomials, and multivariable polynomials. Integrating all three fields and their applications in Maple, Mathematica, and MATLAB, this book fosters interdisciplinary understanding and inspires new avenues of research in mathematics, engineering, physics, and computer science. It also provides a glimpse into future research directions in these areas, including potential applications in emerging fields of applied mathematics and interdisciplinary collaborations. Each chapter begins with an introduction, includes sections on theory, followed by sections on applications, and ends with exercises, problems, references and suggested readings.

Mathematics and Biomedical Engineering in Medicine, Physiology and Health Sciences

1st Edition
January 1, 2026
Dhanjoo N. Ghista + 3 more
English

Introduction to Mathematics in Physiology, Medicine, and Health Sciences provides a quantitative handbook for physiology and biological systems, so researchers, practitioners, and clinicians can have a quantitative foundation, and medicine can incorporate more precise diagnostics. This book’s purpose is to demonstrate how fundamental mathematics can be incorporated into biomedical engineering, 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 more quantitative formulation of medical procedures, towards supporting the growing field of precision medicine. The book guides readers though the foundations of mathematics as it is applied to modeling of physiological systems, medicine, biology, and health sciences. Each chapter includes a robust introduction to the mathematical concepts and principles necessary to understand their application to the indicated medical and biological systems, beginning with the fundamental relationships among biological variables in Chapter 2, introduction to basic calculus and rate of change in biomedical variables in Chapter 3, and the principles of linear algebra and vectors applied to medicine in Chapter 4. Chapters 5-7 cover the fundamentals of exponential and logarithmic biomedical functions, maximum and minimum values of a function, and integration applications such as summation, area, and volume. Chapter 8 provides an in-depth look into biomedical applications of Ordinary and Partial Differential Equations, which are important modeling tools for flow and variable systems. Chapter 9 provides extensive coverage of Organ System Analyses, which is the core of the physiological system modeling in the book, with a wide range of applied examples. Chapters 10 and 11 extend the modeling applications to medical devices and signal processing. Each chapter provides in-depth guidance on the mathematical concepts, methodology, and procedures for applying the mathematical 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.

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
August 1, 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.

Integral Manifolds for Impulsive Differential Problems with Applications

1st Edition
April 24, 2025
Ivanka Stamova + 1 more
English
Paperback
9 7 8 0 4 4 3 3 0 1 3 4 6
eBook
9 7 8 0 4 4 3 3 0 1 3 5 3

Integral Manifolds for Impulsive Differential Problems with Applications offers readers a comprehensive resource on integral manifolds for different classes of differential equations which will be of prime importance to researchers in applied mathematics, engineering, and physics. The book offers a highly application-oriented approach, reviewing the qualitative properties of integral manifolds which have significant practical applications in emerging areas such as optimal control, biology, mechanics, medicine, biotechnologies, electronics, and economics. For applied scientists, this will be an important introduction to the qualitative theory of impulsive and fractional equations which will be key in their initial steps towards adopting results and methods in their research.

Mathematical Modeling in Bioscience

1st Edition
March 27, 2025
Hemen Dutta
English
Paperback
9 7 8 0 4 4 3 1 5 4 4 5 4
eBook
9 7 8 0 4 4 3 1 5 4 4 6 1

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.

Statistical Modeling and Robust Inference for One-shot Devices

1st Edition
March 26, 2025
Narayanaswamy Balakrishnan + 1 more
English
Paperback
9 7 8 0 4 4 3 1 4 1 5 3 9
eBook
9 7 8 0 4 4 3 1 4 1 5 2 2

The study of one-shot devices such as automobile airbags, fire extinguishers, or antigen tests, is rapidly becoming an important problem in the area of reliability engineering. These devices, which are destroyed or must be rebuilt after use, are a particular case of extreme censoring, which makes the problem of estimating their reliability and lifetime challenging. However, classical statistical and inferential methods do not consider the issue of robustness.Statistic... Modeling and Robust Interference for One-shot Devices offers a comprehensive investigation of robust techniques of one-shot devices under accelerated-life tests. With numerous examples and case studies in which the proposed methods are applied, this book includes detailed R codes in selected chapters to help readers implement their own codes and use them in the proposed examples and in their own research on one-shot devicetesting data. Researchers, mathematicians, engineers, and students working on acceleratedlife testing data analysis and robust methodologies will find this to be a welcome resource.

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.

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.

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.

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