In an era where engineering challenges are becoming increasingly multifaceted, Mathematical Solutions for Complex Engineering Systems serves as a comprehensive guide bridging the gap between theory and real-world applications. This book explores advanced mathematical modeling techniques, computational approaches, and optimization strategies that drive innovation across various engineering disciplines.This book brings together a diverse collection of research contributions that highlight:Deterministic, stochastic, linear, and nonlinear models essential for analyzing multi-physical systems, from fluid dynamics to reliability engineering.Cutting-edge methods such as finite element analysis, boundary element methods, Keller box techniques, and machine learning-driven modeling for solving complex engineering problems.Case studies on nuclear power plant reliability, eco-epidemiology, nanofluid heat transfer, and pesticide impact on agricultural sustainability.Novel mathematical frameworks, including fractional Taylor wavelets, B-spline methods, and variational principles, for tackling nonlinear differential equations.Advanced concepts such as tunnel mathematics, meshfree methods, and high-resolution computational fluid dynamics (CFD) models for solving contemporary engineering challenges.Designed for researchers, engineers, and graduate students, this book provides a robust foundation in mathematical techniques and their practical applications. With contributions from leading experts, it offers a unique blend of theoretical depth and computational efficiency, making it an essential reference for tackling modern engineering complexities.

This book explains the foundational principles of fuzzy algebra, including fuzzy sets, fuzzy operations, and fuzzy relations. It shows how fuzzy algebra can be applied in artificial intelligence, particularly in areas such as decision-making, pattern recognition, and machine learning, where uncertainty and imprecision are common. It demonstrates the use of fuzzy algebra in engineering disciplines, such as control systems, cybersecurity, signal processing, and robotics, where fuzzy logic can be used to model and solve complex and real-world problems. This makes the book valuable not just for process engineers, but also for researchers in multiple domains.This book is designed to familiarize data science, machine learning and other engineering professionals, in a relatively simple and easy to understand fashion, with decision making skills founded on calculations and case study based quantitative analysis.

This book presents key computational intelligence approaches applied across diverse areas of computer science, demonstrating their effectiveness in solving real-world problems. It highlights how nature-inspired methods are shaping the future of intelligent systems and offering powerful, efficient, and elegant solutions to complex challenges.Computational intelligence (CI) extends far beyond the optimization of complex computations. It provides robust, generic, and adaptable mechanisms for addressing challenging problems across science and technology where traditional mathematical reasoning encounters uncertainty, nonlinearity, and complexity.In computer science, CI strongly influences algorithm design, system architectures, and optimization schemes. Unlike classical artificial intelligence, which is largely rule- and logic-based, computational intelligence relies on nature-inspired methodologies that model learning, adaptation, and evolution.Traditionally, CI has been built upon three foundational paradigms: Neural networks, fuzzy systems, and evolutionary computation. Neural networks emulate the structure and learning behavior of the human brain; fuzzy systems incorporate linguistic reasoning to manage uncertainty and imprecise data; and evolutionary computation draws inspiration from biological evolution, incorporating mechanisms such as selection, mutation, and reproduction.Today, CI has expanded to include machine learning methods, swarm intelligence, support vector machines, and chaotic systems. These techniques enable faster, more accurate, and less complex decision-making across a wide range of computational problems.

The research in this book looks at the likelihood and level of use of implemented technological components with regard to the adoption of different precision agricultural technologies. To identify the variables affecting farmers' choices to embrace more precise technology, zero-inflated Poisson and negative binomial count data regression models are utilized. Outcomes from the count data analysis of a random sample of various farm operators show that various aspects, including farm dimension, farmer demographics, soil texture, urban impacts, farmer position of liabilities, and position of the farm in a state, were significantly associated with the approval severity and likelihood of precision farming technologies.Technical topics discussed in the book include:Precision agricultureMachine learningWireless sensor networksIoTDeep learning

This book contains a detailed discussion of the matrix operation, its properties, and its applications in finding the solution of linear equations and determinants. Linear algebra is a subject that has found the broadest range of applications in all branches of mathematics, physical and social sciences, and engineering. It has a more significant application in information sciences and control theory.A definition of linear algebra is that it is a part of algebra which is concerned with equations of the first degree. Thus, at the fundamental level, it involves the discussion of matrices and determinants, and the solutions of systems of linear equations, which have a wide application in further discussion of this subject.Technical topics discussed in the book include: MatricesVector spacesEigenvalue and eigenvectorsLinear transformationInner product spacesDiagonalizationsApplications to conics and quadricsCanonical formsLeast squares problems

This book is an excellent collection of various topics of mathematics which include numerical methods, integral equations, and differential equations. The book is recommended to readers to refresh their understanding of applied mathematics with theory and applications. It will be useful to students, researchers, and practitioners working in applied and computational mathematics.

Sir Isaac Newton, one of the greatest scientists and mathematicians of all time, introduced the notion of a vector to define the existence of gravitational forces, the motion of the planets around the sun, and the motion of the moon around the earth. Vector calculus is a fundamental scientific tool that allows us to investigate the origins and evolution of space and time, as well as the origins of gravity, electromagnetism, and nuclear forces. Vector calculus is an essential language of mathematical physics, and plays a vital role in differential geometry and studies related to partial differential equations widely used in physics, engineering, fluid flow, electromagnetic fields, and other disciplines. Vector calculus represents physical quantities in two or three-dimensional space, as well as the variations in these quantities.The machinery of differential geometry, of which vector calculus is a subset, is used to understand most of the analytic results in a more general form. Many topics in the physical sciences can be mathematically studied using vector calculus techniques.This book is designed under the assumption that the readers have no prior knowledge of vector calculus. It begins with an introduction to vectors and scalars, and also covers scalar and vector products, vector differentiation and integrals, Gauss's theorem, Stokes's theorem, and Green's theorem. The MATLAB programming is given in the last chapter.This book includes many illustrations, solved examples, practice examples, and multiple-choice questions.

Industry 4.0 is used interchangeably with the fourth industrial revolution and represents a new stage in the organization asnd control of the industrial value chain. Cyber-physical systems form the basis of industry 4.0 (e.g., 'smart machines'). They use modern control systems, have embedded software systems, can be addressed via IoT (the Internet of Things), and may use extensive data analytics and/or articifical inteligence systems to operate autonomously.The aim of this book is to provide detailed insights into the state of art techniques in AI, IoT, Blockchain technology and associated technologies which play a vital role in the implementation of a successful project for upcoming and practicing engineers. Owing to its multidisciplinary nature, Industry 4.0 is not a single topic but a combination of a multitude of technologies from different domains. Keeping this in mind the book includes the following topics:Artificial intelligence Internet of thingsBlockchain technologyDigital manufacturing RoboticsCybersecurityThe book will be a comprehensive guide to academicians and engineers who want to align with recent trends of fourth industrial revolution.

The proclivity of today’s technology to think like humans may be seen in new developing disciplines such as neural computing, fuzzy logic, evolutionary computation, machine learning, and probabilistic reasoning. These strategies are grouped together into one main technique known as "soft computing." This book discusses the most recent soft computing and fuzzy logic-based applications and innovations in industrial advancements, supply chain and logistics, system optimization, decision-making, artificial intelligence, smart systems, and other rapidly evolving technologies. In today’s competitive world, the book provides soft computing solutions to help companies overcome the obstacles posed by sophisticated decision-making systems.

Infectious diseases are leading threats and are of highest risk to the human population globally. Over the last two years, we saw the transmission of Covid-19. Millions of people died or were forced to live with a disability. Mathematical models are effective tools that enable analysis of relevant information, simulate the related process and evaluate beneficial results. They can help to make rational decisions to lead toward a healthy society. Formulation of mathematical models for a pollution-free environment is also very important for society. To determine the system which can be modelled, we need to formulate the basic context of the model underlying some necessary assumptions. This describes our beliefs in terms of the mathematical language of how the world functions.This book addresses issues during the Covid phase and post-Covid phase. It analyzes transmission, impact of coinfections, and vaccination as a control or to decrease the intensity of infection. It also talks about the violence and unemployment problems occurring during the post-Covid period. This book will help societal stakeholders to resume normality slowly and steadily.

This book introduces the basic concepts of set theory, measure theory, the axiomatic theory of probability, random variables and multidimensional random variables, functions of random variables, convergence theorems, laws of large numbers, and fundamental inequalities. The idea is to present a seamless connection between the more abstract advanced set theory, the fundamental concepts from measure theory, and integration, to introduce the axiomatic theory of probability, filling in the gaps from previous books and leading to an interesting, robust and, hopefully, self-contained exposition of the theory.This book also presents an account of the historical evolution of probability theory as a mathematical discipline. Each chapter presents a short biography of the important scientists who helped develop the subject. Appendices include Fourier transforms in one and two dimensions, important formulas and inequalities and commented bibliography. Many examples, illustrations and graphics help the reader understand the theory.

This book presents orthotropic vibration modeling and analysis of carbon nanotubes (CNTs) which be helpful in applications such as oscillators and in non-destructive testing, and also vibrations characteristics of armchair double-walled CNT by means of nonlocal elasticity shell model. The nonlocal shell model is established by inferring the nonlocal elasticity equations in to Kelvin’s theory, which is our particular motivation. The suggested method to investigate the solution of fundamental Eigen relations is wave propagation, which is a well-known and efficient technique to develop the fundamental frequency equations. The frequencies of three different types of SWCNTs are calculated. Also, the vibrations of the chiral single-walled carbon nanotube (SWCNTs) with non-local theory using wave propagation approach is investigated. It has been investigated that by increasing the nonlocal parameter decreases the frequencies and on increasing the aspect ratio increases the frequencies throughout the computation frequencies of clamped-free lower than that of clamped-clamped.Carbon nanotubes have a variety of applications because of their distinctive molecular structure and show unique electronic and mechanical properties because of their curvature. Nanotubes and micro-beams can be cited as one of the very applicable micro- and nano-structures in various systems, namely, sensing devices, communications and the quantum mechanics. The application of the tiny structures, specifically, carbon nanotubes in the sensors and actuators enforce the engineers to study vibrational properties of those structures experimentally and theoretically. In addition, they are utilized in different fields such as bioengineering, tissue engineering, computer engineering, optics, energy and environmental systems.

In an era where engineering challenges are becoming increasingly multifaceted, Mathematical Solutions for Complex Engineering Systems serves as a comprehensive guide bridging the gap between theory and real-world applications. This book explores advanced mathematical modeling techniques, computational approaches, and optimization strategies that drive innovation across various engineering disciplines.This book brings together a diverse collection of research contributions that highlight:Deterministic, stochastic, linear, and nonlinear models essential for analyzing multi-physical systems, from fluid dynamics to reliability engineering.Cutting-edge methods such as finite element analysis, boundary element methods, Keller box techniques, and machine learning-driven modeling for solving complex engineering problems.Case studies on nuclear power plant reliability, eco-epidemiology, nanofluid heat transfer, and pesticide impact on agricultural sustainability.Novel mathematical frameworks, including fractional Taylor wavelets, B-spline methods, and variational principles, for tackling nonlinear differential equations.Advanced concepts such as tunnel mathematics, meshfree methods, and high-resolution computational fluid dynamics (CFD) models for solving contemporary engineering challenges.Designed for researchers, engineers, and graduate students, this book provides a robust foundation in mathematical techniques and their practical applications. With contributions from leading experts, it offers a unique blend of theoretical depth and computational efficiency, making it an essential reference for tackling modern engineering complexities.

This book explains the foundational principles of fuzzy algebra, including fuzzy sets, fuzzy operations, and fuzzy relations. It shows how fuzzy algebra can be applied in artificial intelligence, particularly in areas such as decision-making, pattern recognition, and machine learning, where uncertainty and imprecision are common. It demonstrates the use of fuzzy algebra in engineering disciplines, such as control systems, cybersecurity, signal processing, and robotics, where fuzzy logic can be used to model and solve complex and real-world problems. This makes the book valuable not just for process engineers, but also for researchers in multiple domains.This book is designed to familiarize data science, machine learning and other engineering professionals, in a relatively simple and easy to understand fashion, with decision making skills founded on calculations and case study based quantitative analysis.

This book presents key computational intelligence approaches applied across diverse areas of computer science, demonstrating their effectiveness in solving real-world problems. It highlights how nature-inspired methods are shaping the future of intelligent systems and offering powerful, efficient, and elegant solutions to complex challenges.Computational intelligence (CI) extends far beyond the optimization of complex computations. It provides robust, generic, and adaptable mechanisms for addressing challenging problems across science and technology where traditional mathematical reasoning encounters uncertainty, nonlinearity, and complexity.In computer science, CI strongly influences algorithm design, system architectures, and optimization schemes. Unlike classical artificial intelligence, which is largely rule- and logic-based, computational intelligence relies on nature-inspired methodologies that model learning, adaptation, and evolution.Traditionally, CI has been built upon three foundational paradigms: Neural networks, fuzzy systems, and evolutionary computation. Neural networks emulate the structure and learning behavior of the human brain; fuzzy systems incorporate linguistic reasoning to manage uncertainty and imprecise data; and evolutionary computation draws inspiration from biological evolution, incorporating mechanisms such as selection, mutation, and reproduction.Today, CI has expanded to include machine learning methods, swarm intelligence, support vector machines, and chaotic systems. These techniques enable faster, more accurate, and less complex decision-making across a wide range of computational problems.

The research in this book looks at the likelihood and level of use of implemented technological components with regard to the adoption of different precision agricultural technologies. To identify the variables affecting farmers' choices to embrace more precise technology, zero-inflated Poisson and negative binomial count data regression models are utilized. Outcomes from the count data analysis of a random sample of various farm operators show that various aspects, including farm dimension, farmer demographics, soil texture, urban impacts, farmer position of liabilities, and position of the farm in a state, were significantly associated with the approval severity and likelihood of precision farming technologies.Technical topics discussed in the book include:Precision agricultureMachine learningWireless sensor networksIoTDeep learning

This book contains a detailed discussion of the matrix operation, its properties, and its applications in finding the solution of linear equations and determinants. Linear algebra is a subject that has found the broadest range of applications in all branches of mathematics, physical and social sciences, and engineering. It has a more significant application in information sciences and control theory.A definition of linear algebra is that it is a part of algebra which is concerned with equations of the first degree. Thus, at the fundamental level, it involves the discussion of matrices and determinants, and the solutions of systems of linear equations, which have a wide application in further discussion of this subject.Technical topics discussed in the book include: MatricesVector spacesEigenvalue and eigenvectorsLinear transformationInner product spacesDiagonalizationsApplications to conics and quadricsCanonical formsLeast squares problems

This book is an excellent collection of various topics of mathematics which include numerical methods, integral equations, and differential equations. The book is recommended to readers to refresh their understanding of applied mathematics with theory and applications. It will be useful to students, researchers, and practitioners working in applied and computational mathematics.

Sir Isaac Newton, one of the greatest scientists and mathematicians of all time, introduced the notion of a vector to define the existence of gravitational forces, the motion of the planets around the sun, and the motion of the moon around the earth. Vector calculus is a fundamental scientific tool that allows us to investigate the origins and evolution of space and time, as well as the origins of gravity, electromagnetism, and nuclear forces. Vector calculus is an essential language of mathematical physics, and plays a vital role in differential geometry and studies related to partial differential equations widely used in physics, engineering, fluid flow, electromagnetic fields, and other disciplines. Vector calculus represents physical quantities in two or three-dimensional space, as well as the variations in these quantities.The machinery of differential geometry, of which vector calculus is a subset, is used to understand most of the analytic results in a more general form. Many topics in the physical sciences can be mathematically studied using vector calculus techniques.This book is designed under the assumption that the readers have no prior knowledge of vector calculus. It begins with an introduction to vectors and scalars, and also covers scalar and vector products, vector differentiation and integrals, Gauss's theorem, Stokes's theorem, and Green's theorem. The MATLAB programming is given in the last chapter.This book includes many illustrations, solved examples, practice examples, and multiple-choice questions.

Industry 4.0 is used interchangeably with the fourth industrial revolution and represents a new stage in the organization asnd control of the industrial value chain. Cyber-physical systems form the basis of industry 4.0 (e.g., 'smart machines'). They use modern control systems, have embedded software systems, can be addressed via IoT (the Internet of Things), and may use extensive data analytics and/or articifical inteligence systems to operate autonomously.The aim of this book is to provide detailed insights into the state of art techniques in AI, IoT, Blockchain technology and associated technologies which play a vital role in the implementation of a successful project for upcoming and practicing engineers. Owing to its multidisciplinary nature, Industry 4.0 is not a single topic but a combination of a multitude of technologies from different domains. Keeping this in mind the book includes the following topics:Artificial intelligence Internet of thingsBlockchain technologyDigital manufacturing RoboticsCybersecurityThe book will be a comprehensive guide to academicians and engineers who want to align with recent trends of fourth industrial revolution.

The proclivity of today’s technology to think like humans may be seen in new developing disciplines such as neural computing, fuzzy logic, evolutionary computation, machine learning, and probabilistic reasoning. These strategies are grouped together into one main technique known as "soft computing." This book discusses the most recent soft computing and fuzzy logic-based applications and innovations in industrial advancements, supply chain and logistics, system optimization, decision-making, artificial intelligence, smart systems, and other rapidly evolving technologies. In today’s competitive world, the book provides soft computing solutions to help companies overcome the obstacles posed by sophisticated decision-making systems.

Infectious diseases are leading threats and are of highest risk to the human population globally. Over the last two years, we saw the transmission of Covid-19. Millions of people died or were forced to live with a disability. Mathematical models are effective tools that enable analysis of relevant information, simulate the related process and evaluate beneficial results. They can help to make rational decisions to lead toward a healthy society. Formulation of mathematical models for a pollution-free environment is also very important for society. To determine the system which can be modelled, we need to formulate the basic context of the model underlying some necessary assumptions. This describes our beliefs in terms of the mathematical language of how the world functions.This book addresses issues during the Covid phase and post-Covid phase. It analyzes transmission, impact of coinfections, and vaccination as a control or to decrease the intensity of infection. It also talks about the violence and unemployment problems occurring during the post-Covid period. This book will help societal stakeholders to resume normality slowly and steadily.

This book introduces the basic concepts of set theory, measure theory, the axiomatic theory of probability, random variables and multidimensional random variables, functions of random variables, convergence theorems, laws of large numbers, and fundamental inequalities. The idea is to present a seamless connection between the more abstract advanced set theory, the fundamental concepts from measure theory, and integration, to introduce the axiomatic theory of probability, filling in the gaps from previous books and leading to an interesting, robust and, hopefully, self-contained exposition of the theory.This book also presents an account of the historical evolution of probability theory as a mathematical discipline. Each chapter presents a short biography of the important scientists who helped develop the subject. Appendices include Fourier transforms in one and two dimensions, important formulas and inequalities and commented bibliography. Many examples, illustrations and graphics help the reader understand the theory.

This book presents orthotropic vibration modeling and analysis of carbon nanotubes (CNTs) which be helpful in applications such as oscillators and in non-destructive testing, and also vibrations characteristics of armchair double-walled CNT by means of nonlocal elasticity shell model. The nonlocal shell model is established by inferring the nonlocal elasticity equations in to Kelvin’s theory, which is our particular motivation. The suggested method to investigate the solution of fundamental Eigen relations is wave propagation, which is a well-known and efficient technique to develop the fundamental frequency equations. The frequencies of three different types of SWCNTs are calculated. Also, the vibrations of the chiral single-walled carbon nanotube (SWCNTs) with non-local theory using wave propagation approach is investigated. It has been investigated that by increasing the nonlocal parameter decreases the frequencies and on increasing the aspect ratio increases the frequencies throughout the computation frequencies of clamped-free lower than that of clamped-clamped.Carbon nanotubes have a variety of applications because of their distinctive molecular structure and show unique electronic and mechanical properties because of their curvature. Nanotubes and micro-beams can be cited as one of the very applicable micro- and nano-structures in various systems, namely, sensing devices, communications and the quantum mechanics. The application of the tiny structures, specifically, carbon nanotubes in the sensors and actuators enforce the engineers to study vibrational properties of those structures experimentally and theoretically. In addition, they are utilized in different fields such as bioengineering, tissue engineering, computer engineering, optics, energy and environmental systems.