Engineering Mathematics 2024

This book provides a comprehensive overview of analytical methods for solving optimization problems, covering principles and mathematical techniques alongside numerical solution routines, including MAPLE and MAXIMA optimization routines. Each method is explained with practical applications and ANSYS APDL scripts for select problems. Chapters delve into topics such as scaling methods, torsion compliance, shape variation, topological optimization, anisotropic material properties, and differential geometry. Specific optimization problems, including stress minimization and mass reduction under constraints, are addressed. The book also explores isoperimetric inequalities and optimal material selection principles. Appendices offer insights into tensors, differential geometry, integral equations, and computer algebra codes. Overall, it's a comprehensive guide for engineers and researchers in structural optimization.

This comprehensive book delves into the intricacies of Newton-type methods for nonlinear equations, offering insights into their convergence, accelerations, and extensions. Divided into three parts, the book explores higher-order iterations for nonlinear equations and their systems, and their applications in linear algebra and some nonlinear problems of theoretical physics. Emphasizing the pivotal role of iteration parameters in shaping convergence and expanding the domain, the authors draw from their extensive collaborative research to systematically compile and elucidate these findings. Catering to readers, graduate students, and researchers in applied mathematics, numerical analysis, and related disciplines, this book serves as a valuable resource, synthesizing decades of research to advance understanding and practical application in the field.

This book benefits researchers, engineers, and graduate students in the field of fractional-order complex dynamical networks. Recently, the dynamical behaviors (e.g., passivity, finite-time passivity, synchronization, and finite-time synchronization, etc.) for fractional-order complex networks (FOCNs) have attracted considerable research attention in a wide range of fields, and a variety of valuable results have been reported. In particular, passivity has been extensively used to address the synchronization of FOCNs.

This book provides a new model for clustering, classification, and time series prediction by using artificial neural networks to computationally simulate the behavior of the cognitive functions of the brain is presented. This model focuses on the study of intelligent hybrid neural systems and their use in time series analysis and decision support systems. Therefore, through the development of eight case studies, multiple time series related to the following problems are analyzed: traffic accidents, air quality and multiple global indicators (energy consumption, birth rate, mortality rate, population growth, inflation, unemployment, sustainable development, and quality of life). The main contribution consists of a Generalized Type-2 fuzzy integration of multiple indicators (time series) using both supervised and unsupervised neural networks and a set of Type-1, Interval Type-2, and Generalized Type-2 fuzzy systems. The obtained results show the advantages of the proposed model of Generalized Type-2 fuzzy integration of multiple time series attributes. This book is intended to be a reference for scientists and engineers interested in applying type-2 fuzzy logic techniques for solving problems in classification and prediction. We consider that this book can also be used to get novel ideas for new lines of research, or to continue the lines of research proposed by the authors of the book.

This book aims to emphasize the state-of-the-art research in realizing the optimal synthesis of microgrid voltage regulation problems using adaptive multi-agent control theory. The contents of this book are divided into four parts. The book describes the microgrid voltage regulation model construction. Building upon this foundation, the book investigates fault-tolerant and event-triggered control problems under different constraints. The effectiveness and applicability of the design methods are verified by simulation arithmetic and applications.

The second edition of this study guide is written and designed for students taking a precalculus course. It includes new and expanded exercises with final answers that will help students to review and sharpen their knowledge of the subject and enhance their performance in the classroom. The author uses methods typically found in instructor-recommended textbooks, offering detailed solutions, multiple methods for solving problems, and clear explanations of concepts. This hands-on guide will improve students’ problem-solving skills and foster a solid understanding of calculus, which will benefit them in all of their calculus-based courses.