The book explores the foundational concepts of multiplicative surfaces, detailing the multiplicative first fundamental form and key differentiation rules. It also addresses essential regularity conditions for these surfaces. To enhance understanding, the author includes numerous examples and problems, making complex theories more accessible and practical for readers.
The textbook offers a comprehensive collection of exercises focused on partial differential equations, featuring 96 examples, 222 exercises, and 289 problems, all accompanied by detailed solutions or hints. It covers a wide range of topics essential for mathematically oriented scientific disciplines, including physics, engineering, differential geometry, and variational calculus, making it an invaluable resource for students and professionals in these fields.
Focusing on the qualitative theory of quantum curve fittings, this book serves as a resource for senior undergraduate and beginning graduate students in engineering and science. It covers the essential aspects of curve fitting, including interpolation and smoothing, and discusses their applications in data visualization and variable relationships. The book is structured into four pedagogically organized chapters, each ending with practical problems to reinforce learning and application of the concepts presented.
The latest advancements in time scale calculus are the focus of this book. New types of time-scale integral transforms are discussed in the book, along with how they can be used to solve dynamic equations. Novel numerical techniques for partial dynamic equations on time scales are described. New time scale inequalities for exponentially convex functions are introduced as well.
Focusing on iso-mathematics, this book aims to equip readers with foundational concepts for their research. It comprises six chapters, each filled with results, proofs, examples, and exercises, complete with solutions. Advanced practical problems are also included at the end of each chapter, enhancing the learning experience. The content is presented in a clear and mathematically rigorous manner, making it accessible for readers seeking to deepen their understanding of the subject.
Focusing on the theory of distributions, this book serves as an accessible introduction for upper undergraduate and graduate students, as well as mathematicians. It integrates concepts from various mathematical fields, including functional analysis, harmonic analysis, differential geometry, and topology, addressing the complexities involved in studying partial differential equations. The second edition features 10 chapters, making it ideal for a one-semester course while providing a comprehensive overview of fundamental ideas in this area.
Focusing on the application of dynamic equations in various fields such as control theory and mathematical biology, this book explores the integration of fuzzy theory and interval analysis to address uncertainty in modeling. It systematically reviews recent advancements, unifying concepts in fuzzy dynamic equations and optimal control on time scales. Additionally, the author proposes new extensions to different fuzzy dynamic systems and dynamic inclusions, aiming to enhance understanding and application of these theories in complex problem-solving scenarios.
Focusing on advancements in linear and nonlinear integral inequalities within the framework of time scales, this book serves as a comprehensive resource for dynamic calculus, dynamic equations, and integral equations. It is tailored for readers with a mathematical background in time scales calculus and is suitable for graduate-level courses. The content emphasizes recent developments, making it a valuable tool for both study and research in this specialized area of mathematics.
Focusing on the qualitative theory of functional dynamic equations on time scales, this book offers a comprehensive overview of recent advancements in the area. It establishes foundational concepts related to time scales and dynamic systems while exploring applications in mathematical physics. The text includes practical problems, making it suitable as a graduate-level textbook and a reference for specialists in mathematics, physics, engineering, and biology, particularly in studying oscillations and nonoscillations of solutions.