Applications Of Differential Transform To Real World Problems
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Applications of Differential Transform to Real World Problems
This book is an invaluable resource for applied researchers to find the analytical solution of differential equations describing the dynamical system with less computational effort and time. It describes the basic concepts of the differential transform method and solution of various real-world problems described by simple to complicated differential equations. It provides a computational technique that is not only conceptually simple and easy to use but also readily adaptable for computer coding. Different chapters of the book deal with the basic differential equations involved in the physical phenomena as well as a complicated system of differential equations described by the mathematical model. The book offers comprehensive coverage of the most essential topics, including Basic concepts and fundamental properties of the proposed technique with proof The solution of linear, nonlinear, homogeneous, and nonhomogeneous ordinary differential equations (ODEs) and partial differential equations (PDEs) The initial and boundary value problems Real-world ODE and PDE problems are also discussed Applications of Differential Transform to Real World Problems is primarily aimed at undergraduates, graduates, and researchers studying differential equations. Scientists dealing with complicated differential equations or systems of differential equations will also find this book useful.
Differential Transformation Method for Mechanical Engineering Problems
Differential Transformation Method for Mechanical Engineering Problems focuses on applying DTM to a range of mechanical engineering applications. The authors modify traditional DTM to produce two additional methods, multi-step differential transformation method (Ms-DTM) and the hybrid differential transformation method and finite difference method (Hybrid DTM-FDM). It is then demonstrated how these can be a suitable series solution for engineering and physical problems, such as the motion of a spherical particle, nanofluid flow and heat transfer, and micropolar fluid flow and heat transfer. - Presents the differential transformation method and why it holds an advantage over higher-order Taylor series methods - Includes a full mathematical introduction to DTM, Ms-DTM, and Hybrid DTM - Covers the use of these methods for solving a range of problems in areas such as nanofluid flow, heat transfer, and motion of a spherical particle in different conditions - Provides numerous examples and exercises which will help the reader fully grasp the practical applications of these new methods
Applications of Differential Equations
Unlock the power of mathematics with "Applications of Differential Equations," a comprehensive guide that demystifies this essential tool. Our book is crafted for students, educators, and practitioners, offering a deep dive into the theory, techniques, and real-world applications of differential equations across diverse fields, including physics, engineering, biology, and economics. We start with a solid foundation in the basic concepts, making the book accessible to beginners while providing valuable insights for advanced learners. Clear explanations and illustrative examples guide readers through the classification of differential equations, methods for solving first-order equations, and techniques for analyzing their behavior. Step-by-step solutions and practical exercises reinforce learning, ensuring confidence in tackling a wide range of problems. Delving into advanced topics, we cover higher-order differential equations, systems of differential equations, and Laplace transforms. We emphasize mathematical modeling, showcasing how differential equations represent real-world phenomena and predict their behavior. What sets this book apart is its focus on practical applications. Real-world examples and case studies illustrate how differential equations model and analyze phenomena such as population dynamics, fluid mechanics, and electrical circuits. This approach bridges theory and practice, highlighting the versatility and power of differential equations in addressing challenges and advancing knowledge. Designed for a global audience, our book ensures accessibility and relevance for readers from diverse backgrounds. Whether you're a student, educator, or practitioner, "Applications of Differential Equations" is your go-to resource for mastering this powerful mathematical tool.