Modern Mathematical Methods For Scientists And Engineers: A Street-smart Introduction

Modern Mathematical Methods for Scientists and Engineers is a modern introduction to basic topics in mathematics at the undergraduate level, with emphasis on explanations and applications to real-life problems. It also includes an Application section with topics drawn from various areas, such as neural networks, fluid dynamics, and financial markets. The book presents several modern and computationally efficient topics, such as feedforward neural networks, wavelets, generalized functions, stochastic optimization methods, and numerical methods. A unique and novel feature of the book is the introduction of the unified transform method for solving partial differential equations (PDEs), which is a challenge for many scientists and engineers. The unified transform greatly facilitates this task, deriving generalizations of solutions to wave equations and heat equations and providing new solutions with analytical and numerical advantages. The book is broad in scope but pedagogical in style and content, making it an excellent introduction to powerful mathematical concepts and modern tools for students in science and engineering.

Format: Hardback
Length: 568 pages
Publication date: 19 February 2023
Publisher: World Scientific Europe Ltd

Modern Mathematical Methods for Scientists and Engineers is a comprehensive and contemporary introduction to fundamental mathematical concepts at the undergraduate level, with a strong emphasis on providing clear explanations and practical applications to real-world problems. The book encompasses a wide range of topics, including neural networks, fluid dynamics, and the behavior of put and call options in financial markets. Each chapter concludes with an Application section, featuring topics drawn from diverse areas such as these.

The book presents several cutting-edge and computationally efficient topics, such as feedforward neural networks, wavelets, generalized functions, stochastic optimization methods, and numerical methods. A unique and innovative aspect of this text is the introduction of a recently developed method for solving partial differential equations (PDEs), known as the unified transform. PDEs are fundamental mathematical tools used to describe a vast array of phenomena, ranging from quantum mechanics to ocean waves, heat diffusion in matter, and the behavior of financial markets. Despite the efforts of numerous renowned mathematicians, physicists, and engineers, the solution of PDEs remains a challenging task.

The unified transform significantly simplifies this process. For instance, over two and a half centuries after Jean d'Alembert formulated the wave equation and presented a solution for solving a simple problem related to this equation, the unified transform readily derives a generalization of the d'Alembert solution, valid for general boundary value problems. Moreover, two centuries after Joseph Fourier introduced the classical tool of the Fourier series for solving the heat equation, the unified transform constructs a new solution to this ubiquitous PDE, offering significant analytical and numerical advantages over classical solutions.

In summary, Modern Mathematical Methods for Scientists and Engineers serves as an invaluable resource for students seeking to develop a strong foundation in mathematics while gaining practical insights into real-world applications. With its comprehensive coverage, innovative approach, and practical examples, this book is an essential tool for anyone interested in advancing their knowledge in the fields of science, engineering, and finance.

ISBN-13: 9781800611801