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

Athanassios Fokas

ISBN 10: 1800611838 / ISBN 13: 9781800611832

Editore: World Scientific Europe Ltd Mär 2023, 2023

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Neuware - 'Partial differential equations (PDEs) are the mathematical cornerstone for describing an astonishingly wide range of phenomena, from quantum mechanics and ocean waves, to the diffusion of heat in matter and the behavior of financial markets. Despite the efforts of many famous mathematicians, physicists and engineers, the solution of partial differential equations remains a challenge. This book's authors introduce a novel method, the unified transform, which greatly facilitates this challenge. Two and a half centuries after Jean d'Alembert formulated the wave equation and presented a solution for solving a simple problem for this equation, this book introduces a generalization of the d'Alembert solution, which is 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, it offers a new solution of this problem, which has important analytical and numerical advantages in comparison to the classical solutions. The authors present the unified transform pedagogically, building all the necessary background, including functions of real and of complex variables and the Fourier transform, illustrating the method with numerous examples. 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. There are also 'Application' sections at the end of each chapter, with topics drawn from a variety of areas, including neural networks, fluid dynamics, and the behavior of put and call options in financial markets. In addition to the unified transform, the book presents several modern important and computationally efficient topics, including feed-forward neural networks, wavelets, generalized functions, stochastic optimization methods, and numerical methods. Broad in scope, but pedagogical in style and content, the book is an introduction to powerful mathematical concepts and modern tools for students in science and engineering'.

Codice articolo 9781800611832

Dati bibliografici

• Titolo: Modern Mathematical Methods For Scientists And Engineers: A Street-smart Introduction
• Editore: World Scientific Europe Ltd Mär 2023
• Data di pubblicazione: 2023
• Lingua: Inglese
• ISBN 10: 1800611838
• ISBN 13: 9781800611832
• Rilegatura: Taschenbuch
• Condizione: Neu
• Dimensioni: 280 L x 216 A x 20 P (millimetri) 280 millimetri di larghezza per 216 millimetri di altezza per 20 millimetri di profondità
• Peso: 1132 grammi

Descrizione articolo

Riassunto

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. There is also an "Application" section at the end of each chapter, with topics drawn from a variety of areas, including neural networks, fluid dynamics, and the behavior of "put" and "call" options in financial markets. The book presents several modern important and computationally efficient topics, including feedforward neural networks, wavelets, generalized functions, stochastic optimization methods, and numerical methods. A unique and novel feature of the book is the introduction of a recently developed method for solving partial differential equations (PDEs), called the unified transform. PDEs are the mathematical cornerstone for describing an astonishingly wide range of phenomena, from quantum mechanics to ocean waves, to the diffusion of heat in matter and the behavior of financial markets. Despite the efforts of many famous mathematicians, physicists and engineers, the solution of partial differential equations remains a challenge. The unified transform greatly facilitates this task. For example, two and a half centuries after Jean d'Alembert formulated the wave equation and presented a solution for solving a simple problem for this equation, the unified transform derives in a simple manner 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, with important analytical and numerical advantages in comparison to the classical solutions. The authors present the unified transform pedagogically, building all the necessary background, including functions of real and of complex variables and the Fourier transform, illustrating the method with numerous examples. Broad in scope, but pedagogical in style and content, the book is an introduction to powerful mathematical concepts and modern tools for students in science and engineering.