Modern Mathematical Methods For Scientists And Engineers: A Street-smart Introduction
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A01=Athanassios Fokas
A01=Efthimios Kaxiras
Author_Athanassios Fokas
Author_Efthimios Kaxiras
Bayes
Black-Scholes
BlackAcAEURA"Scholes
Black–Scholes
Category=PBKF
Cauchy
Cauchy-Riemann
CauchyAcAEURA"Riemann
Cauchy–Riemann
Complex Analysis
Complex Variables
Contour Integration
D'alembert
Derivatives
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Evolution PDEs
Fokas Method
Fokker-Planck
FokkerAcAEURA"Planck
Fokker–Planck
Fourier Series
Fourier Transform
Function Optimization
Gaussian Integrals
Helmholtz
Inverse Function
Laplace
Numerical Methods
ODEs
Ordinary Differential Equations
Partial Differential Equations
PDEs
Poisson
Polynomials
Probability Theory
Real Functions
Series Expansions
Single Variable
Singularities
Stochastic Methods
Stochastic Optimization Methods
Unified Transform
Wave Equation
Product details
- ISBN 9781800611801
- Publication Date: 08 Mar 2023
- Publisher: World Scientific Europe Ltd
- Publication City/Country: GB
- Product Form: Hardback
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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.
