Advanced Mathematical Methods For Scientists And Engineers i

The triumphant vindication of bold theories-are these not the pride and justification of our life's work? -Sherlock Holmes, The Valley of Fear Sir Arthur Conan Doyle The main purpose of our book is to present and explain mathematical methods for obtaining approximate analytical solutions to differential and difference equations that cannot be solved exactly. Our objective is to help young and also establiShed scientists and engineers to build the skills necessary to analyze equations that they encounter in their work. Our presentation is aimed at developing the insights and techniques that are most useful for attacking new problems.

This book comprehensively presents topics, such as Dirac notation, tensor analysis, elementary differential geometry of moving surfaces, and k-differential forms. Additionally, two new chapters of Cartan differential forms and Dirac and tensor notations in quantum mechanics are added to this second edition.

Linear Algebra, Calculus, Optimization for Machine Learning and AI Fundamentals

Presents a methodology for systematically constructing individual computer programs, emphasizing the finite difference approach for solving differential equations, and with new consideration for the finite element method. Each chapter includes FORTRAN programs for implementing algorithms, with more than 2600 mathematical expressions.

Machine Learning, Data-Driven Engineering, Wavelet Analysis, Fourier Transforms, and Dynamical Systems

Machine Learning, Data-Driven Engineering, Wavelet Analysis, Fourier Transforms, and Dynamical Systems

Machine Learning, Data-Driven Engineering, Wavelet Analysis, Fourier Transforms, and Dynamical Systems

This book provides a comprehensive introduction to computational fluid dynamics (CFD), encompassing fundamental theory, mathematical and numerical techniques, and practical applications. The book demonstrates common post-processing and visualization techniques, such as contour plots, streamlines, vectors, and charts. It provides encompassing the essential theory, methods, and applications, making it an ideal choice as a textbook for graduate and post-graduate students or a reference for researchers and engineers working on CFD simulations.