Название: Numerical Methods for Engineering and Data ScienceАвтор: Rolf Wuthrich, Carole El Ayoubi
Издательство: CRC Press
Год: 2025
Страниц: 478
Язык: английский
Формат: pdf (true), epub
Размер: 43.5 MB
Numerical Methods for Engineering and Data Science guides students in implementing numerical methods in engineering and in assessing their limitations and accuracy, particularly using algorithms from the field of Machine Learning.
The textbook presents key principles building upon the fundamentals of engineering mathematics. It explores classical techniques for solving linear and nonlinear equations, computing definite integrals and differential equations. Emphasis is placed on the theoretical underpinnings, with an in-depth discussion of the sources of errors, and in the practical implementation of these using Octave. Each chapter is supplemented with examples and exercises designed to reinforce the concepts and encourage hands-on practice. The second half of the book transitions into the realm of Machine Learning. The authors introduce basic concepts and algorithms, such as linear regression and classification. As in the first part of this book, a special focus is on the solid understanding of errors and practical implementation of the algorithms. In particular, the concepts of bias, variance, and noise are discussed in detail and illustrated with numerous examples.
Machine Learning, a subset of Artificial Intelligence, leverages algorithms and statistical models to enable computers to improve their performance on tasks through experience. This textbook aims to present both domains. A particular focus is on a solid understanding of the concept of error. In both cases, numerical algorithms to approximate problems such as solving ordinary differential equations or computing definite integrals, and Machine Learning approaches aiming to predict an outcome based on existing data, errors play a key role. Any algorithm will only provide approximations. It is, therefore, essential to estimate the error associated with these approximations to decide if the provided numerical value is acceptable or not for the targeted application.
The first part of the textbook covers the fundamentals of numerical methods. We explore classical techniques for solving linear and nonlinear equations, computing definite integrals, and differential equations. Emphasis is placed both on the theoretical underpinnings, with in-depth discussion of the sources of errors, and in the practical implementation of these using Octave, an open-source software specialized for numerical calculations. Each chapter is supplemented with examples and exercises designed to reinforce the concepts and encourage hands-on practice.
The second part transitions into the realm of machine learning. We start with basic concepts and algorithms, such as linear regression and classification. As we progress, we introduce some other algorithms. As in the first part of this book, a special focus is on the solid understanding of errors and practical implementation of the algorithms. In particular, the concepts of bias, variance, and noise are discussed in detail and illustrated with numerous examples.
In the present book, we use Octave for the first part, and the Python library SciKit Learn in the second part. Octave is particularly well suited for numerical algorithms that are written in matrix forms. The software comes with an integrated development environment from which calculations can be performed either interactively or in the form of scripts. GNU Octave is a scientific programming language for scientific computing and numerical computation. Octave helps in solving linear and nonlinear problems numerically, and for performing other numerical experiments using a language that is mostly compatible with MATLAB.
The Python Library SciKit Learn is a popular, very well-documented Python library implementing a large collection of numerical methods from the field of Machine Learning. Readers not familiar with Python are encouraged to follow some of the excellent online tutorials on Python first. Contrary to Octave, installing and using Python is less straightforward as it will require the management of libraries. Readers unfamiliar with installing Python libraries are encouraged to use online platforms with pre-installed environments, such as Google Colab.
This book will be of interest to students in all areas of engineering, alongside mathematicians and scientists in industry looking to improve their knowledge of this important field.
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