Textbook in PDF format 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. 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