Numerical Methods for Engineering and Data Science

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.

Carole El Ayoubi, PhD, an accomplished engineering professional, currently serves as the Director of Education at the Concordia Institute of Aerospace Design and Innovation (CIADI). In this pivotal role, she also spearheads two undergraduate programs, namely Mechanical Engineering and Aerospace Engineering. She is also a senior lecturer in the Department of Mechanical, Industrial, and Aerospace Engineering at Concordia University. Dr. El Ayoubi earned her PhD. in mechanical engineering, specializing in aerospace applications, from Concordia University in 2014. With a rich background as an aerodynamics engineer at Pratt & Whitney Canada prior to her doctoral pursuits, she brings invaluable industry experience to her academic leadership. Dr. El Ayoubi is dedicated to fostering multidisciplinary teaching methods and elevating the standards of aerospace education at Concordia University. Passionate about accessibility in higher education, Dr. El Ayoubi firmly believes in making education available to all. Her enthusiasm extends to impactful outreach activities, showcasing her dedication to inspiring the next generation of aerospace professionals. Rolf Wuthrich, PhD, is a professor at the Department of Mechanical, Industrial and Aerospace Engineering as well as the Department of Chemical and Material Engineering at Concordia University. He earned his Master of Engineering Physics in high energy physics from the École Polytechnique Fédérale de Technologie de Lausanne (Switzerland) and his PhD in advanced manufacturing and electrochemistry from the same university in 2002. His current research focus is on advanced manufacturing and digital transformation in manufacturing, where he is leading a research laboratory on advanced manufacturing with a special focus on electrochemical technologies meeting the demand of Industry 4.0. He develops strategies involving real time data streaming, real time data processing and machine learning to enhance the performance of manufacturing processes and to reduce machining overhead. His teaching interests include numerical methods, modeling, and fundamental courses in mechanical engineering. He is heavily involved in the development of online teaching strategies.

1. Introduction Part I - Numerical Methods for Engineering Applications 2. Numerical Errors 3. Solving Algebraic Equations 4. Systems of Linear Equations 5. Orthogonality 6 Linear Least Square Regression 7. Polynomial Interpolation 8. Numerical Integration 9. Initial Value Problems Part II - Numerical Methods for Data Analysis 10. Machine Learning 11. Regression Models 12. Model Selection 13. Classification 14. Tree-Based Algorithms