Kyle A. Novak Libri

Numerical methods play a crucial role in scientific research, often functioning as algorithmic black boxes. Users of these methods may not fully understand their inner workings, which can lead to inaccuracies or inefficiencies in results. This book demystifies these algorithms, explaining their functionality and potential pitfalls. It fosters both an intuitive grasp of the underlying mathematical theory and the practical skills necessary for effective research. Readers will learn to be critical users and knowledgeable creators of scientific computing algorithms. This text serves as an excellent introduction for senior undergraduates and first-year graduate students, as well as a self-study resource for those familiar with multivariate calculus and linear algebra. It also acts as a modern reference for researchers. The revised edition offers a comprehensive guide to numerical methods in linear algebra, analysis, and differential equations, with detailed examples and exercises. Additionally, it features extensive commentary and code for essential scientific computing languages: Julia, Python, and Matlab/Octave. The author, an applied mathematician and data scientist with over twenty-five years of experience, has contributed significantly to various fields, including autonomous systems and cryptanalysis.