Introduction to Numerical Mathematics: Theory, Practice and Numerous Examples (Mathematics Study Resources, 25)

This textbook presents the theoretical foundations of numerical mathematics in a modern, application-oriented, and comprehensive way.In addition to the standard content, it includes numerous examples and practical excursions to sustainably enhance understanding.Proofs are presented in a very detailed, step-by-step manner.The recurring core concepts of numerical mathematics like accuracy, efficiency, robustness and stability are explicitly addressed and clearly distinguished from one another.Specific example calculations for the described algorithms are carried out using provided Python codes.Numerical modeling for aspects of machine learning and neural networks are taken into consideration.Furthermore, numerical methods from linear algebra and analysis are presented separately, which significantly facilitates students’ access to numerical mathematics - based on the two main lectures within undergraduate studies in mathematics.Therefore, the book is ideally suited for students of mathem