Many applied mathematical disciplines, such as dynamical systems and optimization theory as well as classical mathematical disciplines like differential geometry and the theory of Lie groups, have a common foundation in general topology and multivariate calculus in normed vector spaces. In this book, students from both pure and applied subjects are offered an opportunity to work seriously with fundamental notions from mathematical analysis that are important not only from a mathematical point of view but also occur frequently in the theoretical parts of, for example, the engineering sciences. The book provides complete proofs of the basic results from topology and differentiability of mappings in normed vector spaces. It is a useful resource for students and researchers in mathematics and the many sciences that depend on fundamental techniques from mathematical analysis.In this second edition, the notions of compactness and sequentially compactness are developed with independent proofs for the main results. Thereby the material on compactness is apt for direct applications also in functional analysis, where the notion of sequentially compactness prevails. This edition also covers a new section on partial derivatives, and new material has been incorporated to make a more complete account of higher order derivatives in Banach spaces, including full proofs for symmetry of higher order derivatives and Taylor's formula. The exercise material has been reorganized from a collection of problem sets at the end of the book to a section at the end of each chapter with further results. Readers will find numerous new exercises at different levels of difficulty for practice.

This textbook provides a thorough introduction to Newtonian Mechanics and is intended for university students in physics, astronomy and engineering. It is based on a course for which Dr. Knudsen earned an award for the best teaching at the University of Copenhagen, Denmark. More than 100 problems with solutions and 89 worked examples help the student to grasp the essential aspects of the subject, and to develop proficiency in using the powerful methods of Newtonian mechanics. Moreover, the fundamental problem of motion and the concept of inertial frames is faced from the very beginning, and runs through the entire development of classical mechanics. This new and fresh approach is presented in its third edition, which has been revised and enlarged.