Many advanced mathematical disciplines, such as dynamical systems, calculus of variations, differential geometry and the theory of Lie groups, have a common foundation in general topology and calculus in normed vector spaces. In this book, mathematically inclined engineering students are offered an opportunity to go into some depth with fundamental notions from mathematical analysis that are not only important from a mathematical point of view but also occur frequently in the more theoretical parts of the engineering sciences. The book should also appeal to university students in mathematics and in the physical sciences.
Sample Chapter(s)
Chapter 1: Basic concepts in topology (1,887 KB)
Contents:
- Basic Concepts in Topology
- Differentiation in Normed Vector Spaces
- The Inverse Function Theorem
- Differentiable Manifolds
- An Introduction to Singularity Theory
- An Introduction to Geometric Variational Problems
Readership: Lecturers and students in pure mathematics, theoretical engineering and the physical sciences.
