Classical analysis on normed spaces

Description

This book provides an elementary introduction to the classical analysis on normed spaces, paying special attention to nonlinear topics such as fixed points, calculus and ordinary differential equations. It is aimed at beginners who want to get through the basic material as soon as possible and then move on to do their own research immediately. It assumes only general knowledge in finite-dimensional linear algebra, simple calculus and elementary complex analysis. Since the treatment is self-contained with sufficient details, even an undergraduate with mathematical maturity should have no problem working through it alone. Various chapters can be integrated into parts of a Master degree program by course work organized by any regional university. Restricted to finite-dimensional spaces rather than normed spaces, selected chapters can be used for a course in advanced calculus. Engineers and physicists may find this book a handy reference in classical analysis. Read more... Abstract: This book provides an elementary introduction to the classical analysis of normed spaces, paying attention to non-linear topics such as fixed points, calculus and ordinary differential equations. It is aimed at beginners who want to move on to do their own research as soon as possible. Read more... Content: Ch. 1. Metric Spaces -- Ch. 2. Complete, Compact and Connected Sets -- Ch. 3. Banach Spaces -- Ch. 4. Simplicial Complexes -- Ch. 5. Topological Fixed Points -- Ch. 6. Foundation of Functional Analysis -- Ch. 7. Natural Constructions -- Ch. 8. Complex Analysis -- Ch. 9. Differentiation in Banach Spaces -- Ch. 10. Polynomials and Higher Derivatives -- Ch. 11. Ordinary Differential Equations -- Ch. 12. Compact Linear Operators -- Ch. 13. Operators on Hilbert Spaces -- Ch. 14. Spectral Properties of Hilbert Spaces -- Ch. 15. Tensor Products.