A Companion to Analysis: A Second First and First Second Course in Analysis
T W Körner
Price
2450
ISBN
9780821868782
Language
English
Pages
608
Format
Paperback
Dimensions
180 x 240 mm
Year of Publishing
2011
Territorial Rights
Restricted
Imprint
American Mathematical Society
Catalogues

Many students acquire knowledge of a large number of theorems and methods of calculus without being able to say how they work together. This book provides those students with the coherent account that they need. A Companion to Analysis explains the problems that must be resolved in order to procure a rigorous development of the calculus and shows the student how to deal with those problems.

Starting with the real line, the book moves on to finite-dimensional spaces and then to metric spaces. Readers who work through this text will be ready for courses such as measure theory, functional analysis, complex analysis, and differential geometry. Moreover, they will be well on the road that leads from mathematics student to mathematician.

With this book, well-known author Thomas Körner provides able and hard-working students a great text for independent study or for an advanced undergraduate or first-level graduate course. It includes many stimulating exercises. An appendix contains a large number of accessible but non-routine problems that will help students advance their knowledge and improve their technique.

T W Körner, University of Cambridge, England.

  1. The real line
  2. A first philosophical interlude
  3. Other versions of the fundamental axiom
  4. Higher dimensions
  5. Sums and suchlike $\heartsuit$
  6. Differentiation
  7. Local Taylor theorems
  8. The Riemann integral
  9. Developments and limitations of the Riemann integral $\heartsuit$
  10. Metric spaces
  11. Complete metric spaces
  12. Contraction mappings and differential equations
  13. Inverse and implicit functions
  14. Completion
Appendices
Executive summary
Exercises
Bibliography
Index