A companion to analysis : a second first and first second course in analysis / T.W. Körner.

Includes bibliographical references (p. 583-584) and index.

Ch. 1. The Real Line -- Ch. 2. A First Philosophical Interlude -- Ch. 3. Other Versions of the Fundamental Axiom -- Ch. 4. Higher Dimensions -- Ch. 5. Sums and Suchlike -- Ch. 6. Differentiation -- Ch. 7. Local Taylor Theorems -- Ch. 8. The Riemann Integral -- Ch. 9. Developments and Limitations of the Riemann Integral -- Ch. 10. Metric Spaces -- Ch. 11. Complete Metric Spaces -- Ch. 12. Contraction Mappings and Differential Equations -- Ch. 13. Inverse and Implicit Functions -- Ch. 14. Completion -- App. A. Ordered Fields -- App. B. Countability -- App. C. The Care and Treatment of Counterexamples -- App. D. A More General View of Limits -- App. E. Traditional Partial Derivatives -- App. F. Another Approach to the Inverse Function Theorem -- App. G. Completing Ordered Fields -- App. H. Constructive Analysis.

"Many students acquire knowledge of a large number of theorems and methods of calculus without being able to say how they hang together. This book provides such students with the coherent account that they need. A Companion to Analysis explains the problems which must be resolved in order to obtain a rigorous development of the calculus and shows the student how those problems are dealt with. Starting with the real line, it moves on to finite dimensional spaces and then to metric spaces. Readers who work through this text will be ready for such courses as measure theory, functional analysis, complex analysis and differential geometry. Moreover, they will be well on the road which leads from mathematics student to mathematician." "Able and hard working students can use this book for independent study, or it can be used as the basis for an advanced undergraduate or elementary graduate course. An appendix contains a large number of accessible but non-routine problems to improve knowledge and technique."--BOOK JACKET.