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M H Protter

A first course in real analysis : second edition - 2nd ed. - USA: Springer- Verlag, [c1991] - 534 p. - Undergraduate Texts in Mathematics .

Ch 1. The Real Number System
Ch 2. Continuity and Limits
Ch 3. Basic Properties of Functions on ℝ1
Ch 4. Elementary Theory of Differentiation
Ch 5. Elementary Theory of Integration
Ch 6. Elementary Theory of Metric Spaces
Ch 7. Differentiation in ℝN
Ch 8. Integration in ℝN
Ch 9. Infinite Sequences and Infinite Series
Ch 10. Fourier Series
Ch 11. Functions Defined by Integrals; Improper Integrals
Ch 12. The Riemann—Stieltjes Integral and Functions of Bounded Variation
Ch 13. Contraction Mappings, Newton’s Method, and Differential Equations
Ch 14. Implicit Function Theorems and Lagrange Multipliers
Ch 15. Functions on Metric Spaces; Approximation
Ch 16. Vector Field Theory; the Theorems of Green and Stokes

Many changes have been made in this second edition of A First Course in Real Analysis. The most noticeable is the addition of many problems and the inclusion of answers to most of the odd-numbered exercises. The book's readability has also been improved by the further clarification of many of the proofs, additional explanatory remarks, and clearer notation. --- summary provided by publisher

ISBN: 9789624300130

LC Class. No.: QA300.P