Advanced calculus

This is a very good book -- very clear, rigorous and with good exercises. There are answers to some of the more "mechanical" kind of exercises at the end of the book. The table of contents: PART I (Functions of one variable) 1. Numbers and sequences 2. Continuous functions 3. Differentiable functions 4. Integration 5. Sequences and series of functions PART II (Functions of several variables) 6. Space of several variables and continuous functions on it 7. Differentiation 8. Multiple integrals 9. Line and surface integrals 10. Selected topics Chapter 10 covers (not extensively, of course) Euler's summation formula, asymptotic series, Fourier series, Lagrange multipliers, the divergence theorem in R^n, harmonic functions, ODE and the Riemman-Steiltjes integral.

Good starter book for advanced calculus with a good selection of topics and workable (read -> concept enforcing) problems. Nothing too tough or tricky. If you want an "advanced calculus" book, this is a bargain. The other choice would be Apostol's advanced calculus book, which is a classic, but does cost more. Of the advanced calculus books available from Dover, this is probably the one you want to buy.