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This rigorous two-part treatment advances from functions of one variable to those of several variables. Intended for students who have already completed a one-year course in elementary calculus, it defers the introduction of functions of several variables for as long as possible, and adds clarity and simplicity by avoiding a mixture of heuristic and rigorous arguments.
The first part explores functions of one variable, including numbers and sequences, continuous functions, differentiable functions, integration, and sequences and series of functions. The second part examines functions of several variables: the space of several variables and continuous functions, differentiation, multiple integrals, and line and surface integrals, concluding with a selection of related topics. Complete solutions to the problems appear at the end of the text.
- Sales Rank: #414749 in eBooks
- Published on: 2012-10-16
- Released on: 2012-10-16
- Format: Kindle eBook
About the Author
Avner Friedman is Director of the Mathematical Biosciences Institute at Ohio State University.
Most helpful customer reviews
23 of 24 people found the following review helpful.
Good advanced calc book at a good price.
By A Buyer
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.
21 of 22 people found the following review helpful.
Very nice book
By W. Ghost
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.
4 of 4 people found the following review helpful.
Probably the best book on real analysis
By Mahmoud
Many books cover real analysis only through a single variable. This book takes it a step further by dedicating several chapters to covering the n dimensional calculus Very clear writing with detailed proofs.
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