Wade W.R. An Introduction to Analysis

4th Edition. — Pearson Prentice Hall, 2010. — 695 p. — ISBN 978-0-13-229638-0.For one- or two-semester junior orsenior level courses in Advanced Calculus, Analysis I, or Real Analysis. This title is part of the Pearson Modern Classicsseries. This text prepares students for future coursesthat use analytic ideas, such as real and complex analysis, partial andordinary differential equations, numerical analysis, fluid mechanics, anddifferential geometry. This book is designed to challenge advanced studentswhile encouraging and helping weaker students. Offering readability,practicality and flexibility, Wade presents fundamental theorems and ideas froma practical viewpoint, showing students the motivation behind the mathematicsand enabling them to construct their own proofs.ONE-DIMENSIONAL THEORY
The Real Number System
Sequences in R
Functions on R
Differentiability on R
Integrability on R
Infinite Series of Real Numbers
Infinite Series of Functions
MULTIDIMENSIONAL THEORY
Euclidean Spaces
Convergence in Rn
Metric Spaces
Differentiability on Rn
Integration on Rn
Fundamental Theorems of Vector Calculus
Fourier Series
Appendices