Description
Book SynopsisThis book develops the theory of multivariable analysis, building on the single variable foundations established in the companion volume, Real Analysis: Foundations and Functions of One Variable.
Trade Review“This book develops a thorough treatment of multivariate derivatives, viewing them both as linear transformations and as partial derivatives. … The book is consistent in addressing the classical analysis of real functions of several variables. This volume will appeal to students in pure and applied mathematics, as well as scientists looking to acquire a firm footing in mathematical analysis.” (Teodora-Liliana Rădulescu, zbMATH 1407.26001, 2019)
“The explicit intent of the authors is to present material gradually, and to develop precision based on intuition with the help of well-designed examples. The book contains 600 exercises. In my opinion this interesting book represents an alternative viewpoint in real analysis.” (Zbigniew Grande, Mathematical Reviews, August, 2018)
Table of ContentsFunctions of Several Variables.- 1. R^p → R functions.- 2. R^p → R^q functions.- 3. The Jordan Measure.- 4. The Integral of Multivariable Functions I.- 5. The Integral of Multivariable Functions II.- 6. Infinite Series.- 7. Sequences and Series of Functions.- 8. Miscellaneous Topics.- 9. Hint, Solutions.- References.- Index.- Notation.
