First Course in Real Analysis
Edition: 2nd 1991 (Revised)
List price: $74.95
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This book is designed for a first course in real analysis following the standard course in elementary calculus. Since many students encounter rigorous mathematical theory for the first time in this course, the authors have included such elementary topics as the axioms of algebra and their immediate consequences as well as proofs of the basic theorems on limits. The pace is deliberate, and the proofs are detailed. The emphasis of the presentation is on theory, but the book also contains a full treatment (with many illustrative examples and exercises) of the standard topics in infinite series, Fourier series, multidimensional calculus, elements of metric spaces, and vector field theory. There are many exercises that enable the student to learn the techniques of proofs and the standard tools of analysis.In this second edition, improvements have been made in the exposition, and many of the proofs have been simplified. Additionally, this new edition includes an assortment of new exercises and provides answers for the odd-numbered problems.
List price: $74.95
Copyright year: 1991
Publication date: 3/7/1997
Size: 6.50" wide x 9.75" long x 1.25" tall
|The Real Number System|
|Continuity and Limits|
|Basic Properties of Functions on R|
|Elementary Theory of Differentiation|
|Elementary Theory of Integration|
|Elementary Theory of Metric Spaces|
|Differentiation in R|
|Integration in R|
|Infinite Sequences and Infinite Series|
|Functions Defined by Integrals; Improper Integrals|
|The Riemann-Stieltjes Integral and Functions of Bounded Variation|
|Contraction Mappings, Newton's Method, and Differential Equations|
|Implicit Function Theorems and Lagrange Multipliers|
|Functions on Metric Spaces; Approximation|
|Vector Field Theory; the Theorems of Green and Stokes|