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Introductory Analysis

The Theory of Calculus

Introductory Analysis, Second Edition, is intended for the standard course on calculus limit theories that is taken after a problem solving first course in calculus (most often… Read more

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Description

Introductory Analysis, Second Edition, is intended for the standard course on calculus limit theories that is taken after a problem solving first course in calculus (most often by junior/senior mathematics majors). Topics studied include sequences, function limits, derivatives, integrals, series, metric spaces, and calculus in n-dimensional Euclidean space

Key features

  • Bases most of the various limit concepts on sequential limits, which is done first
  • Defines function limits by first developing the notion of continuity (with a sequential limit characterization)
  • Contains a thorough development of the Riemann integral, improper integrals (including sections on the gamma function and the Laplace transform), and the Stieltjes integral
  • Presents general metric space topology in juxtaposition with Euclidean spaces to ease the transition from the concrete setting to the abstract

New to This Edition

  • Contains new Exercises throughout
  • Provides a simple definition of subsequence
  • Contains more information on function limits and L'Hospital's Rule
  • Provides clearer proofs about rational numbers and the integrals of Riemann and Stieltjes
  • Presents an appendix lists all mathematicians named in the text
  • Gives a glossary of symbols

Readership

Researchers, professionals, the general public, and librarians who want to expand or enhance their knowledge of calculus limit theories

Table of contents

Introduction: Mathematical Statements and Proofs
Ordering of the Real Numbers
Sequence Limits
Completeness of the Real Numbers
Continuous Functions
Consequences of Continuity
The Derivative
The Riemann Integral
Improper Integrals
Infinite Series
The Riemann-Stieltjes Integral
Function Sequences
Power Series
Metric Spaces and Euclidean Spaces
Continuous Transformations
Differential Calculus in Euclidean Spaces
Area and Integration in E²

Appendix
A. Mathematical Induction
B. Countable and Uncountable Sets
C. Infinite Products

Product details

About the author

JF

John A. Fridy

Affiliations and expertise
Kent State University, Ohio, U.S.A.