A Concise Approach to Mathematical Analysis

A Concise Approach to Mathematical Analysis by Mangatiana A. Robdera.

A Concise Approach to Mathematical Analysis introduces the undergraduate student to the more abstract concepts of advanced calculus. The main aim of the book is to smooth the transition from the problem-solving approach of standard calculus to the more rigorous approach of proof-writing and a deeper...

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Bibliographic Details
Main Author: Robdera, Mangatiana A. (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: London : Springer London : Imprint: Springer, 2003.
Edition:1st ed. 2003.
Series:Springer eBook Collection.
Subjects:
Mathematical analysis.
Analysis (Mathematics).
Functions of real variables.
Difference equations.
Functional equations.
Fourier analysis.
Sequences (Mathematics).
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • Numbers and Functions
  • Real Numbers
  • Subsets of ?
  • Variables and Functions
  • Sequences
  • Definition of a Sequence
  • Convergence and Limits
  • Subsequences
  • Upper and Lower Limits
  • Cauchy Criterion
  • 3. Series
  • Infinite Series
  • Conditional Convergence
  • Comparison Tests
  • Root and Ratio Tests
  • Further Tests
  • 4. Limits and Continuity
  • Limits of Functions
  • Continuity of Functions
  • Properties of Continuous Functions
  • Uniform Continuity
  • Differentiation
  • Derivatives
  • Mean Value Theorem
  • L'Hôspital's Rule
  • Inverse Function Theorems
  • Taylor's Theorem
  • Elements of Integration
  • Step Functions
  • Riemann Integral
  • Functions of Bounded Variation
  • Riemann-Stieltjes Integral
  • Sequences and Series of Functions
  • Sequences of Functions
  • Series of Functions
  • Power Series
  • Taylor Series
  • Local Structure on the Real Line
  • Open and Closed Sets in ?
  • Neighborhoods and Interior Points
  • Closure Point and Closure
  • Completeness and Compactness
  • Continuous Functions
  • Global Continuity
  • Functions Continuous on a Compact Set
  • Stone—Weierstrass Theorem
  • Fixed-point Theorem
  • Ascoli-Arzelà Theorem
  • to the Lebesgue Integral
  • Null Sets
  • Lebesgue Integral
  • Improper Integral
  • Important Inequalities
  • Elements of Fourier Analysis
  • Fourier Series
  • Convergent Trigonometric Series
  • Convergence in 2-mean
  • Pointwise Convergence
  • A. Appendix
  • A.1 Theorems and Proofs
  • A.2 Set Notations
  • A.3 Cantor's Ternary Set
  • A.4 Bernstein's Approximation Theorem
  • B. Hints for Selected Exercises.

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