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Look Inside Elementary Real Analysis

Elementary Real Analysis

  • Date Published: December 2008
  • availability: Available
  • format: Paperback
  • isbn: 9780521098687


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About the Authors
  • This textbook covers all the theoretical aspects of real variable analysis which undergraduates reading mathematics are likely to require during the first two or three years of their course. It is based on lecture courses which the author has given in the universities of Wales, Cambridge and London. The subject is presented rigorously and without padding. Definitions are stated explicitly and the whole development of the subject is logical and self-contained. Complex numbers are used but the complex variable calculus is not. 'Applied analysis', such as differential equations and Fourier series, is not dealt with. A large number of examples is included, with hints for the solution of many of them. These will be of particular value to students working on their own.

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    Product details

    • Date Published: December 2008
    • format: Paperback
    • isbn: 9780521098687
    • length: 296 pages
    • dimensions: 216 x 140 x 17 mm
    • weight: 0.38kg
    • availability: Available
  • Table of Contents

    Notation and Conventions
    1. Enumerability and sequences
    2. Bounds for sets of numbers
    3. Bounds for functions and sequences
    4. Limits of the sequences
    5. Monotonic sequences
    two important examples
    irrational powers of positive real numbers
    6. Upper and lower limits of real sequences: the general principle of convergence
    7. Convergence of series
    absolute convergence
    8. Conditional convergence
    9. Rearrangement and multiplication of absolutely convergent series
    10. Double series
    11. Power series
    12. Point set theory
    13. The Bolzano-Weierstrass, Cantor and Heine-Borel theorems
    14. Functions defined over real or complex numbers
    15. Functions of a single real variable
    limits and continuity
    16. Monotonic functions
    functions of bounded variation
    17. Differentiation
    mean-value theorems
    18. The nth mean-value theorem: Taylor's theorem
    19. Convex and concave functions
    20. The elementary transcendental functions
    21. Inequalities
    22 The Riemann integral
    23. Integration and differentiation
    24. The Riemann-Stiltjes integral
    25. Improper integrals
    convergence of integrals
    26. Further tests for the convergence of series
    27. Uniform convergence
    28. Functions of two real variables. Continuity and differentiability
    Hints on the solution of exercises and answers to exercises

  • Author

    H. G. Eggleston

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