Description

Book Synopsis

It provides a transition from elementary calculus to advanced courses in real and complex function theory and introduces the reader to some of the abstract thinking that pervades modern analysis.



Table of Contents


1. The Real and Complex Number Systems.


2. Some Basic Notions of Set Theory.


3. Elements of Point Set Topology.


4. Limits and Continuity.


5. Derivatives.


6. Functions of Bounded Variation and Rectifiable Curves.


7. The Riemann-Stieltjes Integral.


8. Infinite Series and Infinite Products.


9. Sequences of Functions.


10. The Lebesgue Integral.


11. Fourier Series and Fourier Integrals.


12. Multivariable Differential Calculus.


13. Implicit Functions and Extremum Problems.


14. Multiple Riemann Integrals.


15. Multiple Lebesgue Integrals.


16. Cauchy's Theorem and the Residue Calculus.

Mathematical Analysis

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    A Paperback by Tom M. Apostol

    £999.99

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      Book details

      Publisher Pearson Education
      Published 1 January 1974
      ISBN-13 9780201002881
      978-0201002881
      ISBN-10 0201002884
      Also in:
      Calculus

      Description

      Book Synopsis

      It provides a transition from elementary calculus to advanced courses in real and complex function theory and introduces the reader to some of the abstract thinking that pervades modern analysis.



      Table of Contents


      1. The Real and Complex Number Systems.


      2. Some Basic Notions of Set Theory.


      3. Elements of Point Set Topology.


      4. Limits and Continuity.


      5. Derivatives.


      6. Functions of Bounded Variation and Rectifiable Curves.


      7. The Riemann-Stieltjes Integral.


      8. Infinite Series and Infinite Products.


      9. Sequences of Functions.


      10. The Lebesgue Integral.


      11. Fourier Series and Fourier Integrals.


      12. Multivariable Differential Calculus.


      13. Implicit Functions and Extremum Problems.


      14. Multiple Riemann Integrals.


      15. Multiple Lebesgue Integrals.


      16. Cauchy's Theorem and the Residue Calculus.

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