Skip to main content

Abstract

The set ℝ of all real numbers can be characterized by axioms. (The real numbers can also be constructed by successively extending the domains of the natural numbers ℕ, the integers ℤ, and the rational numbers ℚ. We cannot go into this approach.)

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

3.1 Differential and integral calculus

  1. T. Apostol, Mathematical analysis, Addison-Wesley, Reading, MA, 1957.

    MATH  Google Scholar 

  2. T. Apostol, Calculus, 2 vols., Blaisdell, New York, 1961.

    Google Scholar 

  3. R. G. Bartle, The elements of real analysis, Wiley, New York-London, 1964.

    Google Scholar 

  4. J. C. Burkill, A first course in mathematical analysis, Cambridge University Press, Cambridge, 1962.

    MATH  Google Scholar 

  5. R. Courant, Differential and integral calculus (translated from the German), 2 vols., Blackie and Son, Glasgow, 1945.

    Google Scholar 

  6. H. G. Eggleston, Elementary real analysis, Cambridge University Press, Cambridge, 1962.

    Google Scholar 

  7. T. M. Flett, Mathematical analysis, McGraw-Hill, London, 1966.

    MATH  Google Scholar 

  8. E. W. Hobson, The theory of functions of a real variable and the theory of Fourier’s series, 2 vols., reprint, Dover, New York, 1957.

    Google Scholar 

  9. K. Knopp, Theory and application of infinite series (translated from the German), Hafner, New York, 1951.

    MATH  Google Scholar 

  10. S. Lang, Analysis. I, Addison-Wesley, Reading, MA, 1968.

    MATH  Google Scholar 

  11. A. S.-T. Lue, Basic pure mathematics, II, Van Nostrand Reinhold, New York-London, 1974.

    Google Scholar 

  12. D. B. Scott and S. R. Tims, Mathematical analysis, Cambridge University Press, Cambridge, 1966.

    MATH  Google Scholar 

  13. G. L. Simmons, Introduction to topology and modern analysis, McGraw-Hill, New York-London, 1963.

    MATH  Google Scholar 

  14. M. Spivak, Calculus, Addison-Wesley, Reading, MA, 1973.

    Google Scholar 

  15. E. T. Whittaker and G. N. Watson, Modern analysis, 6th ed., Cambridge University Press, Cambridge, 1957.

    Google Scholar 

3.2 Calculus of variations and optimal processes

  1. R. Courant, Differential and integral calculus (translated from the German), vol. 2, Blackie and Son, Glasgow, 1945.

    Google Scholar 

  2. R. Courant and D. Hilbert, Methods of mathematical physics (translated from the German), vol. 1, Wiley, New York-London, 1953.

    Google Scholar 

  3. I. Gumowski and C. Mira, Optimization in control theory and practice, Cambridge University Press, Cambridge, 1968.

    MATH  Google Scholar 

  4. H. and B. S. Jeffreys, Methods of mathematical physics, Cambridge University Press, Cambridge, 1946.

    MATH  Google Scholar 

  5. A. G. J. MacFarlane, Dynamical system models, Harrap, London, 1970.

    MATH  Google Scholar 

  6. L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko, The mathematical theory of optimal processes (translated from the Russian), Wiley, New York-London, 1962.

    MATH  Google Scholar 

  7. G. Stephenson, Inequalities and optimal problems in mathematics and the sciences, Longman, London, 1971.

    MATH  Google Scholar 

3.3 Differential equations

  1. T. Apostol, Calculus, 2 vols., Blaisdell, New York, 1961.

    Google Scholar 

  2. J. C. Burkill, The theory of ordinary differential equations, Oliver and Boyd, Edinburgh-London, 1962.

    MATH  Google Scholar 

  3. R. Courant, Differential and integral calculus (translated from the German), 2 vols., Blackie, Glasgow, 1945.

    Google Scholar 

  4. R. Courant and D. Hilbert, Methods of mathematical physics (translated from the German), vol. 2, Wiley, New York-London, 1953.

    Google Scholar 

  5. B. Friedman, Principles and techniques of applied mathematics, Wiley, New York-London, 1956.

    MATH  Google Scholar 

  6. S. H. Gould, Variational methods for eigenvalue problems, University of Toronto Press, Toronto, 1957.

    MATH  Google Scholar 

  7. E. L. Ince, Ordinary differential equations (reprint), Dover, New York, 1956.

    Google Scholar 

  8. A. Jeffrey, Mathematics for engineers and scientists, 2nd ed., Van Nostrand Reinhold, New York-London, 1979.

    Google Scholar 

  9. H. and B. S. Jeffreys, Methods of mathematical physics, Cambridge University Press, Cambridge, 1946.

    MATH  Google Scholar 

  10. S. Lang, Analysis, I, Addison-Wesley, Reading, MA, 1968.

    MATH  Google Scholar 

  11. P. M. Morse and H. Feshbach, Methods of theoretical physcs, I, McGraw-Hill, New York-London, 1953.

    Google Scholar 

  12. G. E. H. Reuter, Elementary differential equations and operators, Routledge-Kegan Paul, London, 1958.

    Google Scholar 

  13. Sommerfeld, A., Partial differential equations in physics (translated from the German), Academic Press, New York-London, 1967.

    Google Scholar 

  14. G. N. Watson, A treatise on the theory of Bessel functions, 2nd ed., Cambridge University Press, Cambridge, 1944.

    MATH  Google Scholar 

  15. A. J. White, Real analysis: an introduction, Addison-Wesley, Reading, MA, 1968.

    MATH  Google Scholar 

  16. E. T. Whittaker and G. N. Watson, Modern analysis, 6th ed., Cambridge University Press, Cambridge, 1957.

    Google Scholar 

3.4 Theory of functions of a complex variable

  1. L. V. Ahlfors, Complex analysis, McGraw-Hill, New York-London, 1953.

    MATH  Google Scholar 

  2. T. M. Apostol, Mathematical analysis, Addison-Wesley, Reading, MA, 1957.

    MATH  Google Scholar 

  3. C. Carathéodory, Theory of functions of a complex variable (translated from the German), 2 vols., Chelsea, New York, 1954.

    Google Scholar 

  4. E. T. Copson, An introduction to the theory of functions of a complex variable, Oxford University Press, Oxford, 1935.

    Google Scholar 

  5. H. and B. S. Jeffreys, Methods of mathematical physics, Cambridge University Press, Cambridge, 1946.

    MATH  Google Scholar 

  6. K. Knopp, Theory of functions (translated from the German), 2 vols., Dover, New York, 1947.

    Google Scholar 

  7. N. W. McLachlan, Complex variable theory and transform calculus (with technical applications), 2nd ed., Cambridge University Press, Cambridge, 1963.

    Google Scholar 

  8. E. G. Phillips, Functions of a complex variable, Oliver and Boyd, Edinburgh, 1940.

    MATH  Google Scholar 

  9. W. Rudin, Real and complex analysis, McGraw-Hill, New York-London, 1970.

    Google Scholar 

  10. E. C. Titchmarsh, The theory of functions, Oxford University Press, Oxford, 1939.

    MATH  Google Scholar 

  11. E. T. Whittaker and G. N. Watson, Modern analysis, 6th ed., Cambridge University Press, Cambridge, 1957.

    Google Scholar 

Download references

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1979 Springer Fachmedien Wiesbaden

About this chapter

Cite this chapter

Bronshtein, I.N., Semendyayev, K.A. (1979). Analysis. In: Handbook of Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-25651-0_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-25651-0_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-23574-4

  • Online ISBN: 978-3-662-25651-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics