Methodical system of studying of continuous functions

The article identifies the problems, analyzes their causes, presents methodological approaches to the study of the continuity of the function, knowledge of which has a significant impact on both the mathematical and methodological training of future specialists. The formation of intuitivevisual representations is a primary task for mastering the concept of continuity. Assessment of the level of mastering of concepts should be conducted, basically, not by the ability to reproduce the definitions of the continuity of a function at a point, but at the level of identification.

Methodical system of studying of continuous functions

The article identifies the problems, analyzes their causes, presents methodological approaches to the study of the continuity of the function, knowledge of which has a significant impact on both the mathematical and methodological training of future specialists. The formation of intuitivevisual representations is a primary task for mastering the concept of continuity. Assessment of the level of mastering of concepts should be conducted, basically, not by the ability to reproduce the definitions of the continuity of a function at a point, but at the level of identification.

___

  • 1. Sinkevich G.I. Uliss Dini i ponyatie nepreryvnosti // Istoriya nauki I tekhniki. – (2012) № 10. – 3–11 pp.
  • 2. Il'in V.A., Poznjak Je.G. Osnovy matematicheskogo analiza: ucheb. dlja vuzov: v 2 ch. Ch. 1, 7-e izd. stereotip. (Kurs vysshej matematiki i matematicheskoj fiziki), Fizmatlit, Moscow, (2005) 648 p.
  • 3. Il'in V.A., Sadovnichij V.A. ,Sendov B.H. Matematicheskij analiz: ucheb. dlja bakalavrov: v 2 ch. Ch. 1, 4-e izd, Jurajt, Moscow, (2013) 660 p.
  • 4. Maron I.A. (2008). Differencial'noe i integral'noe ischislenie v primerah i zadachah. Funkcii odnoj peremennoj: ucheb. posobie dlja vuzov, 3-e izd., stereotip, Lan', St. Petersburg, 399 p.
  • 5. William F. Trench, (2013). Introduction to real analysis, San Antonio, Texas, USA, 586 p.
  • 6. Andrew M. Bruckner, Judith B. Bruckner, Brian S. Thomson, (2008). Classical RealAnalysis. Second Edition com, xiv 656 pp.
  • 7. Keneth A. Ross, (2013). Elementary Analysis, The Theory of Calculus Springer New York Heidelberg Dordrecht London, 409 p.
  • 8. Robert S. Strichartz, (2000). The Way of Analysis, Boston, MA : Jones and Bartlett Publishers, 739 p.
  • 9. Walter Rudin, (1976). Principles of Mathematical Analysis, McGraw-Hill, 351 p.
  • 10. Marcel B. Finan, (2009). An Introductory Single Variable Real Analysis: A Learning Approach through Problem Solving, 157 p.
  • 11. Stephen Abbott, (2001). Understanding Analysis, Springer-Verlag, New York, 543 p.
  • 12. Tom M. Apostol, (1981). Mathematical Analysis, Addison-Wesley publishing kompany, Amsterdam, London, Manila, Singapore, Sidney, Tokyo, 256 p.
  • 13. Peter L. Duren, (2012). Invitation to Classical Analysis, American Mathematical Society, 392 p.
  • 14. William Dunham, (2004). The Calculus Gallery, Princeton University Press, 256 p.
  • 15. Thomas W. Korner, (2004). A Companion to Analysis, American Mathematical Society, 623 p.
  • 16. Jerrold E. Marsden & Michael J. Hoffman, (1993). Elementary Classical Analysis, New York, N.Y.: W. H. Freeman, 738 p.