publication . Preprint . 2015

Early Transcendental Analysis

Cowell, Simon; Poulin, Philippe;
Open Access English
  • Published: 10 Jun 2015
Abstract
In Early Transcendentals (The American Mathematical Monthly, Vol. 104, No 7) Steven Weintraub presents a rigorous justifcation of the "early transcendental" calculus textbook approach to the exponential and logarithmic functions. However, he uses tools such as term-by-term differentiation of infinite series. We present a rigorous treatment of the early transcendental approach suitable for a first course in analysis, using mainly the supremum property of the real numbers.
Subjects
free text keywords: Mathematics - History and Overview
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32 references, page 1 of 3

[1] R. P. Agnew, Calculus - Analytic Geometry and Calculus, with Vectors, McGraw-Hill, 1962

[2] Bartle R. G. and Sherbert D. R., Introduction to Real Analysis, 3rd Edition, Wiley, 2000

[3] J. C. Burkill, A First Course in Mathematical Analysis, Vikas Publishing House PVT Ltd., 1979

[4] J. C. Burkill and H. Burkill, A Second Course in Mathematical Analysis, Cambridge University Press, 1980

[5] C. W. Burrill and J. R. Knudsen, Real Variables, Holt, Rinehart and Winston, Inc., 1969

[6] R. Cooper, Functions of Real Variables - A Course of Advanced Calculus, D. Van Nostrand Co., 1966

[7] Richard Courant , Differential and Integral Calculus Volume I, Wiley and Sons, 1968

[8] Richard Courant and Fritz John, Introduction to Calculus and Analysis Volume I, Interscience Publishers, 1965

[9] C. H. Edwards, The Historical Development of the Calculus, Springer-Verlag, 1979

[10] Watson Fulks, Advanced Calculus, 2nd Edition, Wiley and Sons, 1969

[11] Edward D. Gaughan, Introduction to Analysis, 4th Edition, Brooks / Cole, 1993

[12] Edward D. Gaughan, Introduction to Analysis, 5th Edition, Brooks / Cole, 1998

[13] Herbert S. Gaskill and P. P. Narayanaswami, Foundations of Analysis - the Theory of Limits, Harper and Row, 1989

[14] Richard R. Goldberg, Methods of Real Analysis, 2nd Edition, Wiley and Sons, 1976

[15] Larry J. Goldstein, David C. Lay and David I. Schneider, Calculus and its Applications, 5th Edition, Prentice-Hall International, 1990

32 references, page 1 of 3
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