A Web Page in Real Analysis
by Michael W. Botsko

My publications | Publications citing my work | Links

This will be an ongoing web page in the area of undergraduate Real Analysis. I am a professor of mathematics at Saint Vincent College and chairman of the Mathematics Department. My main interest lies in the area of Real Analysis where I have published the following papers in The American Mathematical Monthly, Mathematics Magazine, and in The Real Analysis Exchange.

 

M. W. Botsko and R. Gosser, On the Differentiability of Functions of Several Variables, The American Mathematical Monthly, 92 (1985), 663-665.

M. W. Botsko and R. Gosser, Stronger Versions of the Fundamental Theorem of Calculus, The American Mathematical Monthly, 93 (1986), 294-296.

M. W. Botsko, A First Derivative Test for Functions of Several Variables, The American Mathematical Monthly, 93 (1986), 558-561.

M. W. Botsko, An Easy Generalization of the Riemann Integral, The American Mathe-matical Monthly, 93 (1986), 728-732.

M. W. Botsko, A Unified Treatment of Various Theorems in Elementary Analysis, The American Mathematical Monthly, 94 (1987), 450-452.

M. W. Botsko, An Elementary Proof that a Bounded a.e. Continuous Function is Riemann Integrable, The American Mathematical Monthly, 95 (1988), 24-252.

M. W. Botsko, The Use of Full Covers in Real Analysis, The American Mathematical Monthly, 96 (1989), 328-333.*

Michael W. Botsko, Jean-Pierre Grivauz, Marcin E. Kuczma, Solution to Problem E3329, The American Mathematical Monthly, 98 (1991), 267-268.

M. W. Botsko, A Fundamental Theorem of Calculus that Applies to all Riemann Integrable Functions, Mathematics Magazine, 64 (1991), 347-348.

M. W. Botsko, When is the Product of Two Derivatives a Derivative?, Mathematics Magazine, 65 (1992), 186-187.

Michael W. Botsko, A Simple Proof of the Derivative of the Indefinite Riemann-Complete Integral, The Real Analysis Exchange, 28(1) (2002/2003), 215-220.

Michael W. Botsko, An Elementary Proof of Lebesgue's Differentiation Theorem, The American Mathematical Monthly, 110 (2003), 834-838.

Michael W. Botsko, Q943 and A943, Mathematics Magazine, 77 No. 4, (2004), 321 and 326-327.

Michael W. Botsko, Q953 and A953, Mathematics Magazine, 78 No. 4, (2005), 324 and 328.

 Michael W. Botsko, Proposed Problem 11207, The American Mathematical Monthly, 113 (2006), 180.

Michael W. Botsko, Q960 and A960, Mathematics Magazine, 79 No. 2, (2006), 151 and 155.

Michael W. Botsko, Q961 and A961, Mathematics Magazine, 79 No. 3, (2006), 219 and 226.

Michael W. Botsko, Proposed Problem 11232, The American Mathematical Monthly, 113 (2006), 567.

Michael W. Botsko, Q966 and A966, Mathematics Magazine, 79 No. 5, (2006), 394 and 399.

Michael W. Botsko, Solution to Problem 11166, The American Mathematical Monthly, 114 (2007), 83.

Michael W. Botsko, Q967 and A967, Mathematics Magazine, 80 No. 1, (2007), 78 and 82.

Michael W. Botsko, Problem 1766, Mathematics Magazine, 80 No. 2, (2007), 145.

Michael W. Botsko, Exactly Which Bounded Darboux Functions Are Derivatives?, The American Mathematical Monthly, 114 No. 3, (2007), 242-246.

Michael W. Botsko, Q971 and A971, Mathematics Magazine, 80 No. 3, (2007), 231 and 236.

Michael W. Botsko, Q975 and A975, Mathematics Magazine, 80 No. 5, (2007), 393 and 398.

Michael W. Botsko, Problem 1788, Mathematics Magazine, 81 No. 1, (2008), 63.

Michael W. Botsko, Q977 and A977, Mathematics Magazine, 81 No. 1, (2008), 64 and 68.

Michael W. Botsko, Q979 and A979, Mathematics Magazine, 81 No. 2, (2008), 156 and 161.

Michael W. Botsko, Q982 and A982, Mathematics Magazine, 81 No. 3, (2008), 221 and 226.

Michael W. Botsko, Problem 2003, Mathematics Magazine, 81 No. 4, (2008), 304.

Michael W. Botsko, Q990 and A990, Mathematics Magazine, 82 No. 2, (2009), 148 and 152.

Michael W. Botsko, Q991 and A991, Mathematics Magazine, 82 No. 3, (2009), 228 and 232.

Michael W. Botsko, Q993 and A993, Mathematics Magazine, 82 No. 4, (2009), 311 and 316.

Michael W. Botsko, Q996 and A996, Mathematics Magazine, 82 No. 5, (2009), 383 and 390.

*This article was translated and published in a Chinese journal of Mathematics.

In addition I wrote the following text which is basically the two semester Real Analysis course that I have taught at Saint Vincent College for the past ten years.

M. W. Botsko, An Invitation to Real Analysis, 3rd Edition, Eadmer Press, Greensburg, PA, 2004.

 

Below are some articles and texts I enjoyed reading which are related to my work and have cited some of my papers.

Solomon Leader, A Concept of Differential Based on Variational Equivalence under Generalized Riemann Integration, Real Analysis Exchange, 12, No. 1, (1986-87) 144-175.

D. Rutledge and R. Worth, A Comparison of two generalizations of the Riemann integral, Real Analysis Exchange, 13, No. 2, (1987-88) 432-435.

Charles Swartz and Brian S. Thomson, More on the Fundamental Theorem of Calculus, The American Mathematical Monthly, 95, No. 7 (1988) 644-648.

R. Vyborny  and R. Nester, First derivative tests for extrema, Int. J. Math. Educ. Sci. Technol., 1989, Vol. 20, No. 5 (1989) 755-762.

Charles Swartz, Even more on the Fundamental Theorem of Calculus, Proyecciones, 12, No. 2 (1993) 129-135.

Rudolf Výborný, Some applications of Kurzweil-Henstock integration, Mathematica Bohemica, Vol. 118 (1993), No. 4, 425–441.

D. J. Jeffrey, The Importance of Being Continuous, Mathematics Magazine, 67, No. 4 (1994) 294-300.

R. Vyborny, Existence of a Potential by Kurzweil-Henstock Integration, Proc. Centre Math. Appl. Austral. Nat. Univ. Nat. Univ., Canberra, 1994, 251-257.

Hubert Kalf, A Simple Proof that a bounded a.e. Continuous Function is Riemann Integrable, Classroom notes, (Received 22 August 1994) 628-631.

R. P. Boas, A Primer of Real Functions, 4th ed., Mathematical Association of America, Washington, D. C., 1996.

J. Klippert, Further Generalizations of the Fundamental Theorem of Calculus, Int. J. Math. Educ. Sci. Technol., 27, No. 3, (1996) 355-364.

Russell A. Gorden, The Use of Tagged Partitions in Elementary Real Analysis, The American Mathematical Monthly, 105, No. 2, (1998) 107-117. (my article cited in The Monthly, 105, No. 9 (1998) page 886)

http://www.emis.de/proceedings/Toronto2000/papers/bullen.pdf

Charles Swartz, Introduction to Gauge Integrals, World Scientific, Singapore, 2001.

Robert G. Bartle, A Modern Theory of Integration, Graduate Studies in Mathematics, American Mathematical Society, 2001.

A. Aksoy and M. Martelli, The Wave Equation, Mixed Partial Derivatives, and Fubini's Theorem, The American Mathematical Monthly, 111, No. 4, (2004) 340-347.

J. J. Koliha, A Fundamental Theorem of Calculus for Lebesgue Integration, The American Mathematical Monthly, 113, No. 6, (2006) 551-554.

Li, Yi Xia; Dong, Xin Han; Wang, Ti Fu, The Lebesgue measurability of the G integrable function, Acta Math. Appl. Sin., 30 (2007), No. 2, 327-333.

A Simplified multidimensional integral
Agnes M. Backhausz, Vilmos Komornik, and Tivadar Szilagyi, (2007)
http://arxiv.org/PS_cache/arxiv/pdf/0712/0712.0552v1.pdf

A change of variables theorem for the multidimensional Riemann integral
Z Molnár, I Nagy, and T Szilágyi - Arxiv preprint arXiv:0804.2333, (2008) - arxiv.orghttp://arxiv.org/PS_cache/arxiv/pdf/0804/0804.2333v1.pdf

J. J. Koliha, Mean, Meaner and the Meanest Mean Value Theorem, The American Mathematical Monthly, 116, No. 4, (2009) 356-361.

M. J. Evans and P. D. Humke, Revisiting a Century-Old Characterization of Baire Class One, Darboux Functions, The American Mathematical Monthly, 116, No. 5, (2009), 451-455.


 

Follow the links below to get to the web pages of the above mentioned journals as well as a nice interactive web page in Real Analysis.

The American Mathematical Monthly

Mathematics Magazine

The Real Analysis Exchange

Interactive Real Analysis

Web Pages for Real Analysis

For two interesting functions, try the following links.

The Cantor Function

A continuous nowhere differentiable function