References

Cohn, H. (2006). A short proof of the simple continued fraction expansion of e. American Mathematical Monthly, 113(1), 57–66. Retrieved from http://dist.lib.usu.edu/login?url=http://search.ebscohost.com/login.aspx?direct=true&db=aph&AN=19955774&site=ehost-live

Conrad, K. (n.d.) Irrationality of pi and e. Retrieved from http://www.math.uconn.edu/~kconrad/blurbs/analysis/irrational.pdf

Debnath, L. (2015). A brief history of the most remarkable numbers e , i and γ in mathematical sciences with applications. International Journal of Mathematical Education in Science & Technology, 46(6), 853–878. Retrieved from https://doi-org.dist.lib.usu.edu/10.1080/0020739X.2015.1015266

Doerr, H. M., Meehan, D. J., & O’Neil, A. H. (2012). A natural approach to the number e. Mathematics Teacher, 105(6), 432–439. Retrieved from http://dist.lib.usu.edu/login?url=http://search.ebscohost.com/login.aspx?direct=true&db=aph&AN=73390400&site=ehost-live

Elwes, R. (2007). e: The mystery number. New Scientist, 195(2613), 38–41. Retrieved from http://dist.lib.usu.edu/login?url=http://search.ebscohost.com/login.aspx?direct=true&db=aph&AN=26437852&site=ehost-live

Euler, L. (1731, November 25). Lettre XV [Letter]. Retrieved from http://eulerarchive.maa.org//correspondence/letters/OO0729.pdf

Euler’s formula for complex exponentials. (n.d.) Retrieved from http://math.gmu.edu/~rsachs/m114/eulerformula.pdf

Glaz, S. (2010). The enigmatic number e: A history in verse of its uses in the mathematics classroom. Retrieved from http://www.math.uconn.edu/~glaz/My_Articles/TheEnigmaticNumberE.Convergence10.pdf

Maor, E. (1998). e: The story of a number. Princeton, NJ: Princeton University Press.

Marcus, S., & Nichita, F. F. (2018). On transcendental numbers: New results and a little history. Axioms (2075-1680), 7(1), 1–N.PAG. https://doi-org.dist.lib.usu.edu/10.3390/axioms7010015

McCartin, B. J. (2006). e: The master of all. Mathematical Intelligencer, 28(2), 10–21. Retrieved from http://dist.lib.usu.edu/login?url=http://search.ebscohost.com/login.aspx?direct=true&db=aph&AN=20810310&site=ehost-live

Needham, T. (1998). Visual complex analysis. New York, NY : Oxford University Press.

Niizeki, S., & Araki, M. (2008). Another formulation of Euler’s formula and its application. International Journal of Mathematical Education in Science & Technology, 39(2), 274–276. https://doi-org.dist.lib.usu.edu/10.1080/00207390701722718

Plant, A. (2009). Demonstrating e using areas under curves. Australian Senior Mathematics Journal, 23(1), 37–42. Retrieved from http://dist.lib.usu.edu/login?url=http://search.ebscohost.com/login.aspx?direct=true&db=aph&AN=43453055&site=ehost-live

Shultz, H. S., & Leonard, B. (1989). Unexpected occurrences of the number e. Mathematics Magazine, 62(4), 269. Retrieved from http://dist.lib.usu.edu/login?url=http://search.ebscohost.com/login.aspx?direct=true&db=msn&AN=MR1572769&site=ehost-live

Swenson, C., & Yandl, A. (1993). An alternative definition of the number e. College Mathematics Journal, 24(5), 458. Retrieved from http://dist.lib.usu.edu/login?url=http://search.ebscohost.com/login.aspx?direct=true&db=aph&AN=9403110824&site=ehost-live

White, D. (2008). Introducing exponentials. Mathematics Teaching, (208), 13. Retrieved from http://dist.lib.usu.edu/login?url=http://search.ebscohost.com/login.aspx?direct=true&db=aph&AN=32146747&site=ehost-live

Resources

Better Explained (n.d.). Intuitive understanding of Euler’s formula [web log comment]. Retrieved from https://betterexplained.com/articles/intuitive-understanding-of-eulers-formula/

Better Explained (2010, July 17). Understanding Euler’s formula [Video file]. Retrieved from https://www.youtube.com/watch?v=qpOj98VNJi4

Bourne, M. (2017, February 27). Taylor and Maclaurin series interactive applet [Applet]. Retrieved from https://www.intmath.com/series-expansion/taylor-maclaurin-series-interactive.php

Euler’s formula applet [Applet]. (n.d.) Retrieved from https://www.falstad.com/euler/

Khan, S. (2013, November 18). e and compound interest [Video file]. Retrieved from https://www.khanacademy.org/math/algebra2/exponential-and-logarithmic-functions/e-and-the-natural-logarithm/v/e-through-compound-interest

Khan, S. (2013, November 18). e as a limit [Video file]. Retrieved from https://www.khanacademy.org/math/algebra2/exponential-and-logarithmic-functions/e-and-the-natural-logarithm/v/e-as-limit

Khan, S. (2011, May 17). Euler's formula & Euler's identity [Video file]. Retrieved from https://www.khanacademy.org/math/ap-calculus-bc/bc-series-new/bc-10-14/v/euler-s-formula-and-euler-s-identity

Math Centre (2016, July 29). What is the number e? [Video file]. Retrieved from https://www.youtube.com/watch?v=R0oUeLQIbIk

Math Teacher’s Resource (September 15). Derivation of continuous compound interest formula without calculus [web log comment]. Retrieved from https://blog.mathteachersresource.com/?p=603

Morris, R. (2011, March). Derivatives of exponential functions [Applet]. Retrieved from http://demonstrations.wolfram.com/DerivativesOfExponentialFunctions/

Morris, T. (Producer). (n.d.) In our time: e. Podcast retrieved from https://www.bbc.co.uk/radio/play/b04hz49f

Numberphile (2016, December 19). e (Euler’s number) [Video file]. Retrieved from https://www.youtube.com/watch?v=AuA2EAgAegE

Proof of Euler’s identity. (n.d.) Retrieved from https://www.dsprelated.com/freebooks/mdft/Proof_Euler_s_Identity.html

Richeson, D. (2010, September 28). The transcendence of e [web log comment]. Retrieved from https://divisbyzero.com/2010/09/28/the-transcendence-of-e/

Schwartz, K. (n.d.) The number ‘e’ [Applet]. Retrieved from https://www.geogebra.org/m/mpzEhxsq#material/sjse4mtB



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