Posts Tagged ‘Differential Equation’

In accordance with normal procedures, previously addressed topics are once again reflected on in this entry. Directly below, the derivative of e^x is dealt with from the perspectives of slope fields and differential equations. Beneath that, the derivative of e^x is considered as a Taylor Series.

Slope Field

Taylor Series Diff Equations2

 

Taylor Series

Taylor Series Diff Equations2Taylor

It is easy for high school students to determine that dy/dx = y for the Taylor Series representation of e^x above. This sets the stage very nicely for an exploration into power series which, in turn, lead directly to some other very cool “discoveries”. Follow the link provided for a more conventional extraction of the derivative of e^x.

Thanks for reading.

 

Reference

Courant, Richard., John, Fritz (1999).  Introduction to Calculus and Analytics: Classics of Mathematics. New York, NY:  Springer-Verlag Berlin Heidelberg.