Blessner, D. (2023, March), Innovative Teaching Technique for the Transcendental Functions   Paper presented at ASEE Zone 1 Conference - Spring 2023, State College,, Pennsylvania. 10.18260/1-2--44703

\bibitem{asee_peer_44703}
  Blessner, D. (2023, March), \emph{Innovative Teaching Technique for the Transcendental Functions }
  Paper presented at ASEE Zone 1 Conference - Spring 2023, State College,, Pennsylvania.
  10.18260/1-2--44703

Daniel Blessner.  "Innovative Teaching Technique for the Transcendental Functions ".  ASEE Zone 1 Conference - Spring 2023, State College,, Pennsylvania, 2023, March.  ASEE Conferences, 2023.  https://strategy.asee.org/44703 Internet.  14 May, 2024

\bibitem{asee_peer_44703}
  Daniel Blessner.
  "Innovative Teaching Technique for the Transcendental Functions ".
  \emph{ASEE Zone 1 Conference - Spring 2023, State College,, Pennsylvania, 2023, March}.
  ASEE Conferences, 2023.
  https://strategy.asee.org/44703 Internet.  14 May, 2024

@INPROCEEDINGS{asee_peer_44703
author = "Daniel Blessner"
title = "Innovative Teaching Technique for the Transcendental Functions "
booktitle = "ASEE Zone 1 Conference - Spring 2023"
year = "2023"
month = "March"
address = "State College,, Pennsylvania"
publisher = "ASEE Conferences"
note = {https://strategy.asee.org/44703}
number = {10.18260/1-2--44703}
}

TY  - CPAPER
AB  - Great Ideas for Teaching and Talking with Students. Making engineering education accessible to under prepared students is difficult due to the demanding mathematical requirements. One specific area of great difficulty for under prepared students is understanding transcendental functions. A transcendental function is written as a Power Series Expansion that is comprised of an infinite number of terms. The key word is INFINITE. This fact in most cases, eliminates the equation form from ever being seen by students. Students know them as only calculator buttons SIN, COS, TAN, LOG and LN. The first goal of this paper is to provide a simplified notation for each of the above transcendental functions and their inverses. This will help students better understand the relationship between a one-to-one function and its inverse function. This means that the standard inverse notation will NOT be used. For example, if a one-to-one function is written as y = f(x), the inverse function will be written simply as x = f(y). This will help reinforce what an inverse function does. The trigonometric functions have many different notations. Students find this confusing. There is an overuse of the variable “y”. The second goal of this paper is to provide examples using the actual Power Series formulas in calculations. This will give engineering students the hands on feel of working with familiar functions such as parabolas. For simplicity in computation purposes, only the first three terms in the Power Series will be used. A few examples will compare the results from the formulas to the calculator obtained number. Hopefully this will eliminate the mystery of the above calculator buttons. They will see the actual formula has been programmed into their calculator. This paper which is written in the form of a supplemental chapter is only intended to help students become better familiarized with the notation used and to present the transcendental functions as “Real Functions”. Most students don’t even realize that the familiar f in f(x) is being replaced by sin, cos, tan, and ln. For example, in y = sin(x), “sin” is replacing “f”. A separate section of this paper will show the various standard current notations and an explanation of the simplified version. This is strictly for educators.
In addition, this paper is not written from a research perspective. There was no collected student data from surveys as to the effectiveness of this supplemental chapter. This paper will contain the full written abbreviated chapter needed to be included in any first semester trigonometry or pre-calculus course. Formula derivations will not be included, and knowledge of radian measure will be assumed. It will contain the appropriate number of fully worked example problems. Students will use a calculator to calculate the first three terms of the Power Series Expansion for each transcendental function. For example, they will not use the calculator SIN button to determine the sine of say 30 degrees. This paper is intended only as a learning resource for engineering students and math and engineering educators.
AU  - Daniel Blessner
CY  - State College,, Pennsylvania
DA  - 2023/03/30
PB  - ASEE Conferences
TI  - Innovative Teaching Technique for the Transcendental Functions 
UR  - https://strategy.asee.org/44703
DO  - 10.18260/1-2--44703
ER  -