June 15, 2019
June 15, 2019
June 19, 2019
A good understanding of power series requires comprehending the meaning of infinitely many terms that appear in the summation of functions’ power series expansion. Applications of derivative and integral mathematical operations to power series of functions have important real-life applications such as calculating the noise differentiation of wave lengths and observing the area between the wave length and input information by integrating the function as a part of the Fourier analysis. Several other results on students majoring in mathematics and physics power series’ knowledge was conducted in various studies ([1-9]). Pedagogical research on engineering majors’ understanding of how to apply mathematical operations to series expansion of functions received hardly any attention from researchers (). In this work, the emphasis is given to engineering and mathematics students’ ability to apply the derivative and integral mathematical operations on exponential function’s series expansion. The analysis of the data in this work is performed by using the mathematical logic statement “iff (i.e. if and only if)” that is frequently used in mathematical statements such as theorems and lemmas. The collected data is analyzed qualitatively and quantitatively by using two survey questions collected from seventeen undergraduate and graduate students at a large Midwest teaching and research institution in the United States as a part of a more extensive questionnaire after receiving institutional IRB approval. The written questionnaire responses are used for quantitative analysis while the qualitative analysis depended on the interview data for further investigating the written responses. The results indicated participants’ ability to calculate derivatives and integrals as a part of Taylor series terms while they showed weakness for dealing with infinity and index terms in the Taylor series. The observed misconceptions can be used for improving STEM teaching.
Tokgoz, E. (2019, June), Board 95: STEM Majors’ Ability to Calculate Taylor Series’ Derivative & Integral Paper presented at 2019 ASEE Annual Conference & Exposition , Tampa, Florida. https://peer.asee.org/32468
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