Conference Session

Mathematics Division Technical Session 3

Collection

2018 ASEE Annual Conference & Exposition

Authors

John W. Sanders, California State University, Fullerton

Tagged Divisions

Mathematics

advantage of the geometric approach:replacing the onerous task of checking that a tensor’s components obey the proper transformationrule with the (usually) easier task of identifying a linear tensor relationship.As already mentioned, tensors of rank greater than two can also be regarded as linear operators.When a tensor of rank three operates on a vector, the result is a tensor of rank two. When a tensorof rank four operates on a tensor of rank two, the result is a tensor of rank two. When a tensor ofrank 4,086 operates on a tensor of rank 1,237, the result is a tensor of rank 2,849. And so on andso forth. In general, a tensor Q of rank k has 3k components given, similarly to (11), by Qi1 i2 ...ik−1 ik = ((· · · ((Q · e

Conference Session

Mathematics Division Technical Session 2

Collection

2018 ASEE Annual Conference & Exposition

Authors

Leszek Gawarecki, Kettering University; Yaomin Dong, Kettering University; Gina Rablau, Kettering

Tagged Divisions

Mathematics

. 5. Total cost and profit.In the electric field of a line of charge example, a thin, uniformly charged rod of length L withtotal charge Q generates an electric field. Students are guided to find the strength of the field atdistance d in the plane that bisects the rod. Figure 1 Line of ChargeThe total charge Q is divided into many small point-like charges ΔQ located at points 𝑦𝑖 and theelectric field from each of them is determined. The net field can be found by summing the fieldsof all the point-like charges ΔQ and forming a Riemann sum. By taking the limit as the numberof point-like charges ΔQ increases to infinity, the Riemann sum will converge to a definiteintegral. The integral can be

Conference Session

Mathematics Division Technical Session 4

Collection

2018 ASEE Annual Conference & Exposition

Authors

Emre Tokgoz, Quinnipiac University; Hazal Ceyhan, Ankara University

Tagged Topics

Diversity

Tagged Divisions

Mathematics

) > 0 when x > 2 , f ′′( c ) = 0 for an x = c such that − 1 < c < 1 .A similar research question in the literature was used to understand STEM undergraduate and graduate students’ability to answer the following research question19:Q. Please draw the graph of f ( x ) = x x +1 at (e) below by finding and applying each of the following information ifthey are applicable.a) Vertical and horizontal asymptotes of f(x) and limiting values of f(x) at the vertical asymptotes if there exists any vertical asymptote.b) Local maximum, local minimum and inflection