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Physical Sciences and Mathematics Commons™
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Full-Text Articles in Physical Sciences and Mathematics
Coordinating Stem Core Courses For Student Success, Cristina Villalobos, Hyung Won Kim, Timothy J. Huber, Roger Knobel, Shaghayegh Setayesh, Lekshmi Sasidharan, Anahit Galstyan, Andras Balogh
Coordinating Stem Core Courses For Student Success, Cristina Villalobos, Hyung Won Kim, Timothy J. Huber, Roger Knobel, Shaghayegh Setayesh, Lekshmi Sasidharan, Anahit Galstyan, Andras Balogh
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
Research indicates multi-section coordination improves the academic performance of students in STEM education. This paper describes the process of coordination in Precalculus, Calculus 1, and Calculus 2 courses undertaken by a large department that grew from the merger of two institutions through a pilot program, and a project grant. Components introduced in the project courses are documented, including collaborative problem-solving sessions, student learning assistants, Q&A sessions, and additional technology resources. Preliminary data is provided on the impacts of the initiative on student success. The study findings provide a template for coordination, faculty buy-in, and increased student engagement at similar institutions …
Generalized Local Test For Local Extrema In Single-Variable Functions, Eleftherios Gkioulekas
Generalized Local Test For Local Extrema In Single-Variable Functions, Eleftherios Gkioulekas
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
We give a detailed derivation of a generalization of the second derivative test of single-variable calculus which can classify critical points as local minima or local maxima (or neither), whenever the traditional second derivative test fails, by considering the values of higher-order derivatives evaluated at the critical points. The enhanced test is local, in the sense that it is only necessary to evaluate all relevant derivatives at the critical point itself, and it is reasonably robust. We illustrate an application of the generalized test on a trigonometric function where the second derivative test fails to classify some of the critical …
Zero-Bounded Limits As A Special Case Of The Squeeze Theorem For Evaluating Single-Variable And Multivariable Limits, Eleftherios Gkioulekas
Zero-Bounded Limits As A Special Case Of The Squeeze Theorem For Evaluating Single-Variable And Multivariable Limits, Eleftherios Gkioulekas
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
Many limits, typically taught as examples of applying the ‘squeeze’ theorem, can be evaluated more easily using the proposed zero-bounded limit theorem. The theorem applies to functions defined as a product of a factor going to zero and a factor that remains bounded in some neighborhood of the limit. This technique is immensely useful for both single-variable limits and multidimensional limits. A comprehensive treatment of multidimensional limits and continuity is also outlined.
On Equivalent Characterizations Of Convexity Of Functions, Eleftherios Gkioulekas
On Equivalent Characterizations Of Convexity Of Functions, Eleftherios Gkioulekas
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
A detailed development of the theory of convex functions, not often found in complete form in most textbooks, is given. We adopt the strict secant line definition as the definitive definition of convexity. We then show that for differentiable functions, this definition becomes logically equivalent with the first derivative monotonicity definition and the tangent line definition. Consequently, for differentiable functions, all three characterizations are logically equivalent.