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Full-Text Articles in Physical Sciences and Mathematics
Introductory Calculus: Through The Lenses Of Covariation And Approximation, Caleb Huber
Introductory Calculus: Through The Lenses Of Covariation And Approximation, Caleb Huber
Graduate Student Portfolios, Professional Papers, and Capstone Projects
Over the course of a year, I investigated reformative approaches to the teaching of calculus. My research revealed the substantial findings of two educators, Michael Oehrtman and Pat Thompson, and inspired me to design a course based upon two key ideas, covariation and approximation metaphors. Over a period of six weeks, I taught a course tailored around these ideas and documented student responses to both classroom activities and quizzes. Responses were organized intonarratives, covariation, rates of change, limits, and delta notation. Covariation with respect to rates of change was found to be incredibly complex, and students would often see it …
A Dual State Hierarchical Ensemble Kalman Filter Algorithm, William J. Cook, Jesse Johnson, Marko Maneta, Doug Brinkerhoff
A Dual State Hierarchical Ensemble Kalman Filter Algorithm, William J. Cook, Jesse Johnson, Marko Maneta, Doug Brinkerhoff
Graduate Student Theses, Dissertations, & Professional Papers
Dynamic models that simulate processes across large geographic locations, such as hydrologic models, are often informed by empirical parameters that are distributed across a geographical area and segmented by geological features such as watersheds. These parameters may be referred to as spatially distributed parameters. Spatially distributed parameters are frequently spatially correlated and any techniques utilized in their calibration ideally incorporate existing spatial hierarchical relationships into their structure. In this paper, a parameter estimation method based on the Dual State Ensemble Kalman Filter called the Dual State Hierarchical Ensemble Kalman Filter (DSHEnKF) is presented. This modified filter is innovative in that …