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Full-Text Articles in Physical Sciences and Mathematics
A Comparison Of Van Hiele Levels And Final Exam Grades Of Students At The University Of Southern Mississippi, Cononiah Watson
A Comparison Of Van Hiele Levels And Final Exam Grades Of Students At The University Of Southern Mississippi, Cononiah Watson
Honors Theses
This research analyzed students final exam scores in a college mathematics class with geometric components and their van Hiele levels upon entering the class. After the class was completed, each student’s final exam grade was calculated. The researcher used a Spearman correlation to compare the two; the result was a correlation coefficient of 0.742. The researcher then reported that the results of the van Hiele test are a major component in predicting a student’s success in such a class.
Approximation Of Elements Of Exponentials Of Differential Operators With Rational Quadrature, Daniel Elwood Lanterman
Approximation Of Elements Of Exponentials Of Differential Operators With Rational Quadrature, Daniel Elwood Lanterman
Master's Theses
We explore the possibility of improving the accuracy of approximations of elements of exponentials of differential operators, by using a rational function, instead of a polynomial function, as the interpolating function. Since a rational function behaves more like a decaying exponential function, it seems logical that the approximation should be more accurate. Through the use of high accuracy rational interpolants, we experiment with a numerical integration method to determine explicitly whether the error produced by a rational type approximation will indeed be less than that produced by a polynomial type approximation.
A Comparison Of Two Boundary Methods For Biharmonic Boundary Value Problems, Jaeyoun Oh
A Comparison Of Two Boundary Methods For Biharmonic Boundary Value Problems, Jaeyoun Oh
Master's Theses
The purpose of this thesis is to solve biharmonic boundary value problems using two different boundary methods and compare their performances. The two boundary methods used are the method of fundamental solutions (MFS) and the method of approximate fundamental solutions (MAFS). The Delta-shaped basis function with the Abel regularization technique is used in the construction of the approximate fundamental solutions in MAFS. The MFS produces more accurate results but needs known fundamental solutions for the differential operator. The MAFS can provide comparable results, and is applicable to more general differential operators. The numerical results using both methods are presented.
Rapid Approximation Of Bilinear Forms Involving Matrix Functions Through Asymptotic Analysis Of Gaussian Node Placement, Elisabeth Marie Palchak
Rapid Approximation Of Bilinear Forms Involving Matrix Functions Through Asymptotic Analysis Of Gaussian Node Placement, Elisabeth Marie Palchak
Master's Theses
Technological advancements have allowed computing power to generate high resolution model s. As a result, greater stiffness has been introduced into systems of ordinary differential equations (ODEs) that arise from spatial discreti zation of partial differential equations (PDEs). The components of the solutions to these systems are coupled and changing at widely varying rates, which present problems for time-stepping methods. Krylov Subspace Spectral methods, developed by Dr. James Lambers, bridge the gap between explicit and implicit methods for stiff problems by computing each Fouier coefficient from an individualized approximation of the solution operator. KSS methods demonstrate a high order of …