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Physical Sciences and Mathematics Commons™
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Articles 1 - 5 of 5
Full-Text Articles in Physical Sciences and Mathematics
Simulating The Spread Of The Common Cold, R. Corban Harwood
Simulating The Spread Of The Common Cold, R. Corban Harwood
Faculty Publications - Department of Mathematics
This modeling scenario guides students to simulate and investigate the spread of the common cold in a residence hall. An example floor plan is given, but the reader is encouraged to use a more relevant example. In groups, students run repeated simulations, collect data, derive a differential equation model, solve that equation, estimate parameter values by hand and through regression, visually evaluate the consistency of the model with their data, and present their results to the class.
1-65-S-Algal Blooms: Algal Blooms Threatening Lake Chapala, R. Corban Harwood
1-65-S-Algal Blooms: Algal Blooms Threatening Lake Chapala, R. Corban Harwood
Faculty Publications - Department of Mathematics
This modeling scenario investigates the massive algal blooms that struck Lake Chapala, Mexico, starting in 1994. After reading a summary of articles written on the incidents, students are guided through the process of creating a first order differential equation from a verbal model of the factors and analyze the nonautonomous ODE using direction field, parameter evaluation, and exact solution computation to fully describe the population behavior. Students are expected to be familiar with the separable method and direction fields. Students will learn building and improving a model from qualitative descriptions, nondimensionalization, evaluating parameters, and how to use DFIELD software to …
Logistics Of Mathematical Modeling-Focused Projects, R. Corban Harwood
Logistics Of Mathematical Modeling-Focused Projects, R. Corban Harwood
Faculty Publications - Department of Mathematics
Projects provide tangible connections to course content and can motivate students to learn at a deeper level. This article focuses on the implementation of projects in both lower and upper division math courses which develop and analyze mathematical models of a problem based upon known data and real-life situations. Logistical pitfalls and insights are highlighted as well as several key implementation resources. Student feedback demonstrate a positive correlation between the use of projects and an enhanced understanding of the course topics when the impact of logistics is reduced. Best practices learned over the years are given along with example project …
An Elementary Proof Of Dodgson's Condensation Method For Calculating Determinants, R. Corban Harwood, Mitch Main, Micah Donor
An Elementary Proof Of Dodgson's Condensation Method For Calculating Determinants, R. Corban Harwood, Mitch Main, Micah Donor
Faculty Publications - Department of Mathematics
In 1866, Charles Ludwidge Dodgson published a paper concerning a method for evaluating determinants called the condensation method. His paper documented a new method to calculate determinants that was based on Jacobi's Theorem. The condensation method is presented and proven here, and is demonstrated by a series of examples. The condensation method can be applied to a number of situations, including calculating eigenvalues, solving a system of linear equations, and even determining the different energy levels of a molecular system. The method is much more efficient than cofactor expansions, particularly for large matrices; for a 5 x 5 matrix, the …
Oscillation-Free Method For Semilinear Diffusion Equations Under Noisy Initial Conditions, R. Corban Harwood, Likun Zhang, V. S. Manoranjan
Oscillation-Free Method For Semilinear Diffusion Equations Under Noisy Initial Conditions, R. Corban Harwood, Likun Zhang, V. S. Manoranjan
Faculty Publications - Department of Mathematics
Noise in initial conditions from measurement errors can create unwanted oscillations which propagate in numerical solutions. We present a technique of prohibiting such oscillation errors when solving initial-boundary-value problems of semilinear diffusion equations. Symmetric Strang splitting is applied to the equation for solving the linear diffusion and nonlinear remainder separately. An oscillation-free scheme is developed for overcoming any oscillatory behavior when numerically solving the linear diffusion portion. To demonstrate the ills of stable oscillations, we compare our method using a weighted implicit Euler scheme to the Crank-Nicolson method. The oscillation-free feature and stability of our method are analyzed through a …