Date of Award

5-2024

Degree Type

Honors College Thesis

Academic Program

Mathematics BS

Department

Mathematics

First Advisor

James V. Lambers, Ph.D.

Advisor Department

Mathematics

Abstract

In this project, analogies are employed to make complex math concepts approachable to beginners who may only have a basic understanding of calculus and linear algebra. Serving as the focal point of this project, Allen-Manandhar’s method solves an equation, known as an ordinary differential equation (ODE). The mentioned equation with its coefficients is comparable to a pie recipe with ingredients. With the outcome to a recipe seen as its solution, the solution to our pie recipe is a perfectly baked pie, as in without error. The chosen method for baking a pie then classifies as its baking approach that when executed “solves” the recipe. However, with more complicated ingredients (variable coefficients), the resulting pie must become approximated, which introduces error. Allen-Manandhar’s method is the baking approach analyzed for how well it finds the baked pie solution to the recipe equation and then compared to another pie baking approach. Using this analogy and a convergence analysis, the goal is to determine if our baking approach produces the most perfect pie possible. To see the inner workings of the method itself, physical steps to perform on a cube help translate what mathematical steps the method performs on the equation to find its solution. Compared to another baking approach, the results show that our method loses in accuracy and efficiency when solving linear, variable-coefficient ODEs in two-point boundary value problems. While our baking approach does not bake the best or fastest pie in comparison, it shows promise with constant coefficients in certain situations.

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