Mathematics Articles

Colin Mitchell

 

Numerical Differentiation

            -Implicit Method for Solving a Boundary Condition Differential Equation

            -Deriving a Fourth Order Central Difference Approximation for f'

            -Deriving an Arbitrary Predictor-Corrector Method for ODEs

 

Calculus

            -A Population Equation

                        Observing an autonomous ordinary differential equation

                        to find significant points in the harvesting of farm-grown

                        fish populations.

            -Probability and Linear Difference Equations

            -Probability and Continuous Density Functions

            -Probability and Discrete Density Functions

            -Calculus of Variations: An Area Problem

                        Using Euler's Equation with a constraint to find the largest area

                        enclosable by a fixed length of rope.

            -Calculus of Variations: Surface Area Example

            -Deriving a Closed Form for the Fibonacci Sequence

 

Personal Projects

            -Designing and Constructing a High-Power Audio Amplifier

                        Designing circuitry for an 800W bass amplifier.

            -Ballistics for the .223 Rem

                        An attempt at deriving an equation for the trajectory

                        of a .223 Rem rifle cartridge.

            -Modeling Lobster Populations with the Diffusion Equation

            -The Wave Equation and Elastic Strings

                        -Derivation

                                    A derivation using discrete string elements, and

                                    taking the limit as the size of the string elements

                                    go to zero.

                        -Solution

                                    Solving the finite boundary conditions problem

                                    with the separation of variables technique.

                        -Investigation

                                    Analyzing the resulting equation.