# Math 43

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As part of the MIPS Grant and working alongside other students as part of the St. Mary's College vCalc Team, this page includes all of the equations and calculators that we, Savannah Bergen and Caleb Svobodny, created during Summer 2016. We worked under the guidance of Dr. Emek Kose, a Mathematics professor at St. Mary's College of Maryland.

## Equations

• Row Echelon Form of a 3x3 Matrix
• Characteristic Polynomial of a 2x2 Matrix
• Classifying Equilibria for a 2x2 Matrix
• Eigenvalues of a 2x2 Matrix
• General Solution for Second-Order Lin Hom Equations
• Laplace Transform for cos(at)
• Laplace Transform for e^(at)sin(bt)
• Newton's Law of Cooling - Time
• Scalar Form of Gen Solution for Second-Order Lin Hom Equations
• Trace of a 2x2 Matrix
• Characteristic Polynomial of a 3x3 Matrix
• Determinant of a 2x2 Matrix
• Euler's Formula
• Inverse of a 2x2 Matrix
• Laplace Transform for e^(at)
• Laplace Transform for sin(at)
• Mixing Problem
• SIR Epidemic Model
• Trace of a 3x3 Matrix
• Classification of Harmonic Oscillators with Damping
• Eigenvalues and Eigenvectors of a 2x2 Matrix
• General Solution for a First-Order Hom. Lin. System of Equations
• Inverse of a 3x3 Matrix
• Laplace Transform for e^(at)cos(bt)
• Mixing Problem with Initial Condition
• SIS Epidemic Model
• V2- Determinant as Related to the Right Hand Rule
• V3-Determinant as Related to the Right Hand Rule
• Conversion from Cartesian to Polar Coordinates
• Conversion from Cartesian Coordinates to Spherical Coordinates
• Conversion from Cartesian Coordinates to Cylindrical Coordinates
• Infinite Geometric Series
• Stirling Numbers
• Multiplication of a 3x3 Matrix by a Scalar
• Multiplication of a 2x2 Matrix by a Scalar
• Multiplication of a 2x3 Matrix and a 3x2 Matrix
• Multiplication of a 3x3 Matrix and a 3x1 Matrix
• Multiplication of a 2x2 Matrix by a 2x1 Matrix
• Laplace Transform for t^n
• Laplace Transform for t^(n) e^(at)