# Introduction

Differential Equations is a sub field of Mathematics where the relationship between a function and its derivative is studied. One of the most important aspects of differential equations is its use in modeling, where the applications for differential equations expand everyday. Polking, Boggess, and Arnold write, "The use of differential equations makes available to us the full power of the calculus" (1). There are numerical, analytic, and qualitative techniques for solving differential equations, each proving useful for different domains of study. Although the direct computation of an explicit solution to a differential equation may be considered Math, differential equations helps us to predict the future, and can be applicable to the study of physics, chemistry, biology, and many other subject areas.

Here we provide some equations, calculators, and collections that we hope will help you expand your knowledge of differential equations.

Sources:
"Differential Equation." Wikipedia. Wikimedia Foundation, n.d. Web. 24 May 2016.

Polking, John C., Albert Boggess, and David Arnold. "Introduction to Differential Equations." Differential Equations With Boundary Value Problems. Upper Saddle River, NJ: Pearson/Prentice Hall, 2006. 1-15. Print.

## Differential Equations Equations

• Inverse of a 3x3 Matrix
• Characteristic Polynomial of a 2x2 Matrix
• Characteristic Polynomial of a 3x3 Matrix
• Classification of Harmonic Oscillators with Damping
• Classifying Equilibria for a 2x2 Matrix
• Determinant of a 2x2 Matrix
• Eigenvalues and Eigenvectors of a 2x2 Matrix
• Eigenvalues of a 2x2 Matrix
• Euler's Formula
• General Solution for a First-Order Hom. Lin. System of Equations
• General Solution for Second-Order Lin Hom Equations
• Inverse of a 2x2 Matrix
• Inverse of a 3x3 Matrix
• Laplace Transform for cos(at)
• Laplace Transform for e^(at)
• Laplace Transform for e^(at)cos(bt)
• Laplace Transform for e^(at)sin(bt)
• Laplace Transform for sin(at)
• Laplace Transform for t^(n) e^(at)
• Laplace Transform for t^n
• Mixing Problem
• Mixing Problem with Initial Condition
• Multiplication of a 2x2 Matrix by a 2x1 Matrix
• 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
• Newton's Law of Cooling - Time
• Scalar Form of Gen Solution for Second-Order Lin Hom Equations
• SIR Epidemic Model
• SIS Epidemic Model
• Trace of a 2x2 Matrix
• Trace of a 3x3 Matrix