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Tag Archives for "Differential Equations"

Defining Laplace Transformations in Differential Equations

Laplace transformations are one of the most powerful tools for solving linear differential equations with constant coefficients. In these notes, we’ll review basic properties of Laplace trans

What to Know about Eigenvalues and Eigenvectors

In these eigenvalues and eigenvectors notes, we’ll review some results from linear algebra that are important for studying differential equations. Here, you will find the definitions and meth

How to Use the Arc Length Formula in Differential Equations

In this article we will take an old formula, the formula for arc length of curves in the plane, and adapt it for use with vector functions in 3 dimensions. We begin with a brief review of the arc l

Inverse Laplace Transforms: A Differential Equations Review

Laplace transforms are important tools for us to use when solving linear differential equations. The Laplace transform is a relation of the form – As we can see, the Laplace transformation co

Equations of Planes: A Differential Equations Review

It is known that the solution of a differential equation can be displayed graphically as a family of integral curves in the plane which is usually called the phase plane. Properties of planes are t

First Order Differential Equations: What to Know for Studying Calculus

First-order differential equationsare equations involving some unknown function and its first derivative. The main purpose of this CalculusIIIreview article is to discuss the properties of solution

How to Use the Newton-Raphson Method in Differential Equations

The Newton-Raphson method, also known as Newton’s method, is one of the most powerful numerical methods for solving algebraic and transcendental equations of the form f(x)=0. This method is c