MATH 305 Lecture Notes - Lecture 1: Coefficient Matrix, Row And Column Vectors, Cruise Control
Document Summary
Systems of linear first-order differential equations are a powerful tool for modeling and analyzing complex systems in engineering, physics, biology, and other fields. A system of linear first-order differential equations is a set of equations that describe how a set of variables changes over time, where each equation involves the first derivative of one of the variables. These equations are called "linear" because the coefficients of the variables are constants, and the equations are first-order because they involve the first derivative of the variables with respect to time. One of the key advantages of systems of linear first-order differential equations is that they can be solved using matrix algebra. This is because the equations in the system can be written in matrix form, where the coefficients of the variables are organized into a matrix, and the variables are organized into a column vector.
