How to Understand Differential Equations


Differential equations contain at least one derivative function of one or more variables. They are useful for describing changing quantities and their rates of change in a variety of disciplines ranging from economic to physics. Differential equations are usually not taught until at least the junior level in college and a student will need a background in integral calculus.

  • Begin your study with first order ordinary differential equations (ODEs.) This form contains a function of one dependent variable and the first derivative with respect to one independent variable. This is the simplest possible true differential equation and must be thoroughly understood before advancing.

  • Take up second order ODEs. These equations involve first and second derivatives. They also have linear and non-linear forms, but only linear homogenous equations where the differential equation is equal to zero should be studied at this point.

  • Examine non-homogeneous ODEs. These differential equations are equal to a function of the independent variable. It should be understood that only special cases of these types of equations can be solved.

  • Advance to partial differential equations (PDEs.) These equations involve a function of multiple independent variables and its partial derivatives with respect to those variables. PDEs must be covered thoroughly as they have practical applications in many disciplines, particularly engineering.

  • Study additional topics throughout the course. Fourier series, LaPlace transforms and systems of differential equations may be taught at different points in the course.

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