Basic Mathematical Models; Direction Fields

A Falling Object

Modeling with Differential Equations 1.Identify the dependent and independent variables. 2.Choose units of measurement. 3.Articulate the basic principle that underlies or governs the problem. 4.Express the principles in terms of the variables. 5.Make sure your units are consistent. 6.Use additional differential equations if necessary.

A Field Mice Population

Example

Initial Value Problems An initial condition is a data point that a solution must pass through. A differential equation together with an initial condition is called an initial value problem. A general expression for the set of solutions is called the general solution.

Example