First-Order Ordinary Differential Equations

Background--Simple iteration from a Fixed Boundary Condition

Background--Simple iteration from a Specified Boundary Condition

Visualizing Trajectories: Initial Conditions Define a Set of Curves that "Cover" the Plane.

Finite Differencing Methods (Method 1): Explicit Forward Differences

Visualizing Trajectories from the  Explicit Forward Differences Method

Finite Differencing Methods (Method 2): Implicit Forward Differences

Visual Comparison of Trajectories from the  Explicit and Implicit Methods

Intuitive Understanding of First-Order ODEs

Geometry of Flows of First-Order ODEs: Vector Fields (Simple Example: Newton's Law of Cooling)

Geometry of Flows of First-Order ODEs: Vector Fields (More Complex Example)

Using Mathematica's DSolve function on Example used for Finite Differencing Examples

Comparison of Exact Solution to Finite Differencing Methods

DSolve on a First-Order ODE: More Complex Example

Created by Wolfram Mathematica 6.0  (06 November 2007)