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th Math 340 Lecture – Introduction to Ordinary Differential Equations – January 25 , 2016 What We Covered: 1. Worksheet 2: Direction Fields a. Highlights i. How direction fields correspond to distinct differential equations ii. You can get more practice with direction fields by visiting the Math 340 website 1. Under “Other Course Materials” you can download dfield 2. Course Content – Chapter 2: First-Order Equations a. Section 2.1: Differential Equations and Solutions Continued i. Direction Field: the geometric meaning of a differential equation and its solutions 1. Essentially, we use directional fields as a way to show the slope of the function at each point which then gives you a visual of the differential equation’s behavior ′ 2. Suppose you are given the diff eq: = (,). We want to define this graphically which means we need to take into account the domain and range: = { , | ≤ ≤ ≤ ≤ }. Then there is the matter of defining the slopes of the equation at each point which is the soluti