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Unformatted text preview: Math 341 Review Fall 2010 Broadly speaking, this course had three components: 1. Single differential equations 2. Linear algebra 3. Systems of differential equations. This document is an attempt to briefly summarize what we did and to give you some suggestions for studying. 1. Single differential equations This topic consisted of Chapters 1, 2, and 3 of Edwards and Penney (note that we only covered the early part of Chapter 2). The order of a differential equation is the highest order of derivative that appears in the equation. Typically, an n th order differential equation will have an n-parameter family of solutions, and to get a unique solution, we typically need n initial conditions. We can also classify differential equations as linear or nonlinear . For a first-order differential equation dy/dx = f ( x,y ), we can draw a slope field even if f is a complicated function. This might help us say something about the solution, even if we cant solve the equation explicitly. But thereabout the solution, even if we cant solve the equation explicitly....
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