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Chapter 4 Differential Equations

DVI file created at 14:20, 21 May 2008 Copyright 1994, 2008 Five Colleges, 4 Differential EquationsThe rate Equations with which we began our study of calculus are calleddifferential equationswhen we identify the rates of change that appearwithin them as derivatives of functions. Differential Equations are essentialtools in many area of mathematics and the sciences. In this Chapter weexplore three of their important uses: Modellingproblems using differential Equations ; Solvingdifferential Equations , both through numerical techniqueslikeEuler s method and, where possible, through finding formulas whichmake the Equations true; Definingnew functions by differential also introduce two important functions theexponential functionandthelogarithmic function which play central roles in the theory of solvingdifferential Equations .

ferential equations. (The name is something of an historical accident. Since the equations involve functions and their derivatives, we might bet-ter call them derivative equations.) Euler’s method treats the differential equations for a set of variables as a prescription for finding future values of those variables.

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