Transcription of Chapter 4 Differential Equations
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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 .
formula for R(t) given above, our model would predict that after 20years (t = 240) there will be more than 50 trillion rabbits! While rabbit populations can, under good conditions, grow at a nearly constant per capita rate for a surprisingly long time (this happened in Australia during the 19th century), our model is ultimately unrealistic.
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