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week_02_1.3,2.1,2.2,2.6

week_02_1.3,2.1,2.2,2.6 - MATH2860U Chapter 1 cont 2 1...

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MATH2860U: Chapter 1 cont...; 2 1 FIRST ORDER DIFFERENTIAL EQUATIONS cont... Differential Equations as Mathematical Models (1.3, pg. 19) Definition: The mathematical description of a system or a phenomenon is called a mathematical model and is constructed with certain goals in mind. 1. Construct Model (state assumptions; define variables and units; determine relationships between variables) 2. Solve (graphically; numerically; algebraically) 3. Compare to data (is the result reasonable? Does it match with data?) Engineering Terminology: Dynamical System means differential equation State variables mean dependent variables Response of system means solution of differential equation Recall: Back in Calculus II, we studied various applications of differential equations, and how to set up such equations. Application: A 1000L tank contains 80 L of water with 0.2 kg/L of dissolved salt. Water containing 0.3 kg of salt per litre enters the tank at a rate of 7 L/min. The solution is kept thoroughly mixed and drains from the tank at a rate of 6 L/min.

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