# 1.1 - Math 334 Lecture#1 1.1 Mathematical Modeling Direction Fields The Steps of Mathematical Modeling Consider an object falling in the atmosphere

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Math 334 Lecture #1 § 1.1: Mathematical Modeling; Direction Fields The Steps of Mathematical Modeling. Consider an object falling in the atmo- sphere near sea level. [NOTE the assumptions: object falling; in the atmosphere; near sea level.] Step 1 : Identify the dependent and independent variables. Let v be the velocity of the falling object. [This describes the “falling” of the object.] Let t be the time. As the velocity presumably changes with time, velocity is a function of time: v = v ( t ) . Step 2 : Choose consistent units of measurement for the variables. Measure t in seconds (sec or s). Measure v in metres per second (m/s). Step 3 : Articulate the physical law or principle that governs the physical process. The motion of the falling object is governed by Newton’s second law: sum of the forces = ma, where m is the mass of the object, and a is its acceleration. [This introduces a “parameter” m and the variable a .] Step 4 : Express the physical principle in terms of the variables declared in Step 1. Since acceleration is the time derivative of velocity, it follows that

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## This note was uploaded on 03/08/2011 for the course MATH 334 taught by Professor Smith during the Spring '11 term at Vanderbilt.

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1.1 - Math 334 Lecture#1 1.1 Mathematical Modeling Direction Fields The Steps of Mathematical Modeling Consider an object falling in the atmosphere

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