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

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

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

Page1 / 3

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online