ch01_1 - Ch 1.1: Basic Mathematical Models; Direction...

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Ch 1.1: Basic Mathematical Models; Direction Fields Differential equations are equations containing derivatives. The following are examples of physical phenomena involving rates of change: Motion of fluids Motion of mechanical systems Flow of current in electrical circuits Dissipation of heat in solid objects Seismic waves Population dynamics A differential equation that describes a physical process is often called a mathematical model .
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Example 1: Free Fall (1 of 4) Formulate a differential equation describing motion of an object falling in the atmosphere near sea level. Variables: time t , velocity v Newton’s 2 nd Law: F = ma = m (d v /d t ) net force Force of gravity: F = mg downward force Force of air resistance: F = γ v upward force Then Taking g = 9.8 m/sec 2 , m = 10 kg, = 2 kg/sec, we obtain v mg dt dv m - = v dt dv 2 . 0 8 . 9 - =
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Example 1: Sketching Direction Field (2 of 4) Using differential equation and table, plot slopes (estimates) on axes below. The resulting graph is called a
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This note was uploaded on 10/05/2010 for the course MATHEMATIC MATH219 taught by Professor Belginkorkmaz during the Fall '09 term at Middle East Technical University.

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ch01_1 - Ch 1.1: Basic Mathematical Models; Direction...

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