notes 1-1

# notes 1-1 - t → ∞ Write down a diﬀerential equation...

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SECTION 1.1 BASIC MODELS AND DIRECTION FIELDS The F = ma model. Suppose we have a falling body for which the drag force due to air resistance is proportional to its velocity. Write a diﬀerential equation for the body’s velocity v ( t ). Put in some numbers for the mass and proportionality constant, then draw a direction ﬁeld for the resulting diﬀerential equation. Analyze the behavior of the body’s velocity as

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Unformatted text preview: t → ∞ . Write down a diﬀerential equation of the form dy/dy = ay + b all of whose solutions approach y =-4 as t → ∞ . Draw a direction ﬁeld for the diﬀerential equation y = ( y-5)( y + 2) and use it to analyze the behavior of y as t → ∞ . HOMEWORK: SECTION 1.1, #1, 2, 3, 8, 9, 12, 14, 15 – 20, 23, 25...
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notes 1-1 - t → ∞ Write down a diﬀerential equation...

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