13.1 Vector Functions and Space Curves

13.1 Vector Functions and Space Curves - Math 224 Calculus...

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Math 224 – Calculus III 1 13.1 Vector Functions and Space Curves Recommended Homework: #1-27, 35, 37, 41 A vector valued function () t r or rt has the form (in 3 ): ( ) ( ), ( ), ( ) t f t g t h t r or ( ) ( ) ( ) ( ) t f t g t h t r i j k This is really just a generalization of the idea of parametric equations, where the component function need not be linear A vector valued function t r is a function whose inputs (domain) are real numbers and whose outputs (range) are vectors. It is convenient to think of the variable t (the parameter) as being “time”. We can think that the vector function describes the position of a particle as it traverse a curve over time. Example: Consider the vector function: 2 ( ) 1 , , ln(2 1) t t t t r What is the domain of t r ? What is the position at time 3 t ? Note : the functions 2 1 , and ln(2 x t y t z t are called the component functions of t r , and they make up the parametric form for the curve (the “ space ” curve). Picture: x y z
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Math 224 – Calculus III 2 Examples: Sketch the following space curves.
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This note was uploaded on 10/31/2010 for the course MATH 224 taught by Professor Harris during the Fall '09 term at Illinois Central.

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13.1 Vector Functions and Space Curves - Math 224 Calculus...

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