Calc_Lecture_08 - Vector-Valued Functions Objectives...

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1 Analyze and sketch a space curve given by a vector-valued function. Extend the concepts of limits and continuity to vector-valued functions. Objectives Vector-Valued Functions
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2 Space Curves and Vector-Valued Functions
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3 Space Curves and Vector-Valued Functions A plane curve is defined as the set of ordered pairs ( f ( t ) , g ( t )) together with their defining parametric equations x = f ( t ) and y = g ( t ) where f and g are continuous functions of t on an interval I .
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4 This definition can be extended naturally to three-dimensional space as follows. A space curve C is the set of all ordered triples ( f ( t ) , g ( t ), h ( t )) together with their defining parametric equations x = f ( t ), y = g ( t ), and z = h ( t ) where f , g and h are continuous functions of t on an interval I . A new type of function, called a vector-valued function, is introduced. This type of function maps real numbers to vectors. Space Curves and Vector-Valued Functions
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5 A Space Curves and Vector-Valued Functions
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6 Be sure you see the distinction between the vector-valued
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This note was uploaded on 10/05/2011 for the course BIO 203, CH taught by Professor Lacey,simmerling,deng,hanson during the Fall '10 term at SUNY Stony Brook.

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Calc_Lecture_08 - Vector-Valued Functions Objectives...

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