Chap13sec2

Chap13sec2 - ( ) 2sin( ),cos( ) t t t = -r with the...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
13.2 Derivatives and Integrals of Vector Functions The derivative of a vector  function   ( ) ( ), ( ), ( ) t f t g t h t = r   is   '( ) '( ), '( ), '( ) t f t g t h t = r . Note that you  differentiate   each   component   separately.   For   example,   look   at   the   2-dimensional   space   curve   defined   by  ( ) 4sin( ), 2cos( ) t t t = - r . If  ( ) t r  is the position function of a particle, then  '( ) t r is the velocity function,  like the  velocity function in one dimension. Let's look at a geometric description of the derivative  '( ) t r . The derivative  '( ) t r  is tangent to the space curve  ( ) t r . The   figure   shown   above   is   the   curve
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ( ) 2sin( ),cos( ) t t t = -r with the derivative vector '( ) 2cos( ), sin( ) t t t = --r shown a two points. The unit tangent vector is the derivative vector, denoted ( ) t T , is the derivative vector divided by its length. '( ) ( ) '( ) t t t = r T r Example: Find the unit vector ( ) t T for 2 1 ( ) , , tan t t t t t-=-r at t=1. Example: Find parametric equations for the tangent line to the curve 2 2 1, 1, 1 x t y t z t =-= + = + at (-1,1,1). Example: Find ( 29 ( 29 2 2 4 2 1 1 4 1 t t t dt +--- i j k-2-1 1 2-1-0.5 0.5 1...
View Full Document

This note was uploaded on 01/20/2012 for the course MATH 2057 taught by Professor Estrada during the Fall '08 term at LSU.

Ask a homework question - tutors are online