Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. See our User Agreement and Privacy Policy.

Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. See our Privacy Policy and User Agreement for details.

Successfully reported this slideshow.

Like this presentation? Why not share!

- Basics of calculus by Dr Ashok Tiwari 2407 views
- Application of calculus in business by M.K.Jahid Shuvo 4870 views
- Calculus by aalothman 4920 views
- All Integral Formulas: A Self-Prepa... by Lakshminarayanan ... 749 views
- Application of Calculus in Real World by milanmath 2419 views
- Application of Calculus by kishor pokar 10403 views

1,640 views

Published on

Stewart Calculus 13.3

No Downloads

Total views

1,640

On SlideShare

0

From Embeds

0

Number of Embeds

7

Shares

0

Downloads

102

Comments

0

Likes

2

No embeds

No notes for slide

- 1. 13.3 Arc Length and Curvature2D Arc Length Formula: = [ ( )] + [ ( )]
- 2. 13.3 Arc Length and Curvature2D Arc Length Formula: = [ ( )] + [ ( )]3D Arc Length Formula: = [ ( )] + [ ( )] + [ ( )]
- 3. 13.3 Arc Length and Curvature2D Arc Length Formula: = [ ( )] + [ ( )]3D Arc Length Formula: = [ ( )] + [ ( )] + [ ( )]Vector Form = | ( )|
- 4. There are in general several parametrizationsof a single curve.Ex: ()= , , , ( )= ,( ) ,( ) , ( )= , , ,they all represent the same curve.There is one parametrization that is special.
- 5. We define the arc length function ( ) by ()= | ( )|Using the Fundamental Theorem of Calculus,we have = | ( )|If we can solve as a function of , we canparametrize the curve with respect to : = ( ( ))
- 6. Ex: Reparametrize the helix curve ( ) = , ,with respect to arc length measured from ( , , ).When = , ( ) = ( , , ). = | ( )| = ()= | ( )| = = = / ( ( )) = , ,
- 7. The unit tangent vector of a curve () isdefined as: () ()= | ( )|The curvature of a curve is = curvature is small curvature is large
- 8. Alternative formulae: | ( )| | () ( )| = = = | ( )| | ( )|Ex: Find the curvature of ()= , , at ( , , ).
- 9. Alternative formulae: | ( )| | () ( )| = = = | ( )| | ( )|Ex: Find the curvature of ()= , , at ( , , ). ()= , , , ()= , ,
- 10. Alternative formulae: | ( )| | () ( )| = = = | ( )| | ( )|Ex: Find the curvature of ()= , , at ( , , ). ()= , , , ()= , , () ()= = , ,
- 11. Alternative formulae: | ( )| | () ( )| = = = | ( )| | ( )|Ex: Find the curvature of ()= , , at ( , , ). ()= , , , ()= , , () ()= = , , | , , | + + ()= = / | , , | ( + + )
- 12. Alternative formulae: | ( )| | () ( )| = = = | ( )| | ( )|Ex: Find the curvature of ()= , , at ( , , ). ()= , , , ()= , , () ()= = , , | , , | + + ()= = / | , , | ( + + ) ( )=
- 13. Ex: Show that the curvature of a circle ofradius is / everywhere.
- 14. Ex: Show that the curvature of a circle ofradius is / everywhere.A circle can be represented as ()= , ,
- 15. Ex: Show that the curvature of a circle ofradius is / everywhere.A circle can be represented as ()= , , ()= , ,
- 16. Ex: Show that the curvature of a circle ofradius is / everywhere.A circle can be represented as ()= , , ()= , , () ()= = , , | ( )|
- 17. Ex: Show that the curvature of a circle ofradius is / everywhere.A circle can be represented as ()= , , ()= , , () ()= = , , | ( )| ()= , ,
- 18. Ex: Show that the curvature of a circle ofradius is / everywhere.A circle can be represented as ()= , , ()= , , () ()= = , , | ( )| ()= , , | ( )| ()= = | ( )|
- 19. Ex: Find the curvature of the parabola =at the point ( , ).
- 20. Ex: Find the curvature of the parabola =at the point ( , ).The curve can be parametrized as ( )= , , .
- 21. Ex: Find the curvature of the parabola =at the point ( , ).The curve can be parametrized as ( )= , , . ( )= , , . ( )= , , .
- 22. Ex: Find the curvature of the parabola =at the point ( , ).The curve can be parametrized as ( )= , , . ( )= , , . ( )= , , . ( ) ( )= , ,
- 23. Ex: Find the curvature of the parabola =at the point ( , ).The curve can be parametrized as ( )= , , . ( )= , , . ( )= , , . ( ) ( )= , , ( )= / ( + )
- 24. Ex: Find the curvature of the parabola =at the point ( , ).The curve can be parametrized as ( )= , , . ( )= , , . ( )= , , . ( ) ( )= , , ( )= / ( + ) ( )= .
- 25. Ex: Find the curvature of the parabola =at the point ( , ).The curve can be parametrized as ( )= , , . ( )= , , . ( )= , , . ( ) ( )= , , ( )= / ( + ) ( )= .In general a plane curve = ( ) has curvature ( ) ( )= / [ + ( ( )) ]

No public clipboards found for this slide

Be the first to comment