{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

mws_gen_dif_ppt_continuous

mws_gen_dif_ppt_continuous - FORWARD DIFFERENCE METHOD PPT

Info icon This preview shows pages 1–10. Sign up to view the full content.

View Full Document Right Arrow Icon
10/14/11 http://numericalmethods.eng.usf.edu 1 Differentiation-Continuous Functions Major: All Engineering Majors Authors: Autar Kaw, Sri Harsha Garapati http://numericalmethods.eng.usf.edu Transforming Numerical Methods Education for STEM Undergraduates
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Differentiation – Continuous Functions http://numericalmethods.eng.usf.edu
Image of page 2
                                            http://numericalmethods.eng.usf.edu 3 Forward Difference Approximation ( 29 ( 29 ( 29 x x f x x f x x f Δ Δ 0 Δ lim - + = For a finite ' Δ ' x ( 29 ( 29 ( 29 x x f x x f x f - +
Image of page 3

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
                                            http://numericalmethods.eng.usf.edu 4 x x+Δx f(x) Figure 1  Graphical Representation of forward difference approximation of first derivative. Graphical Representation Of  Forward Difference  Approximation
Image of page 4
                                            http://numericalmethods.eng.usf.edu 5 Example 1 The velocity of a rocket is given by ( 29 30 0 , 8 . 9 2100 10 14 10 14 ln 2000 4 4 - - × × = t t t t ν where  ' ' ν is given in m/s and  ' ' t is given in seconds.  a) Use forward difference approximation of the first derivative of        to  calculate the acceleration at            . Use a step size of            . b) Find the exact value of the acceleration of the rocket. c) Calculate the absolute relative true error for part (b). ( 29 t ν s t 16 = s t 2 Δ =
Image of page 5

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
                                            http://numericalmethods.eng.usf.edu 6 Example 1 Cont. Solution ( 29 ( 29 ( 29 t t t t a i i i - + ν ν 1 16 = i t 2 Δ = t 18 2 16 1 = + = + = + t t t i i ( 29 ( 29 ( 29 2 16 18 16 ν ν - a
Image of page 6
                                            http://numericalmethods.eng.usf.edu 7 Example 1 Cont. ( 29 ( 29 ( 29 18 8 . 9 18 2100 10 14 10 14 ln 2000 18 4 4 - - × × = ν m/s 02 . 453 = ( 29 ( 29 ( 29 16 8 . 9 16 2100 10 14 10 14 ln 2000 16 4 4 - - × × = ν m/s 07 . 392 = Hence ( 29 ( 29 ( 29 2 16 18 16 ν ν - a
Image of page 7

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
                                            http://numericalmethods.eng.usf.edu 8 Example 1 Cont. 2 07 . 392 02 . 453 - 2 m/s 474 . 30 The exact value of  ( 29 16 a can be calculated by differentiating  ( 29 t t t 8 . 9 2100 10 14 10 14 ln 2000 4 4 - - × × = ν as ( 29 ( 29 [ ] t ν dt d t a = b)
Image of page 8
                                            http://numericalmethods.eng.usf.edu 9 Example 1 Cont. Knowing that ( 29 [ ] t t dt d 1 ln = and  2 1 1 t t dt d - = ( 29 8 . 9 2100 10 14 10 14 10 14 2100 10 14 2000 4 4 4 4 - - × × × - × = t dt d t t a ( 29 ( 29 ( 29 8 . 9 2100 2100 10 14 10 14 1 10 14 2100 10 14 2000 2 4 4 4 4 - - - × × - × - × = t t t t 3 200 4 . 29 4040 + - - - =
Image of page 9

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 10
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern