Holistic Numerical Methods

Transforming Numerical Methods Education for the STEM Undergraduate

 

MOOC | MOBILE | VIDEOS | BLOG | YOUTUBE | TWITTER | COMMENTS | ANALYTICS | ABOUT | CONTACT | COURSE WEBSITES | BOOKS | MATH FOR COLLEGE


MULTIPLE CHOICE TEST

(All Tests)

GAUSS QUADRATURE RULE

(More on Gauss Quadrature Rule)

INTEGRATION

(More on Integration)

 

Pick the most appropriate answer


Q1.  is exactly

 

 

 


Q2. For a definite integral of any third order polynomial, the two-point Gauss quadrature rule will give the same results as the

 

1-segment trapezoidal rule

2-segment trapezoidal rule

3-segment trapezoidal rule

Simpson's 1/3 rule


Q3. The value of  by using the two-point Gauss quadrature rule is most nearly

11.672

11.807

12.811

14.633


Q4. A scientist uses the one-point Gauss quadrature rule based on getting exact results of integration for functions f(x)=1 and x.  The one-point Gauss quadrature rule approximation for





Q5. A scientist develops an approximate formula for integration as

             

 

where

 

The values of c1 and x1 are found by assuming that the formula is exact for the functions of the form a0x + a1x2 polynomial.  Then the resulting formula would therefore be exact for integrating


Q6. You are asked to estimate the water flow rate in a pipe of radius 2m at a remote area location with a harsh environment.  You already know that velocity varies along the radial location, but you do not know how it varies.  The flow rate Q is given by

 

        

 

To save money, you are allowed to put only two velocity probes (these probes send the data to the central office in New York, NY via satellite) in the pipe.  Radial location, r is measured from the center of the pipe, that is r=0 is the center of the pipe and r=2m is the pipe radius.   The radial locations you would suggest for the two velocity probes for the most accurate calculation of the flow rate are 

0,2

1,2

0,1

0.42,1.58


 

Complete Solution

 

 

 

Multiple choice questions on other topics


AUDIENCE |  AWARDS  |  PEOPLE  |  TRACKS  |  DISSEMINATION  |  PUBLICATIONS


Copyrights: University of South Florida, 4202 E Fowler Ave, Tampa, FL 33620-5350. All Rights Reserved. Questions, suggestions or comments, contact kaw@eng.usf.edu  This material is based upon work supported by the National Science Foundation under Grant# Creative Commons License0126793, 0341468, 0717624,  0836981, 0836916, 0836805, 1322586.  Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.  Other sponsors include Maple, MathCAD, USF, FAMU and MSOE.  Based on a work at http://mathforcollege.com/nm.  Holistic Numerical Methods licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.

 

ANALYTICS