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 ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS PARTIAL DIFFERENTIAL EQUATIONS Pick the most appropriate answer.

Q1.  In a general second order linear partial differential equation with two independent variables,

where A , B , C are functions of  x and y, and  D  is a function of x , y , , , then the PDE is elliptic if

B2-4AC<0

B2-4AC>0

B2-4AC=0

B2-4AC0

Q2.  The region in which the following equation

acts as an elliptic equation is

for all values of  x

Q3. The finite difference approximation of  in the elliptic equation

at (x,y)  can be approximated as

Q4.  Find the temperature at the interior node given in the following figure using the direct method

45.19 °C

48.64 °C

50.00 °C

56.79 °C

Q5 Find the temperature at the interior node given in the following figure

Using the Lieberman method and relaxation factor of 1.2, the temperature at  x-=3, y=6  estimated after 2 iterations is (use the temperature of interior nodes as 50°C  for the initial guess)

52.36 °C

53.57 °C

56.20 °C

58.64 °C

Q6. Find the steady-state temperature at the interior node as given in the following figure

53.57 °C

66.40 °C

68.20 °C

69.59 °C

 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# 0126793, 0341468, 0717624,  0836981, , 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