Transforming Numerical Methods Education for the STEM Undergraduate 



MOOC 
MOBILE 
VIDEOS 
BLOG 
YOUTUBE 
TWITTER 
COMMENTS 
ANALYTICS

ABOUT 
CONTACT  COURSE WEBSITES
 BOOKS 
MATH FOR COLLEGE




Q1. To solve the ordinary differential equation , by RungeKutta 4^{th} order method, you need to rewrite the equation as
Q2. Given and using a step size of , the value of using RungeKutta 4^{th} order method is most nearly  0.25011 4297.4
1261.5
Q3. Given , and using a step size of , the best estimate of
RungeKutta 4th order method is most nearly
1.6604 Note: At the end of this document, see formulas used to answer this question as there are a few different versions of the RungeKutta 4^{th} order method. Q4. The velocity (m/s) of a parachutist is given as a function of time (seconds) by
Using RungeKutta 4^{th} order method with a step size of 5 seconds, the distance traveled by the body from to seconds is estimated most nearly as 341.43 m
Note: At the end of this document, see formulas used to answer this question as there are a few different versions of the RungeKutta 4^{th} order method. Q5. RungeKutta method can be derived from using first three terms of Taylor series of writing the value of , that is the value of at , in terms of and all the derivatives of at . If , the explicit expression for if the first five terms of the Taylor series are chosen for the ordinary differential equation , would be
Q6. A hot solid cylinder is immersed in an cool oil bath as part of a quenching process. This process makes the temperature of the cylinder,, and the bath, , change with time. If the initial temperature of the bar and the oil bath is given as 600° C and 27°C, respectively, and Length of cylinder = 30 cm Radius of cylinder = 3 cm Density of cylinder = 2700 kg/m^3 Specific heat of cylinder = 895 J/kgK Convection heat transfer coefficient = 100 W/(m^2K) Specific heat of oil = 1910 J/(kgK) Mass of oil = 2 kg The coupled ordinary differential equations governing the heat transfer are given by
The following equations are used to answer questions#2, 3, and 4

AUDIENCE  AWARDS  PEOPLE  TRACKS  DISSEMINATION  PUBLICATIONS 

Copyrights: University of South Florida, 4202 E Fowler Ave, Tampa, FL 336205350. 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, 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 AttributionNonCommercialNoDerivs 3.0 Unported License. 
