Q1. To solve the ordinary differential equation ,
by Euler’s method, you need to rewrite the equation as
Q2. Given
and using a step size of h=0.3, the value of y(0.9) using Euler’s method is most nearly 35.318 36.458
658.91 Q3. Given
and using a step size of h=0.3, the best estimate of dy/dx(0.9) using Euler’s method is most nearly is
0.37319 Q4. The velocity (m/s) of a body is given as a function of time (seconds) by v(t)=200 ln(1+t) t, t≥0 Using Euler’s method with a step size of 5 seconds, the distance in meters traveled by the body from t=2 to t=12 seconds is most nearly 3133.1 3939.7 5638.0 39397 Q5. Euler’s method can be derived by using the first two terms of the 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 three terms of the Taylor series are chosen for the ordinary differential equation
would be
Q6. A homicide victim is found at 6:00PM in an office building that is maintained at 72˚F. When the victim was found, his body temperature was at 85 ˚F. Three hours later at 9:00PM, his body temperature was recorded at 78˚F. Assume the temperature of the body at the time of death is the normal human body temperature of 98.6˚F. The governing equation for the temperature θ of the body is
where = temperature of the body, ˚F θ_{a} = ambient temperature, ˚F t = time, hours k = constant based on thermal properties of the body and air. The estimated time of death most nearly is
2:11
PM
3:13
PM 5:12 PM

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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. 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. 
