Multiple Choice Questions for Euler's Method of Ordinary Differential Equations

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MULTIPLE CHOICE TEST (All Tests)	EULER'S METHOD (More on Euler's Method)	ORDINARY DIFFERENTIAL EQUATIONS (More on Ordinary Differential Equations)

Pick the most appropriate answer.

1. To solve the ordinary differential equation

by Euler’s method, you need to rewrite the equation as

2. Given

and using a step size of , the value of using Euler’s method is most nearly

-35.318

-36.458

-658.91
-669.05

3. Given

, and using a step size of , the best estimate of using Euler’s method is most nearly is

-0.37319
-0.36288
-0.35381
-0.34341

4. The velocity (m/s) of a body is given as a function of time (seconds) by

Using Euler’s method with a step size of 5 seconds, the distance traveled by the body from to seconds is estimated most nearly as

3133.1 m

3939.7 m

5638.0 m

39397 m

5. Euler’s method can be derived from using first two 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 three terms of the Taylor series are chosen for the ordinary differential equation

, would be

6. 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 your typical normal 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
4:34 PM

5:12 PM

Multiple choice questions on other topics

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 and 0717624. 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.