An FE Exam Math Problem in Differential Calculus

“The Fundamentals of Engineering (FE) exam is generally the first step in the process of becoming a professional licensed engineer (P.E.). It is designed for recent graduates and students who are close to finishing an undergraduate engineering degree from an EAC/ABET-accredited program” – FE Exam NCEES

For most engineering majors, mathematics is a required part of the examination. Here is a question from calculus.

inflection_point

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An FE Exam Math Problem in Analytical Geomtery

“The Fundamentals of Engineering (FE) exam is generally the first step in the process of becoming a professional licensed engineer (P.E.). It is designed for recent graduates and students who are close to finishing an undergraduate engineering degree from an EAC/ABET-accredited program” – FE Exam NCEES

For most engineering majors, mathematics is a required part of the examination. Here is a question in analytical geometry.

perimeter of triangle fe examThis post is brought to you by

How much computational time does it take to find the inverse of a square matrix using Gauss Jordan method?  Part 1 of 2.

Problem Statement

How much computational time does it take to find the inverse of a square matrix using Gauss Jordan method?  Part 1 of 2.

Solution

To understand the solution, you should be familiar with the Gauss Jordan method of finding the inverse of a square matrix.  Peter Young of UCSC describes it briefly in this pdf file while if you like watching an example via a video, you can see PatrickJMT doing so.  You also need to read a previous blog where we calculated the computational time needed for the forward elimination steps on a square matrix in the Naïve Gauss elimination method.   We are now ready to estimate the computational time required for Gauss Jordan method of finding the inverse of a square matrix.

GJ Inverse Blog

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Euler’s Method Example for FE Exam

“The Fundamentals of Engineering (FE) exam is generally the first step in the process of becoming a professional licensed engineer (P.E.). It is designed for recent graduates and students who are close to finishing an undergraduate engineering degree from an EAC/ABET-accredited program” – FE Exam NCEES

For most engineering majors, numerical methods is a required portion of the math part of the examination. Here is an example of using Euler’s method to numerically solve an ordinary differential equation.

eulers_method_fe_exam.jpg

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Computational Time for Forward Elimination Steps of Naive Gaussian Elimination on a Square Matrix

Problem Statement

How much computational time does it take to conduct the forward elimination part of the Naïve Gauss Elimination method on a square matrix?

CTdecomposition

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Global truncation error in Euler’s method

Illustrate through an example that the global truncation error in Euler’s method is proportional to the step size.

euler_truncation_global_pic1
euler_truncation_global_pic2

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Resources for Numerical Methods

Are you taking or teaching a course in Numerical Methods in Spring 2018.   If so, then look at all these resources.

Open CourseWare:

YouTube:

MOOCS:

Blog:

Twitter: http://twitter.com/numericalguy 

Local truncation error is approximately proportional to square of step size in Euler’s method

Question: Show that the local truncation error in Euler’s method is proportional to the square of the step size.

euler_truncation_local_pic1euler_truncation_local_pic2

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I thought Gaussian quadrature requires that the integral must be transformed to the integral limit of [-1,1]?

Question asked on YouTube: I thought Gaussian quadrature requires that the integral must be transformed to the integral limit of [-1,1]?

The answer is given below.

gaussquadlimits

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Converting a date to acceptable format in excel

Currently, I am using Smart Sparrow to collect data for the effectiveness of using adaptive learning platforms to improve the pre-class experience of flipped learning.

Amongst the data, I want to collect is when a student completes the lesson.  If the student is completing the lesson too close to the deadline, his/her data needs to be interpreted differently than the one from who does it within a reasonable time frame.  The latter would help me to better address how the lesson can be improved as a student.  A student racing against the deadline would give unreliable data on how a lesson can be improved.

Smart Sparrow does track the time when a student completes the lesson but the format is as follows.

Dayth Month Year, Hour:Minute AM/PM format (e.g. 7th Sep 2017, 9:40am).

The data is downloadable as in a CSV format.  Unfortunately, they do not give day/time since epoch or in acceptable excel format to find the time difference between when the lesson was completed and the lesson deadline.  So I wrote a VBA module function ‘changedate’ to do this.  Here it is.

function changedate (DateTimeOriginal)
‘This program converts a date/time given in XXth Month Year, Time format
‘Example 19th Sep 2017, 9:40 am
‘to be converted to
’09/19/2017 9:40am
‘to acceptable excel format to subtract from other dates
‘declaring a 12 element long vector for months
Dim monthvector(11) As String
monthvector(0) = “JAN”
monthvector(1) = “FEB”
monthvector(2) = “MAR”
monthvector(3) = “APR”
monthvector(4) = “MAY”
monthvector(5) = “JUN”
monthvector(6) = “JUL”
monthvector(7) = “AUG”
monthvector(8) = “SEP”
monthvector(9) = “OCT”
monthvector(10) = “NOV”
monthvector(11) = “DEC”
‘Uppercasing the date for accurate comparison
DateTimeOriginal = UCase(Trim(DateTimeOriginal))
‘Length of input date

‘Adding a 0 in front if day of month is between 1-9 so that the
‘length of string is same for all dates
If IsNumeric(Mid(DateTimeOriginal, 2, 1)) = False Then DateTimeOriginal = “0” + DateTimeOriginal

‘Capturing Day Number
daynumber = Mid(DateTimeOriginal, 1, 2)

‘Capturing the Year
yearnumber = Mid(DateTimeOriginal, 10, 4)

‘Capturing the Month
For i = 1 To 12
If Mid(DateTimeOriginal, 6, 3) = (monthvector(i – 1)) Then
monthnumber = Str(i)
End If
Next

‘Capturing time of day
timenumber = Right(DateTimeOriginal, 8)

‘Writing the date in acceptable format
changedate = monthnumber + “/” + daynumber + “/” + yearnumber + ” ” + timenumber
changedate = Trim(changedate)
End Function

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