BRIGHAM YOUNG UNIVERSITY
Electrical Engineering Department
Standards for Daily Assignments with Suggestions for
Effective Study
I. THINKING
One purpose of college education is to educate
students in the art of thinking! The
art of thinking is called logic. It is
not possible, however, to learn to think by studying logic. Similarly, it is not possible to develop
muscles by reading books on weight lifting.
To develop "mental muscles," they must be exercised in
vigorous mental activity. The mind can
never be trained to solve difficult problems working on easy problems. Reasoning by analogy with physical training,
it would appear that during the training period, in college, the mind must be
disciplined by mental effort to equal to that which will be required in the
future.
II. EFFICIENT STUDY
Studying requires a great deal of intensive
effort. In order to conserve time, the
effort should be concentrated and free from distractions. Efficient study can be made a habit which
will be useful throughout a professional career. The fact that the student is actually self-employed provides an
incentive for improvement in work habits.
Reading is not study, and going through the motions will not produce
results. Efficiency will be increased
if the student periodically asks: "Why am I doing this?", "What
is the best method?", "What should I be learning from this?".
III. ORDERLY WORK
It is absolutely essential that
an engineer think and work in an orderly fashion. Since the ability to do so is developed by habit, students of
engineering must make every effort to work problems, perform experiments, and
write reports in a manner which is lucid and orderly. A sequence of steps which will be helpful in doing work in the desired
fashion is:
(1) stating
the problem
(2) planning
the manner of solution
(3) executing
the solution
(4) checking
(5) interpreting
the conclusions
In interpreting the conclusions for a particular
problem, one should endeavor to recognize the relationship of the specific case
to the general class which it represents.
One thinks, learns, and works best in the framework of general and
fundamental principles. If one follows
these in thinking, and if one presents work in corresponding fashion, there
will be no doubt on one's part or anyone else's as to what the work represents.
It will be helpful to think of each assignment as
engineering work for a client (perhaps yourself) who truly wants to know
certain things. Consider that you are
hired to find answers and to convince your client of their validity and
importance.
IV. PROBLEM SOLVING AND PRESENTATION OF YOUR SOLUTION
As an aid in the solution of problems, it is advisable to follow a standard form. The purpose of the standard form is not to make all student papers look alike (although this is a great help for the readers), but to ensure that the student's thinking is organized during the process of organizing the work sheet.
A standard form for all daily assignments in the
Electrical Engineering Department is to be used except in those cases where
individual instructors explicitly authorize limited, stipulated deviations.
(1)
Use of engineering problem paper ruled with five lines per inch for the bulk of
calculations. The unruled side of the
sheet is to be used even for graphs. (The lines show through well enough for
most purposes.) Do not write on both
sides of the sheets. On occasion, other
forms of graph paper or charts or curves may be appropriate.
(2)
Use a relatively hard pencil, well pointed. This can be erased and does not smudge excessively. Colored pencils for part of the work
sometimes are helpful where contrasts between two or more conditions in the
problem are displayed. However, it is
well to avoid using red because this is the color graders normally use, and
colors ordinarily do not differentiate on copy machines.
(3)
The written part should be neatly lettered. Some instructors may permit longhand if it is exceptionally neat
and legible.
(4)
Do not crowd work. Leave one or more blank lines
above and below equations.
A sample or a problem in the standard form follows.
(This particular sample is from an elementary circuits course in which the
student is learning to use Ohm's law and Kirchhoff's laws. Many of the steps shown here could be omitted
by an advanced student, but one should still include explicitly the new
concepts and principles illustrated by a new problem.)
The numbered comments below correspond to circled
numbers on the sample. These numbers may be used by
the grader to point out items needing more attention. It will be noted that the student is allowed considerable freedom
to select details of format and presentation.
The guiding principles are neatness, orderliness, completeness, and
precision. Proper attention should be
paid to spelling, grammar, punctuation, etc.
(1)
Course
number and section.
(2)
Student
name (A rubber stamp may be used to make a whole pad of paper quickly.)
(3)
Date
work is turned in
(4)
Page
numbering. The top number is that of
the individual page; the bottom number is the total number of pages in the problem
or assignment.
(5)
Problem
number from textbook or other source in the left margin.
(6)
Statement
of the problem. Normally this will not
be worded the same as in the textbook.
(7)
Circuit
diagram or other sketch illustrating the problem as appropriate. This is part of the statement of the
problem. Note that polarities of
voltages and directions of currents (even for unknown quantities) are indicated
along with component values. This is
important. Show as much given data as
possible and also show how the answers you are seeking relate to the
circuit. Often input waveforms or
signal conditions form part of the statement of the problem and should be shown
on the sketch.
(8)
A
brief indication of the method of solution is normally helpful at the
beginning. In the sample problem, other
methods could have been used for solution such as superposition, Thevenin's
theorem, nodal method, etc.
(9)
Important
equations are numbered for reference when they are used again.
(10)
Left
margin may be used for scratch work. If
extensive scratchwork is required, a part of the center of the page may be
blocked off for this purpose.. Many mistakes are made in scratchwork so it is
important to preserve all such calculations for orderly checking.
(11)
Repeat
headings on each page.
(12)
Repeat
problem number on each page.
(13)
Box
or heavily underline requested answers.
Always indicate the units of the answers.
(14)
Show
answers on a sketch. The answers may be
shown on the original sketch (Item 7 above if this can be done clearly.) In the
illustrated problem, it seemed better to re-draw the circuit because the
original diagram was getting cluttered and because the assumed current Is
and voltage Vs turned out to be negative. The circuit with the answers shown should be studied to see if it
is reasonable. Quick checks on this
circuit show that the voltages in each loop add up correctly and that the
currents add up properly. Also, the
current through the larger voltage source is in the direction expected for that
source as must usually be the case in a dc resistive circuit. These checks need not be written out, but it
is very important to take a minute or two to make them.
(15)
New
problem number or part.
(16)
Comment
or generalization or interpretation or something the problem illustrates is
often called for here.
(17)
Draw
a long double line at the end of every problem and especially if there are
several on the same page. Use the
double line even if the problem ends at the bottom of a page. This is a signal that it is not continued on
the next page. Usually on long
problems, you will receive more personal satisfaction if you start each one on
a new page. Sometimes you will get off
to a bad start and want to begin again; this is hard to do if part of another
problem is on the same page.
(18)
For
handing in assignments, fold them inward neatly once vertically and put name,
date, course number and section on the outside top as shown along with any
other information the instructor may require.



V. COMMON SENSE
There is no substitute for good judgment. A good deal of grief can be avoided in study
and in professional practice by persistently applying common sense to the work.
VI. A GOAL OF ENGINEERING EDUCATION AND HOW TO PURSUE IT
Engineering courses are intended to form the mind,
not just to fill the mind. To accomplish
this, the courses are designed to develop a thorough understanding and
appreciation of fundamental principles, the ability to analyze a problem or
situation, and the ability to apply principles to new situations. These objectives are not achieved by
mere presence in the class or by learning equations and other material by
rote. To enable these benefits to
accrue, you must work and work hard.
It is far better for you to have studied the portion
of the textbook which is discussed in class prior to, rather than after, the
classroom session. The time involved in
either procedure is approximately the same.
However, by studying the text before the session, you can determine
which points are not clear to you and can have them clarified through class discussion. This procedure will pay dividends when you
are solving problems dealing with the text material. Just reading the text is not studying; it is only the first step. In studying, you must reconstruct the ideas
expressed in the text so that they are meaningful to you. You must think constructively about the
material, not memorize it.
Memorizing is of practically no value and may lead to serious
difficulties. Supplementary reading in
other books and in journals is of considerable assistance in clarifying a
concept and in getting different points of view about a topic. If you must miss a session, it is only
reasonable that the work which was covered in the class be made up. Failure to make up work will affect your
understanding of subsequent topics that depend on the concepts which should
have been mastered previously.
The shorter and easier a solution, the less chance
there is of error. It pays, for this
reason alone, to analyze a problem before proceeding with the solution.
VII. CHECKING NUMERICAL RESULTS
Everyone makes mistakes! How then can we ever have confidence in engineering
calculations? The answer comes from
checking. All successful engineers have
developed (and engineering students can develop) the ability to determine with
confidence whether or not a solution is correct. This starts with the realization that a mistake can be made at
any point in a solution -- more often in the simple steps; so, every step must
be checked as a calculation proceeds.
Even the use of an electronic hand calculator does not exempt one from
making checks or results, for incorrectly pushed buttons or even round-off in
some problems yield errors.
An error detected too late in a solution leads to
the loss of the advantage inherent in the use of a good method. An engineer must assume that there will
sometimes be mistakes made and must proceed accordingly, checking as the
solution proceeds. Here is an apt
statement:
"Engineering work not thoroughly checked for
correctness has little value. In the
practice of the engineering profession, there are no answer books, nor can you
check with a classmate, for, although engineers often work in groups, the group
is usually a team with each individual alone responsible for ... part of the
job."[1]
Reliability is more important than speed.
There are many ways of checking results. The one most frequently used and one that
gives the most complete check is to repeat a calculation, when such action is
possible, by using an alternate method or by taking the numbers involved in the
calculation in a different order. The
most rapid method of checking is known as the method of approximation. This method is not used often enough. Many errors in calculations can be detected
by replacing the given numbers by other numbers which are reasonably close in
value and more convenient to use.
Making the calculations with these simpler numbers enables an
approximate result to be computed and its magnitude to be compared with the
previously determined results. Very
frequently the entire approximate calculation can be performed mentally. Although the method of approximation does
not check a result exactly, it is very effective in indicating whether a result
is reasonable.
A
simple example of the use of the approximation method is finding the value of
.
The result obviously must be more than 21.4 and less
than 37.5.
A closer limit of the result can be obtained by
approximating the given expression to be
.
This becomes
or 25. It is unthinkable that a result of 37.8 or
24.8 would be accepted without question.
Another example is the determination of sin(35°) on a calculator. We should estimate what we expect the
approximate result to be while obtaining the desired value, and should stop
short if we obtained 0.798 as the answer (sin 53°). Knowing that sin(30°) is 0.500, we should
expect the value of sin(35°) to be only a little larger. The procedure for estimating the location of
the decimal point for calculations will also check the rounded first
significant figure of the result.
The least excusable of all errors is a misplaced decimal point. Such an error is valid testimony that checking has been neglected and, worse, that the one making the calculations has so meager an understanding of what he is about that an unreasonable result can go unnoticed.
VIII. SUMMARY
Each aspect of the homework from thoughtful,
questioning reading to checking of neat, well-organized calculations has a
definite part to play in the education and morale of the student. The final stages of checking and
interpreting are the ones which bring satisfaction -- the assurance that the
subject material has been understood and correctly applied with meaningful
results. WOULD YOU BE WILLING TO LET
YOUR HOMEWORK REPRESENT YOU?
[1] D. W. VerPlank and B. R. Teare, Jr., Engineering Analysis, An Introduction to Professional Method (New York: John Wiley & Sons, Inc., 1954), p. 229.