...and Systems Integration

{continuation on Chapter 1:  Data Analysis and Systems Integration}

1-5:  Differential Equations and Physics Have Taken a Bad Rap.

Like Physics, calculus has taken a bad rap for being difficult in the initial learning,
and this bad reputation has kept many from getting into the twin disciplines, even
more engineering technology students from delaying the learning benefits for the
second and much later year.  We will show right now how easy differential
equations are to get into {large part of the applications of calculus to technical
programming}, especially with the ease of accessibility of MATLAB to your finger
tips.
Something must definitely be said about the foundation of mathematics in the
history and evolution over the last 50 years of numerical analysis for data analysis.  
You will read more about this in later chapters, especially the one on “The Digital
Atomic Revolution”, but it can be simplified by considering math as passing from an
emphasis on differential equations {which of course like all motion and physical
phenomenon itself are analogous} to the matrix of linear algebra; of course with
mathematical techniques like Taylor series and the LaPlace transform to convert
from an analog to a digital format, or from differential to linear format.  That is where
MATLAB in technical computer applications, much like Microsoft in total computer
applications, has ridden the back of the Digital Atomic Revolution:  MATLAB has
provided the tools in a single concise language {many statements called
commands like “diff” to differentiate and “FF” for the fast fourier transform of the
LaPlace equation} to easily provide calculations in analog, digital, and both.  Then
you throw in the simulation part of MATLAB with “Simulink”, the built in simulator of
MATLAB, and you have a language and software, albeit quite expensive except for
large companies except for the student version used primarily in this book, and
MATLAB can do just about anything for you, including your calculus and linear
algebra homework, except cook your meals.  Even as Microsoft developed into the
more popular software than MAC while not being at all any more functional, so other
software today like FORTRAN, Mathematica, or BASIC depending on the technical
application can be as fucntional as MATLAB, we just have in MATLAB and
Microsoft the more popular means of communicating with our technical, social  and
work environment.
Let us begin right now, to take some of the mystery of differential equations with
introduction to a very simple one of y’ = f(x) = sin(pi*x), where y’ is an easy and
standard way to write dy/dt.  What this equation means then is the first derivative of
y, which is a function of x, that is f(x), which in turn is the speific function of x which is
sin(pi*x).

NOTE:  Get use right at this beginning chapter, that all equations will be written in
the language of MATLAB; that is * for multiplication, and pi for pie.  And what a way
to start feeling at ease with differential equations in terms of what you know so well
for fundamental mathematics, the most common functions of sine and cosine.  
These by the way, written in the language of MATLAB, are among the many built-in
functions of MATLAB.

If you back to the basic definition of the derivative, y’ = dy/dt, the basic concept of
which comes to mind as the rate of change, the rate of change of y, or delta y, as
compared to the change in time, delta time.  What is different about the calculus of
derivations is that the delta change is extremely small; in fact, a small change that
approach infinitesimal.  {It is about the smallest change that you can conceive of.}  
When you operate on a function to get it out of its derivative back into the original
function, like to integrate y’ = -sin(pi*x) to get y {notice we are passing in integration
from y’ to y}, or y = -1/pi * cos(pi*x) + c.
Even as it use to be the custom to take semesters of “analytical geometry and
calculus”, since so many of the concepts of the calculus of differential equations
comes from geometrical visualization and foundations.  For example in the
MATLAB plot above {edited over in the figure windown to show slopes and places
where y is equal to zero}, you can visualize y’ as the slope at different x points on
the y = f(x) = sin(x) curve.  Left to right, and without numbers, you can see that
between 0 and 1/2 pi the slope {delta y/delta x, or so much rise over run} is max;
then at pi, zero slope; then through the sequence of minus max, zero slope, and
max postive.  And intuitively you can see that these slope values in turn plot a
cosine function.  You can also think of differentiation and integration as the
opposites:  diff takes the rate of change of the curve, and int is the anti derivative.  
MATLAB makes it easy for you to switch between functions like y and y’ with the
“int” and “diff” commands.  As we spell out the process of gong back to y from y’
with the proper symbology of differential equations, we get:

MATLAB makes it so easy to pass from y’ to y by use of the “int” command with the
following code {check it out in the command window}.

%drill on integration and differentiation
%since int and diff work with the symbolic sin and cos, or explicit, use %s
for function
s = '-sin(pi*x)'
y = int(s)
yy = numeric(int(s,0,pi))
yyy = numeric(int(s,0,2*pi))
s1 = '-sin(2*pi*x)'
y1 = int(s1)
s2 = '1/2/pi*cos(2*pi*x)'
y2 = diff(s2)
%now to get some intuitive feel for integration, try
s3 = 'abs(x)'
y3 = int(s3,.5,.6)
s4 = 'x'
y4= numeric(int(s4,.5,.6))
y5 = numeric(int(s4,0,pi))
y6 = numeric(int(s4,0,2*pi))
And you can match up the answers in the command window:
s = -sin(pi*x)
y = 1/pi*cos(pi*x)
yy = -0.6056
yyy = -0.1179
s1 = -sin(2*pi*x)
y1 = 1/2/pi*cos(2*pi*x)
s2 = 1/2/pi*cos(2*pi*x)
y2 = -sin(2*pi*x)
s3 = abs(x)
y3 = 11/200
s4 = x
y4 = 0.0550
y5 = 4.9348
y6 = 19.7392

1-6:  Many Threads of Modern Technology Made the Technical Revolution.

You will find many threads that run consistently through the book which will not be in
the chapter titles as at the highest level this is a book of Technical Applications;
however you will see them at the Section Heading Level, like 1-6 above:  numerical
methods, Excel, Mathematica, MINITAB, optimization, sytems ID, linear theory, and
advanced engineering math, even data analysis itself and systems integration.  You
might call some of those threads of book specialization, the “continuity in the book”
like:  optimization, simulation of a transport aircraft and F-16 in MATLAB, data
analysis, the programming of advanced engineering math,  systems integration
{closely related to the process}, parameter estimation and modeling.  These
threads of speciality, along with the engineering and teaching experience of the
author,  help to make this book unqiquely what it is.  Many more specialized, and
much more difficult, books have been written on the specialized and other threads;
but it is the unique selection with applications that makes TECHNICAL
APPLICATIONS OF COMPUTERS.  {Therefore each thread, especially the
specialized threads, will be introduced as early as possible in the chapters of the
book; and then hung onto and progressively applied.}
And yes, along the way I will share with you some of the intuitive excitement of 50
years of working in technology, teaching and engineering.  It takes one who has
experienced, and still remembers often, the excitements of learning physics,
different equations, computers, electronics, and sophisticated systems to boot, to
have those memories; and it is hoped that some of that emotion, with the technical
content, is communicated in this book.  One might call it true learning or scholarship
as contrasted to a priority for gaining a piece of paper to earn money, and might
have its roots in thinking like of Ralph Waldo Emerson in “The American Scholar”,
perhaps you would like to call it “The American Technical Scholar”.   This helps to
make the subject of TECHNICAL APPLICATIONS OF COMPUTERS more
interesting; and you will enjoy simultaneously technically working with your computer
while you make graphs and plots like the MATLAB logo.

%MATLAB logo
load logo
surf(L,R),colormap(M),n=length(L(:,1));
axis off, axis([1 n 1 n-.2,8]), view(-37.5,30)

1-7:  Sharing of Learning Theory.
Another consistent thread throughout this book will be sharing on learning theory.  
Finally, it is apparent that the “you are picking on me” attitude of the boomer
generation just did not work, as the cover-up in education had been blown, even
bigger than the cover-ups in financial institutions and government related to the
economy, American now recognizing that over one/third of high school students do
not graduate.  The proof in is in the pudding, and how can you claim to teach and
the system is working when the results are so miserable.  Poor education of
teachers in colleges and university, and the practicing of poor teaching in high
schools and other levels of education, has sacrificed generations of student drop-
outs on the altar of “you are picking on us”.
As one successful teacher in California recently said, “The education system is
broken.  Teachers can’t teach, and students can’t learn.”  There are several obvious
reasons for this, but more of the responsibility should fall on the education
departments of universities across the nation who have so poorly trained teachers.  
It is a well known fact among college students and alumnus that the easies route to
go in college is to major in eduction, and likewise that when a student has taken
approximately 3 education courses for then on it is a repeat.  Of course, the real
problem, a weakness that has been known for years by these money-making
education organizations like Sylvan, is that of the four levels of learning, teachers
normally take the path of least resistance and use only the lower two levels.  Of the
four levels of learning--rote memory, example, trial and error, and problem solving--
memory work and example learning are the easiest, require less time, and take less
preparation.
An extension of this problem is in continuing education.  The average knowledge
and skill of the average college degree now has a half-life of approximately 8
years.  What that means is simple:  in 8 years after graduation over half of what you
have learned is outdated.  Increasing the average worker, especially in the more
challenging skills of Aerospace, must find practical ways of continue learning in
what is generally called adult education; and yet at the same time, he must avoid the
same systems of education that have made teachers what they are not today!  And
the solution is obviously not in more and higher pieces of paper.  In this book, all
four levels of learning will be encouraged and promoted, especially the highest
levels of trial and error, also of the creative learning of problem solving.
Every 10 years or so America spouts a new cure-it-all for schools, and they never
work because they come from educators of the education departments and not
from science and math departments.  Everyone knows when you go to college,
next to Basketweaving II and Greenhouse IV, education courses from the
education departments are the easiest, also that once you have taken 3 or 4 of
them, you then just repeat subject matter.  The ideal combination for teachers in
STEM would be 3 courses in the technical discipline for every one course from the
education department.  {Even more potential for excellence would be teachers
required to have equal employment time in the technical industries for each year of
teaching experience, but the solution every 10 years follow the path of least
resistance, not the path of challenge and excellence.} STEM, the newest approach
to fix the American education system may offer something, we should give it a
chance with one foot solidly in one of the technical disciplines, and you will find on
the google plus Technical Corner for this website, an invitation for STEM to show its
wares.  However, although there are definitely a few good people and teachers in
both education and education departments, just like in civil service, the system itself
is the big problem that is always seeking the lowest possible level of operation.  
NEVER forget that graduates of education departments by and large of the
American education system thinks if you can teach you can teach anything, the
technical subject matter is not that important, so that increasingly {and the trend
continues as in many decades of the past where there is a failure to modify the
university and college education departments, concentrating rather on the
unfortunate school teachers of high school and below that have been trained by
these universities in the first place} in superficial recommendations for excellence
like New Math, CORE, and STEM.  Can we learn something from them, perhaps,
but let us not put all our eggs in one basket as learning is a many faceted,
interesting, and challenging experience.  It goes with growth from youth to
adulthood and with the excitements of continuing education years.
Since you teachers are most often good at the lowest levels of learning, memory
work and example learning, and practice the same, in this TAC book, you are
offered an example of learning by "Systems Integration", such applying not only to
the included technical subjects, but also learning.

1-8  Ups and Downs of UAV Testing by John Del Frate of NASA.

You will enjoy for perspective on UAV testing the very personable report of Del
Frate in newspaper/magazine format in February 2008, the “Abstract” of which is:
If you could see the road ahead, you might just pass up a fantastic opportunity
because you're blinded by the potential pitfalls. In my case, I was testing the project
management waters at the NASA Dryden Flight Research Center after ten years of
being a research engineer. I was an eager (but ignorant) rookie project manager
(PM) and I was willing to engage in just about any project without knowing what it
would entail. The assignment I accepted was to help NASA's Environment
Research Aircraft and Sensor Technology (ERAST) Project, a partnership with a
fledgling Uninhabited Aerial Vehicle (UAV) industry, to tackle stratospheric flight. I
remember one of our industrial partners querying me about whether or not I
understood what I was getting into. Like one of those bobble-head toys that have
become quite popular, I nodded. But in reality, I didn't have a clue. His response
was, “Hang on, it's going to be a wild ride.” He was right. In retrospect, if I had
clearly understood the ten years of pitfalls that were coming, I might not have “hung
on.” Now I can look back and say that I would not trade the experience for anything.
The lows included the destruction of a number of UAVs on my watch. Later
someone told me that we should not be surprised if we lost one UAV for every ten
flights. We wrote many chapters in the book on what can go wrong with UAVs-and
we are still writing. As you can imagine, each mishap was accompanied by an
investigation. What an education!

Jerry V. McMichael
May 8, 2010
Portales, New Mexico

1-9:  Drilling with FreeMat, MATLAB, SciLab, and Octave Basics.

For some these drills to follow, and at the end of many chapters, may be a review,
and for others they may be a first time; however without the memorization, example
of knowledge and skill in MATLAB and other program languages and algorithms,
there can be no trial and error and creativity.
1.  Some Basic Built In Data Analysis Functions in MATLAB.  {This also applies to
the other free and open software utilized in this course, that is primarily SciLab,
FreeMat, and Octave.}  MATLAB, among many other things, is made for basic data
analysis with built-in functions like mean, median, std {standard deviation}, sum,
trapz {trapezoidal integration}, and others.  You will begin to think, rightly so, that
MATLAB is almost magic, but there is also a built-in function, not so much for data
analysis but will allow us to quickly set up a matrix of data for analysis, which is v =
magic(3), where the 3 in parenthesis stands for a 3x3 matrix of 3 columns and 3
rows.  Perhaps you know by now that MATLAB stands for MATrix LABoratory, and
as such you will find much of the math, like in the basic and built-in functions of data
analysis and also for the magic function are columns oriented.  For example if you
used the plot function on a magic function, it will automatically plot a line for each
column as shown below.

2.  Files, Functions, and Data Structure.
{INTRO* p 79}
3.  Histograms and Cumulative Curves.
{DATA** p 9}

* Introduction of Matlab for Science and Engineering

**Data Analysis for the Earth Sciences

All the figures for this chapter
with the chapter itself is available free as a PDF.  You
can download it by clicking here, and then either save it to your computer or view.  
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adobe at www.adobe.com .