## Posts Tagged ‘method’

### Mathematics: a unifying abstraction?

Posted on: October 26, 2008

Article #52, (September 12, 2006)

“Mathematics: a unifying abstraction for Engineering and Physics Phenomena”

A few examples of mechanical and electrical problems will demonstrate that mathematical equations play a unifying abstraction to various physical phenomena of entirely different physical nature.

Many linear homogeneous differential equations with constant coefficients can be solved by algebraic methods and their solutions are elementary functions known from calculus such as the examples in article 51.  For the differential equations with variable coefficients, the functions are non elementary and they fall within two classes and play an important role in engineering mathematics.

The first class consists of linear differential equations such as Bessel, Legendre, and the hyper geometric equations; these equations can be solved by the power series method.

The second class consists of functions defined by integrals which cannot be evaluated in terms of finite many elementary functions such as the Gamma, Beta, and error functions (used in statistics for the normal distribution) and the sine, cosine, and Fresnel integrals (used in optics and antenna theory); these functions have asymptotic expansions in the sense that their series may not converge but numerical values could be computed for large values of the independent variable.

Entirely different physical systems may correspond to the same differential equations, not only qualitatively, but even quantitatively in the sense that, to a given mechanical system, we can construct an electric circuit whose current will give the exact values of the displacement in the mechanical system when suitable scale factors are introduced.

The practical importance of such an analogy between mechanical and electrical systems may be used for constructing an electrical model of a given mechanical system. In many cases the electrical model provides essential simplification because it is much easier to assemble and the values easily measured with accuracy while the construction of a mechanical model may be complicated, expensive, and time-consuming.

An RLC-circuit offers the following correspondence with a mechanical system such as: Inductance (L) to mass (m), resistance (R) to damping constant (c), reciprocal of capacitance (1/C) to spring modulus (k), derivative of electromotive force to the driving force or input force, and the current I(t) to the displacement y(t) or output.

Here are a few elementary examples:

5)      Ohm’s law: Experiments show that the voltage drop (E) in a close circuit when an electric current flows across a resistor (R) is proportional to the instantaneous current (I), or E = R* I.

Also, that the voltage drop across an inductor (L) is proportional to the instantaneous time rate of change of the current, or E = L*dI/dt.

Also, the voltage drop across a capacitor (C) is proportional to the instantaneous electric charge (Q) on the capacitor, or E = Q*1/C.  Note that I(t) = dQ/dt.

6)    Kirchhoff’s second law:  The algebraic sum of all the instantaneous voltage drops around any closed loop is zero, or the voltage impressed on a closed loop is equal to the sum of the voltage drops in the rest of the loop. Thus,

E(t) = R*I + L*dI/dt + Q*1/C.

For example, a capacitor (C = 0.1 farad) in series with a resistor (R = 200 ohms) is charged from a source (E = 12 volts).  Find the voltage V(t) on the capacitor, assuming that at t = 0 the capacitor is completely uncharged.

7)    Hooke’s Law: Experiments show that when a string is stretched then the force generated from the string is proportional to the displacement of the stretch,

or F = k*s.  If a mass (M) is attached to a string, then when the string is stretched further more (y) after the system is in a static equilibrium, then: F = -k*s(0) – k*y.

Newton’s second law for the resultant of all forces acting on a body says that:

Mass * Acceleration = Force, or My” = -k*y.

Furthermore, if we connect the mass to a dashpot, then an additional force come into play, which is proportional to the rate of change of the displacement due to the viscous substance with constant (c).  The equation is then a homogeneous second order differential equation: M*y” + c*y’ + k*y = 0.  Depending on the magnitude of (c) we have 3 different solutions: either 2 distinct real rots, 2 complex conjugate roots, or a real double root [c(2) = 4*M*k)} corresponding respectively to the conditions of  over damping, under dumping, or critical damping.

For example, determine the motions of the mechanical system described in the last equation, starting from y = 1, initial velocity equal zero, M = 1 kg, k =1 for the various damping constant: c = 0, c = 0.5, c = 1, c =1.5, and c = 2.

8)    Laplace’s equation is one of the most important partial differential equations because it occurs in connection with gravitational fields, electrostatic fields, steady-state heat conduction, and incompressible fluid flow.  The solutions of the Laplace equation fall within the potential theory.

For example, find the potential of the field between two parallel conducting plates extending to infinity which are kept at constant potentials; or the potential between two coaxial conducting cylinders; or the complex potential of a pair of opposite charged sources lines of the same strength at two points.

### New semester, new approach

Posted on: October 26, 2008

Article #42  (April 6, 2006)

“New semester, new approach to teaching the HF course”

This semester ten students enrolled for my class; only one is a computer engineer finishing his degree and the remaining are industrial engineers.  As a reminder, this course is required for IE and the other engineering disciplines managed to open up new elective courses and were trying to market them at the expense of the wishes of many students who wanted to take my course and their petitions were denied.

With a class, one fourth its usual number, I had to capitalize on the advantages of smaller classes, once the shock is under control.  This semester, methods applied in human factors engineering are the focus and the reduction to half the previous semester of body of knowledge in the course materials might encourage my class to appreciate the efforts and time invested by the pool of human factors researchers and professionals to make available practical design guidelines for the other engineering professions.

Whereas in the previous semesters I shun away from exposing my class to new methods, except teaching them explicitly the concept of controlled experimentations, the differences among dependent, independent and controlled variables and correcting their misunderstanding, thinking that there was an abundance of knowledge to assimilate for a meager semester, I boldly changed direction in my teaching approach by investing more time on exposing and explaining the various methods that human factors might be applying in their profession.  The first assignment was using excel to compare 40 methods used in human factors, industrial engineering, industrial psychology, and designers of intelligent machines.  This assignment was a version of article #14, about the taxonomy of methods, from 20 articles that I wrote the previous years and offered them as an introduction to the course, in addition to the course materials. The students were supposed to select five categories from more than the dozen ways to classifying methods such as definition, purpose, applications, inputs, processes, procedures, output/product, mathematical requirements, disciplines teaching them, advantages, disadvantages, sources/links, connections with other methods, and comments.

I expected that, as engineers, they would logically select for columns applications, input, procedure, output, and comments because they are what define a method but somehow they opted for applications, procedures, advantages, disadvantages, and comments mainly because it is how the internet offer information.  After 3 students submitted their assignment on time I handed them over 40 summary sheets for the 16 methods used to analyzing a system or a mission, at least 2 sheets for each of 16 methods, one sheet on the purpose, input, procedure, and output/product of the method and the other sheets as examples of what the output is expected to look for presentation. I then asked the less performing students to concentrate on only the 16 methods for their assignment and most of them did not submit this assignment even two months later.

So far I used up six sessions for methods or related topics such as the methods applied in the process of analyzing systems’ performance, psychophysical procedures, the fundamentals of controlled experimentation methods, human factors performance criteria, and what human factors measure in their experiments.

As for the body of knowledge I extract a few facts from experiments and asked them to participate in providing me with the rationales or processes that might explain these facts. For example, if data show that females on average are two third the strength of males then what could be the underlying causes for that discovery?  Could that fact be explained by the length of the muscles, the cross section thickness of the muscles, the number of muscle fibers, or the length of the corresponding bones?

Facts are entertaining but I figured that they are big boys to be constantly entertained while shovelful of money is being spent for their university education. Facts are entertaining but there have to come a time when these big boys stop and wonder at the brain power, Herculean patience, and hard work behind these amusing sessions.

So far, the products of the two quizzes were complete failures; although most of the questions in the second quiz were from the same chapter sources as the first quiz, it is amazing how ill prepared are the students for assimilating or focusing on the essential ideas, concepts, and methods. So far, with a third of the semester over, I can points to only two students who are delivering serious investment in time, hard work, and excitement and are shooting for a deserved grade of A.

### Multidisciplinary view of design

Posted on: October 26, 2008

Article “31 (December 18, 2005)

“A seminar on a multidisciplinary view of design”

The term “designing” is so commonly used that its all encompassing scope has lamentably shrunken in the mind of graduating engineers. This talk attempts to restore the true meaning of design as a multidisciplinary concept that draw its value from the cooperation and inputs of many practitioners in a team.

This is a scenario of a seminar targeting freshmen engineers, who will ultimately be involved in submitting design projects, is meant to orient engineers for a procedure that might provide their design projects the necessary substance for becoming marketable and effective in reducing the pitfalls in having to redesign. The ultimate purpose is to providing the correct designing behavior from the first year.

Answering the following questions might be the basis of acquiring a proper behavior in design projects, which should be carried over in their engineering careers.  Many of these questions are never formally asked in the engineering curriculum.

Q1. What is the primary job of an engineer?   What does design means?  How do you perceive designing to look like?

A1. The discussion should be reopened after setting the tone for the talk and warming up the audience to alternative requirements of good design.

Q2. To whom are you designing?  What category of people? Who are your target users? Engineer, consumers, support personnel, operators?

A2. Generate from audience potential design projects as explicit examples to develop on that idea.

Q3. What are your primary criteria in designing?  Error free application product? Who commit errors?  Can a machine do errors?

A3.  Need to explicitly emphasize that error in the design and its usage is the primary criterion and which encompass the other more familiar engineering and business criteria

Q4. How can we categorize errors?  Had you any exposure to error taxonomy? Who is at fault when an error is committed or an accident occurs?

A4. Provide a short summary of different error taxonomies; the whole administrative and managerial procedures and hierarchy of the enterprise need also to be investigated.

Q5. Can you foresee errors, near accidents, accidents in your design?

A5. Take a range oven for example, expose the foreseeable errors and accidents in the design, babies misuse and the display and control idiosyncrasy.

Q6. Can we practically account for errors without specific task taxonomy?

A6. Generate a discussion on tasks and be specific on a selected job.

Q7. Do you view yourself as responsible for designing interfaces to your design projects depending on the target users? Would you relinquish your responsibilities for being in the team assigned to designing an interface for your design project? What kinds of interfaces are needed for your design to be used efficiently?

A7. Discuss the various interfaces attached to any design and as prolongement to marketable designs.

Q8. How engineers solve problems?  Searching for the applicable formulas? Can you figure out the magnitude of the answer?  Have you memorized the allowable range for your answers from the given data and restriction imposed in the problem after solving so many exercises? Have you memorize the dimensions of your design problem?

A8.  Figure out the magnitude and the range of the answers before attempting to solve a question; solve algebraically your equations before inputting data; have a good grasp of all the relevant independent variables.

Q9. What are the factors or independent variables that may affect your design project? How can we account for the interactions among the factors?

A9. Offer an exposition to design of experiments

Q10. Have you been exposed to reading research papers? Can you understand, analyze and interpret the research paper data? Can you have an opinion as to the validity of an experiment? Would you accept the results of any peer reviewed article as facts that may be readily applied to your design projects?

A10.  Explain the need to be familiar with the procedures and ways of understanding research articles as a continuing education requirement.

Q11. Do you expect to be in charged of designing any new product or program or procedures in your career? Do you view most of your job career as a series of supporting responsibilities; like just applying already designed programs and procedures?

Q12. Are you ready to take elective courses in psychology, sociology, marketing, business targeted to learning how to design experiments and know more about the capabilities, limitations and behavioral trends of target users? Are you planning to go for graduate studies and do you know what elective courses might suit you better in your career?

A12.  Taking multidisciplinary courses enhances communication among design team members and more importantly encourages reading research papers in other disciplines related to improving a design project. Designing is a vast and complex concept that requires years of practice and patience to encompass several social science disciplines.

Q13. Can you guess what should have been my profession?

A13.  My discipline is Industrial engineering with a major in Human Factors oriented toward designing interfaces for products and systems. Consequently, my major required taking multidisciplinary courses in marketing, psychology and econometrics and mostly targeting various methodologies for designing experiments, collecting data and statistically analyzing gathered data in order to predict system’s behavior.

### Teaching methods anecdotes: Human Factors in Engineering

Posted on: October 26, 2008

“A few anecdotes of my teaching methods”

(Article #17 in the category of Human Factors, written on April 13, 2005)

My composite class of all engineering disciplines takes my course in Human Factors in engineering for different reasons. It is a required course to the industrial engineers, but optional to all the others.

You assume that most university students have discussed with the previous students about the contents, difficulty, novelty and time consuming constraints of this course.

Apparently, the responses generated in class to my query whether the students have any idea about this course prove that they have no knowledge whatsoever of Human Factors discipline, which is to design products and services with health, safety, and ease of use of consumers in mind.

I prompt them by mentioning the term ergonomics, and lo and behold, they have read this term somewhere in ads on ergonomically designed chairs and keyboards.

Another surprise is that when it comes to purchasing course materials and answering old questions in assignments, many succeed in locating previous students who took the course.

I have tried many teaching styles, revised several times the contents and arrangements of the course chapters, and experimented with various methods to encourage the students into reading the course materials on their own volition.

I varied the number of quizzes, exams, assignments and lab projects, tried to encourage them to read research articles, investigated new presentation techniques, gave them hints on how best to read and assimilate the materials, emphasized on thinking like engineers and not memorize information, and I assigned students to read to the class:  I received basically the same observations, no matter how I change the course.

1.Engineering students will read only under duress,

2. Will barely take notes even if bonus points are at stakes,

3. Will start an assignment a couple of days before due date, even if the assignment was handed out several weeks prior to due date,

4. Will remember to ask for clarifications only on due date,

5. Will copy and cheat unabashedly.

Engineering students refuse to carry to class any course material, unless the exam is an open book.

Many don’t bring any paper or pen to take notes, many refuse to redo their assignments for a couple extra points or for closure sake, and most of the redone works show no improvement.

Students can use word processors or any computer applications for their assignments, but the end product has to be hand written, including tables, charts and figures. Guess why I figured out this constraints?

It turned out that my guess was correct: most of the time I can manage to read physicians’ prescriptions better than their handwriting assignment.

There was a time when engineers were trained to submit neat drawings, as engineers should be trained to do, but this time is long gone.

Another advantage of submitting hand written work is that students will actually read what they are writing and rely less on copied CD’s and try their hands on being neat, using rulers, compasses and the long lost engineering working components.

I invented several ways to brute force students to read at least parts of the course materials.

In addition to mid-term and final exams, they have to answer dozens of questions for their mid-term and final take homes exams.

I assign graphs, tables and figures to students to hand write, copy on transparent sheets and present to class with written explanation attached.

All assignments are submitted on composition booklets.

I encourage them to take notes by asking them questions on materials not covered in the course materials, and giving bonuses to anyone who remember to provide a copy of his notes on final day.

I have come to realize that any zest I invest in teaching is for just a couple of students each semesters.

Yes, there is this couple of students who demonstrate this want to learn: it is always refreshing to feel that a few students are serious about the money invested by their parents for them to learn at universities.

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