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IEEE TRANSACTIONS ON EDUCATION, MAY 1976 at the rate of $30.00/h then the professional cost per minute of tape is $61.00. The extra dollar per minute covers the cost of delivering the lecture on camera and reviewing the tape before clearing it for library use. Studio costs are approximately $300.00/h or $5.00/min. My experience has been that every minute of production re- quires approximately 1I- minutes of studio time. Therefore, studio costs are roughly $7.5 0/min. Cassette tapes cost roughly $0.50/min and the cost of the quadrille pads and marking pens amount to no more than $0.05/min. Therefore, my first estimate of the cost of production is 61.00 + 7.50 + 0.50 + 0.05 or $69.05/min. Based on these estimates I think it is prudent to say the general cost of producing a video lecture is approximately $70.00/min. This makes them an order of magnitude cheaper to produce than films. Playback costs are virtually impossible to estirnate because they depend entirely on the number of students using the sys- tem. To get some estimate of the maximum playback cost, I used the following assumptions. 1) Only one student watches the tape each time it is played back. (At Iowa State the cassette system can accommodate up to five students simultaneously at each TV monitor.) 2) Only one copy of the master is dubbed onto a video cassette. 3) The cassette survives 1000 passes through the machine. 4) After 1000 passes the technical content of the tape is obsolete and must be redone. Using my estimate of production costs a 40 minute tape will cost approximately $2800.00 to produce. Therefore, the cost per pass (not figuring overhead) is $2.80. If overhead adds another 25 percent, the maximum cost of a 40 minute tutor- ing lecture is $3.50. In the past two years there has been a substantial growth in the use of video tape cassette material at Iowa State Uni- versity. The College of Education has a set of video-cassette lessons which are required viewing. This means that there are times when a viewer may find it impossible to view a tape the first time he checks in at the Media/Microform facility. This queueing could have a detrimental effect on the video- cassette as a tutoring medium and must be alleviated before it becomes commonplace. At present, the library has five cassette playback systems. So far they have never experienced less than four working units and except for a few isolated in- stants, the repair service has been 24 h or less. The first two years experience with video-cassette tutoring is very encouraging. The 92 percent increase in student use in-one year supports the contention that it is an acceptable medium for tutoring. The experiment with students at Purdue University indicates tutoring lectures can be created which will be acceptable to students beyond the limits of a single campus. Production costs are dominated by the cost of professional creativity. As more expenence with lecture technique and adopted format is acquired, these costs may be somewhat re- duced. However, I feel that present production costs are certainly reasonable. Playback costs depend on the number of viewers. When multiple copies of a lecture are needed to meet viewing demands, the cost of a tutoring lecture will be very small. The format for presenting a tutoring lecture is described in the 1973 paper [ 1 ] . The acceptance of that format by the students means that video-cassette lectures in the future may be designed for a broader clientele. For example, they could be designed to serve as review lectures or as summarizing lec- tures that could be integrated into an off-campus continuing education package. Tutoring Lectures 1) Current-Voltage Polarity References (The Passive Sign Convention) [201. 2) An illustration of Using Topology in Network Analysis [281. 3) A Thevenin Equivalent Circuit When You Have Con- trolled Sources [ 191. 4) Initial Conditions [24]. 5) Solution of a Second Order Circuit [ 191. 6) Magnetic Polarity (The Dot Convention) (271. 7) Real and Reactive Power [ 251. 8) The Phasor Transform [ 29 1. 9) S-Domain Equivalent Circuits [ 25. 10) Partial Fraction Expansions Part I [29]. 11) Partial Fraction Expansions Part 11 [ 37 1. 12) The Impulse Function Part I [33]. 13) The Impulse Function Part 11 [35 . 14) Complex Numbers [38]. l15) The Flip-Flop [ 221]. 16) The Transfer Function [281. 17) Maximum Power Transfer [ 33. 18) RMS Calculations of Periodic Functions [30]. The number in the bracket at the end of each title is the approximate length of the lectute in minutes. REFERENCES [1] J. W. Nilsson, "Tutoring via video tapes," in Proc. 3rd Annu. Fron- tiers in Education Conf., 1973, pp. 303-305. On Teaching an Undergraduate Projects Course S. E. GOODMAN Abstract-Senior project courses are included in many engineering curricula. While the value of such courses is widely accepted, it is also recognized that they often present difficult organizational problems. A format for such a course which has been successful, both in terms of student response and control of faculty effort, is presented. It is hoped this may provide useful guidance to others involved in such courses. INTRODUCTION For the past four years we have been experimenting with a senior projects course for our majors in computer science, ap- plied mathematics, and operations research. The format which has evolved should be suitable for other groups of engineers as well. We think that a projects course helps develop desirable professional qualities in our students, and would recommend it to others. However, a course of this kind seems particularly susceptible to development troubles. At this point we appear to have a manageable and reasonably structured course which tries to meet certain desired goals. This was not always the case. Perhaps by presenting a short summary of the end re- sult of our efforts, we can smooth the way for similar courses elsewhere. COURSE GOALS 1) To have the student do an extended, although not neces- sarily original, piece of work in his/her area of interest. 2) To expand the student's exposure to the technical litera- ture; in particular, to get him/her to use sources other than undergraduate text books. 3) To develop some of the confidence and experience that can only be gotten by doing independent work. 4) To improve both written and oral communication skills. 5) To accomplish the four goals listed above for a class of over 20 students in a manner which does not force the instruc- tor to devote 100 percent of his/her time to this one course. Manuscript received September 22, 1975. The author is with the School of Engineering and Applied Science, University of Virginia, Charlottesville, VA 22901. 74

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Page 1: On Teaching an Undergraduate Projects Course

IEEE TRANSACTIONS ON EDUCATION, MAY 1976

at the rate of $30.00/h then the professional cost per minuteof tape is $61.00. The extra dollar per minute covers the costof delivering the lecture on camera and reviewing the tapebefore clearing it for library use.Studio costs are approximately $300.00/h or $5.00/min.

My experience has been that every minute of production re-quires approximately 1I- minutes of studio time. Therefore,studio costs are roughly $7.5 0/min.Cassette tapes cost roughly $0.50/min and the cost of the

quadrille pads and marking pens amount to no more than$0.05/min.Therefore, my first estimate of the cost of production is

61.00 + 7.50 + 0.50 + 0.05 or $69.05/min. Based on theseestimates I think it is prudent to say the general cost ofproducing a video lecture is approximately $70.00/min. Thismakes them an order of magnitude cheaper to produce thanfilms.Playback costs are virtually impossible to estirnate because

they depend entirely on the number of students using the sys-tem. To get some estimate of the maximum playback cost, Iused the following assumptions.

1) Only one student watches the tape each time it is playedback. (At Iowa State the cassette system can accommodate upto five students simultaneously at each TV monitor.)

2) Only one copy of the master is dubbed onto a videocassette.3) The cassette survives 1000 passes through the machine.4) After 1000 passes the technical content of the tape is

obsolete and must be redone.Using my estimate of production costs a 40 minute tape will

cost approximately $2800.00 to produce. Therefore, the costper pass (not figuring overhead) is $2.80. If overhead addsanother 25 percent, the maximum cost of a 40 minute tutor-ing lecture is $3.50.

In the past two years there has been a substantial growth inthe use of video tape cassette material at Iowa State Uni-versity. The College of Education has a set of video-cassettelessons which are required viewing. This means that thereare times when a viewer may find it impossible to view a tapethe first time he checks in at the Media/Microform facility.This queueing could have a detrimental effect on the video-cassette as a tutoring medium and must be alleviated beforeit becomes commonplace. At present, the library has fivecassette playback systems. So far they have never experiencedless than four working units and except for a few isolated in-stants, the repair service has been 24 h or less.The first two years experience with video-cassette tutoring

is very encouraging. The 92 percent increase in student usein-one year supports the contention that it is an acceptablemedium for tutoring. The experiment with students at PurdueUniversity indicates tutoring lectures can be created which willbe acceptable to students beyond the limits of a single campus.Production costs are dominated by the cost of professionalcreativity. As more expenence with lecture technique andadopted format is acquired, these costs may be somewhat re-duced. However, I feel that present production costs arecertainly reasonable. Playback costs depend on the number ofviewers. When multiple copies of a lecture are needed to meetviewing demands, the cost of a tutoring lecture will be verysmall.The format for presenting a tutoring lecture is described in

the 1973 paper [ 1 ] . The acceptance of that format by thestudents means that video-cassette lectures in the future maybe designed for a broader clientele. For example, they couldbe designed to serve as review lectures or as summarizing lec-tures that could be integrated into an off-campus continuingeducation package.Tutoring Lectures

1) Current-Voltage Polarity References (The Passive SignConvention) [201.

2) An illustration of Using Topology in Network Analysis[281.3) A Thevenin Equivalent Circuit When You Have Con-

trolled Sources [191.4) Initial Conditions [24].5) Solution of a Second Order Circuit [ 191.6) Magnetic Polarity (The Dot Convention) (271.7) Real and Reactive Power [251.8) The Phasor Transform [291.9) S-Domain Equivalent Circuits [25.10) Partial Fraction Expansions Part I [29].11) Partial Fraction Expansions Part 11 [37 1.12) The Impulse Function Part I [33].13) The Impulse Function Part 11 [35 .14) Complex Numbers [38].l15) The Flip-Flop [ 221].16) The Transfer Function [281.17) Maximum Power Transfer [ 33.18) RMS Calculations of Periodic Functions [30].The number in the bracket at the end of each title is the

approximate length of the lectute in minutes.

REFERENCES[1] J. W. Nilsson, "Tutoring via video tapes," in Proc. 3rd Annu. Fron-

tiers in Education Conf., 1973, pp. 303-305.

On Teaching an Undergraduate Projects CourseS. E. GOODMAN

Abstract-Senior project courses are included in many engineeringcurricula. While the value of such courses is widely accepted, it is alsorecognized that they often present difficult organizational problems. Aformat for such a course which has been successful, both in terms ofstudent response and control of faculty effort, is presented. It is hopedthis may provide useful guidance to others involved in such courses.

INTRODUCTIONFor the past four years we have been experimenting with a

senior projects course for our majors in computer science, ap-plied mathematics, and operations research. The format whichhas evolved should be suitable for other groups of engineers aswell. We think that a projects course helps develop desirableprofessional qualities in our students, and would recommend itto others. However, a course of this kind seems particularlysusceptible to development troubles. At this point we appearto have a manageable and reasonably structured course whichtries to meet certain desired goals. This was not always thecase. Perhaps by presenting a short summary of the end re-sult of our efforts, we can smooth the way for similar courseselsewhere.

COURSE GOALS1) To have the student do an extended, although not neces-

sarily original, piece of work in his/her area of interest.2) To expand the student's exposure to the technical litera-

ture; in particular, to get him/her to use sources other thanundergraduate text books.

3) To develop some of the confidence and experience thatcan only be gotten by doing independent work.4) To improve both written and oral communication skills.5) To accomplish the four goals listed above for a class of

over 20 students in a manner which does not force the instruc-tor to devote 100 percent of his/her time to this one course.

Manuscript received September 22, 1975.The author is with the School of Engineering and Applied Science,

University of Virginia, Charlottesville, VA 22901.

74

Page 2: On Teaching an Undergraduate Projects Course

CORRESPONDENCE

One should not discount the importance of goal 5). It isdifficult and inordinately time consuming to simultaneouslysupervise over 20 different independent projects. No matterhow worthwhile a course's educational goals may be, fewdepartments can afford to allocate the full-time services of afaculty member to one course, and few faculty memberswould be willing to sacrifice time that might otherwise be usedfor research, proposal writing, graduate teaching, etc.

OBSERVATIONS AND SUGGESTIONS

1) It is important that the students choose their own topics.This places a good deal of responsibility on the students, andwe consider it to be a crucial step in helping them learn towork independently. The instructor should provide informa-tion on where to look for ideas in the literature, but should befir with the student who "can't think of anything." If thestudent really "can't think of anything," what sort of engineerwill he/she make?

2) Few projects of any substance can be done in one semes-ter. Most students need three to four weeks to find a topicthat appeals to them. They should be encouraged to considera few topics before making a final choice. When their choicesare rushed, they often choose topics whose appeal is shortlived. Nothing is more deadly than a "lame duck" project.By the time a student has found a topic and done some seri-ous reading, over half the semester is over. Since most projectsinvolve an experiment or large computer program, there willbe insufficient time for the students to complete the basicwork and write-up for the project in one term.3) It is our opinion that the best course structure for a pro-

jects course should consist of a two credit-hour course duringthe Fall semester of the senior year, followed by a one credit-hour course diring the Spring term (a credit-hour may be cali-brated by the statement that 17-18 credit hours per semesteris a respectable load for a senior engineering student). Thisarrangement appears to give the students plenty of time to putsome thought into their projects, and permits the few studentswho may abort a project to start and complete a new one bythe end of the year. No more than two credit-hours should begiven during any semester. The nature of most projects, andthe fact that the students are taking other courses, will onlypermit a limited amount of effort to be completed during oneterm. This effort seems to be relatively insensitive to the num-ber of credit-hours given for the course.4) Each student must do his/her own project. This is the

only way the students will get the full educational benefitfrom it. The instructor must keep his/her hands off the pro-jects. The students must see what they can do on their own.Excessive faculty participation is to be avoided, even if it issolicited or would improve the quality of the project.

5) The instructor should establish limited office hours whichare explicitly reserved for individual consultation on thesesenior projects. We have found that one office hour per weekfor every 1 0 students is sufficient. These consultations shouldbe concerned with topic approval, literature suggestions, pro-ject organization, etc. The instructor should not spend timedebugging programs, checking algebra, etc.6) We have our students exhibit their projects in three ways.

a) A 20 minute talk describing the topic shortly after it ischosen.

b) A 45 minute talk on the project when it is complete ornearly complete.

c) A written report when the project is complete or nearlycomplete.Each student completes a) and either b) or c) the first term,

and the remaining item the second term. If a student has notgotten far on his/her project the first term, that student mustaccount for this in b). The course grades are determined bysome suitable weighting of the grades on a)-c) and generalclass participation.

7) Once the students start choosing their topics, the short

talks can begin, and by the time everyone has given a shorttalk there is usually at least one student who is ready to give a45 minute talk. There are periods, usually at the beginning ofthe first term (before anyone has a topic) and at the end of thesecond (after all the long talks have been given), when none ofthe students are available to speak. The early slack period canbe handled by having the instructor discuss literature sources,projects from earlier classes, etc. There is almost invariably atleast one student in the class who has chosen a topic beforethe term starts. Thus, student talks may begin with the secondclass meeting. The slack at the end of the second term isreadily absorbed by inviting other faculty members to speakon research interests that overlap some of the project topics.

Bilinear Transformation of Polynomials

V. V. BAPESWARA RAO AND V. K. AATRE

Abstract-A simple technique for the bilinear transformation of poly-nomials is presented. The algorithm is well suited for clasroom use, ascomputational errors can be checked at all stages.

The need for bilinear transformation of a polynomial arisesin many problems in electrical engineering. Several algorithmsare presented in literature to obtain the transformed polyno-mial without effecting the tedious direct substitution [ 1] -[6] .The coefficients of the transformed polynomial are obtainedeither by a matrix multiplication [ 1 ] -[ 31 or by causing a seriesof simple transformations [4] lThe latter technique involvesless computation but lacks the compact presentation of thetransformation matrix method. When the transformed poly-nomial is to be obtained by longhand computation, as is oftenthe case in a classroom, computational errors are likely tooccur, and it is not easy to locate them in either of the twomethods. In the algorithm outlined in this correspondence,errors occurring at any stage can be detected by a simple checkat that stage.Let

f(z) = al + a2z + a3z2 + * * +akk-1 + * +an+ z n = 0

and

g(s) = bI + b2s+ b3s2 + + bkSk-i + + bn+lsn = O

where

(s- I)Define a set of polynomials

f1 (z) = a1

f2(z)=a, +a2z

f3(z)=al +a2z+a3z2

fk(z) al + a2z+a3Z2 + *+ akzk-

Manuscript received May 30, 1975. This work was supported by theNational Research Council of Canada under Grant A-7237.The authors are with the Department of Electrical Engineering, Nova

Scotia Technical College, Halifax, Nova Scotia, Canada.

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