Paper ID #9852

Multi-Course Alignment for 1st Year Engineering Students: Mathematics,Physics, and Programming in MATLAB

Caroline Liron, Embry-Riddle Aeronautical Univ., Daytona Beach

Caroline Liron is an Assistant Professor in the Engineering Fundamentals Department, at Embry-RiddleAeronautical University (ERAU), where she has been teaching since 2005. She obtained her bachelor’sin aeronautics and space from EPF, Ecole d’Ingenieur (France), and her M.S. in aerospace engineeringfrom ERAU. She currently teaches Introduction to Programming for Engineers. She is involved in devel-oping and maintaining the hybrid version of that class, and researching improvements methods to teachprogramming to incoming freshmen using new technologies.

Dr. Heidi M Steinhauer, Embry-Riddle Aeronautical Univ., Daytona Beach

Heidi M. Steinhauer is the Department Chair of the Freshman Engineering Department and is an As-sociate Professor of Engineering at Embry-Riddle Aeronautical University. Steinhauer holds a Ph.D. inengineering education from Virginia Tech. She has taught Spatial Visualization Development, Engineer-ing Graphics, Introduction to Engineering Design, Automation and Rapid Prototyping, and has developedseveral advanced applications of 3D modeling courses. She is the co-advisor of the only all-women’s BajaSAE Team in the world. Her current research interests center around the development and assessment ofstudents’ spatial visualization skills, effective integration of 3D modeling into engineering design, andwomen’s retention in engineering.

Dr. Jayathi Raghavan, Embry-Riddle Aeronautical Univ., Daytona BeachDr. Bereket Berhane, Embry Riddle Aeronautical University

c©American Society for Engineering Education, 2014

Page 24.920.1

Multi-Course Alignment for 1st Year Engineering Students:

Mathematics, Physics, and Programming in MATLAB

Background

Historically, siloed courses utilizing traditional, deductive, teaching methods have struggled to

effectively promote conceptual understanding. Gains students achieve are usually modest and not

statistically significant; generally students are able to increase their factual knowledge only.

These modest gains are predicated on students having either no preconceptions or correct but

incomplete ones. However, students who have incorrect preconceptions do poorly as they must

change their existing cognitive structure.1 Inductive teaching methods better enable students to

achieve a permanent change to their cognitive structures. Students also have a difficulty

transferring learning horizontally through their courses.

Purpose

First year students struggle to synthesize concepts across Programming for Engineers, Calculus I,

and Physics I courses.2 While calculus and physics are tools to be utilized by engineers to solve

problems, our students are often unable to see that the knowledge presented in the mathematical

and physics context can be transferred to solving engineering problems. Students also tend to

view programming as an isolated component of engineering. They should understand instead that

programming is yet another tool to verify results and to solve more complex problems, reducing

risks of algebraic errors.3

Design/Method

Three faculty members linked their classes to create a STEM (science, technology, engineering,

and mathematics) small-learning-community (SLC). The same set of students is registered for

the three linked courses: Calculus I, Physics I, and Introduction to Programming using

MATLAB. In addition, these same three faculty members also taught one or two non-SLC

sections of the same course; these were the control groups. Students were randomly selected

from the incoming newly admitted students to be within the SLC.

Page 24.920.2

Table 1 describes the topics taught in each course. As a start, only the topics highlighted in bold

were chosen to be developed across all three classes: graphs and functions, integration, related

rates, vectors, free body diagrams, Newton’s laws of Motion, center of mass and its motion.

Table 1: Description of Calculus I, Physics I and Programming Courses

Course Description

Calculus I Graphs and functions; differentiation and integration of algebraic and

elementary trigonometric functions; related rates; applications of first

and second derivatives.4

Physics I Vectors and scalars quantities; geometrical optics, kinematics; free body

diagrams, Newton’s Laws of Motion, work, work-energy, conservation

of energy, conservation of momentum, center of mass and its motion. 4

Introduction to

Programming for

Engineers

Software design and development: specification, requirements, design,

code, and test; scripts, data-types, input and outputs, flow-control,

functions, arrays, files and plotting.

An overarching idea behind the SLC is to help students realize that the topics of Calculus I,

Physics I, and Programming are most effective when used together in engineering. These

concepts in engineering applications are not siloed and nor should the coursework be. Therefore

to address this conceptual misalignment, all three faculty developed mini-projects, or specific

assignments incorporating concepts from each of the three disciplines. All three faculty

collaboratively developed the real-world application problems that required leveraging

knowledge horizontally across all three courses.

The bold faced common themes were then mapped to provide a framework in the development

of the interdisciplinary mini-projects. It was critical to ensure the mini-projects developed

aligned the appropriate topics across all three courses. Table 2 presents the final mapping of the

common course topics and the developed themes of the mini-projects.

Table 2: Mapping of MATLAB topics to Calculus I and Physics I mini-projects

Calculus I Physics I

Flow-control (loops) Integral of a function Calculate slopes during a trajectory

Arrays, plotting Related rates Vector Fundamentals, Cable

Tension, Trajectory Analysis

Files Center of mass of an aircraft

This paper will present the development of and the results from the MATLAB course. Other

specific mini-projects given in Calculus I and Physics I classes are to be presented in future

papers. The next section will present two of the mini-projects developed for the MATLAB

course in detail.

Page 24.920.3

At the start of the semester, students are just beginning to learn many of the theorems of

Calculus I and Physics I and are not ready to solve these types of problems in either course. It

was determined that MATLAB’s plotting capability is a tool that could be presented earlier in

the programming course to help solve these Calculus I and Physics I class problems, thereby

providing students with additional exposure to the material as presented from a programming

context.5 This was the guide for the development of the two mini-projects discussed in this paper

that integrated MATLAB, Calculus I and Physics I knowledge.

Mini-Project #1: Cable Tension (Vectors, Plotting, Free Body Diagrams)

During week four of Physics I, students learn to solve for the magnitude of forces acting on an

object such as tensions in cables holding a weight (Figure 1).

Figure 1. Typical freshman Engineering Physics I problem.

After drawing the free-body diagram as shown in Figure 2, the projections of the vectors on the x

and y-axis help apply Newton’s second law of motion* to solve for the tension in each cable.

Figure 2. Physics solution of forces, using free body diagrams and Newton’s law (week four).

* sum of all forces on a non-moving object is equal to zero

�� ��

�

�� ��

�� ��

�

��cos(�2) ��cos(�1) �

����������= 0

+�� cos(�2) − �� cos(�1) = 0

�� =�� cos(�1)cos(�2)

Mathematical Solution

(Newton’s law)

Therefore: ��

Free Body Diagram

Page 24.920.4

In parallel during the same week, in the MATLAB programming course, a plotting method can

be implemented in replacement of a free-body diagram to solve for the tension in each cable.

There are various advantages to solving the same problem during the same week:

• Student see different methods

• It reinforces the fact that engineers use the same knowledge across all classes

• It reinforces the topic itself, by having student practice the same problem multiple times

• The knowledge of one topic is spread over more time

The first exam in MATLAB is shown in Figure 3 (Refer to Appendix A for the complete

example of Mini-Project #1). Due to the one hour time constraint, students are not required to

draw the free-body diagram to determine the equations. The final linear equations are given to

the students in the exam write-up but instead of algebraically solving them, students are asked to

find the tensions in the cables using a graphical method. The intersection of the two lines lets

students determine tension1 on the x-axis and tension2 on the y-axis on Figure 4.

A weight W (in Newton) is attached to the ceiling by the mean of two cables, as shown here. Calculate

the tension �� and �� (in Newton) using graphical analysis only.

Don’t panic: the equations have been solved for you, and therefore the problem can be solved

graphically. By solving the physics, �� can be expressed as a function of �� by two equations. These

equations are linear equations of the form�(�) = ∗ � + ":

Equation 1: ��(��) = #$%(&')#$%(&() ∗ ��

Equation 2: ��(��) = − %)*(&')%)*(&() ∗ �� ++

%)*(&()

Assuming both angles and the weight are known by the user, develop a program that can solve the

tensions for any similar setup by plotting both equations above and reading (��, ��) on the intersection

of these lines. The cable used can handle a maximum tension of 62N. Will it break? When complete, fill

Figure 3. Exam 1 (week four) - Solving graphically for tension forces in cables.

�� ��

�

�� ��

Page 24.920.5

Figure 4. Graphical Solution. The intersection easily lets students

determine the cable tensions T1 and T2.

Mini-Project #2: Trajectory Analysis (Vectors, Plotting, Equations of Motion)

Students are often uncertain and uncomfortable with polynomial equations and that uncertainty

leads to algebraic errors and poor results. Polynomial equations typically appear when students

learn about equations of motion, specifically with projectile trajectories. Plotting the two curves

with MATLAB allows students to visually solve for the (x,y) coordinates of their intersections,

thus answering actual physics concepts of trajectories.

For example, students typically know that a projectile thrown at a 45° angle will travel the

furthest distance. However, if there is a sloped hill, some students mistakenly believe that 45° is

still the angle that will lead to the furthest distance travelled. In the following lab example, the

curve is a polynomial of the second degree. Yet, the graphical approach applied here is identical

to the cable tension that finds the intersection of the curves and solves for physics property of the

trajectory as shown in Figures 5 and 6. (Refer to Appendix B for the complete example of Mini-

Project #2)

T1

T2

Page 24.920.6

Problem2 (name your file projectileHillImpact.m) – no step needed, most are done for you anyways!

A projectile is thrown on a hill (see figure). Knowing the two angles (angle of throw �. and angle of the

hill �/) and the initial velocity 01 of the projectile, solve graphically for the coordinates (x, y) of the

impact.

Equations: Both height and distances are function of time.

234526(6) = 016748(�.) −1

29.816^2

=476>8?36� � 016 cos�.�

The time interval that should be studied is from 0 seconds to �

@.A�01sin�.� seconds.

Figure 5. MATLAB Lab: Graphically solving the intersection of linear and polynomial equations.

Figure 6. Teaching student to plot trajectories and determine

intersections of curves graphically.

One benefit of writing code is its re-usability. A follow-up lab shown in Figure 7 based on the

same trajectory problem provided students with the opportunity to implement the crucial

re-usability aspect of a program, while again re-enforcing the fact that 45° is not always the angle

that will lead to the furthest distance travelled.

�. �/

(�, ��?

height (m)

distance (m)

height travelled vs. distance

x

y

Page 24.920.7

Problem3 (name your file: GuessProjectile2.m)

Use the solution provided online for Lab4, problem2 (please fix your code from Lab4 so that it works

properly before continuing!). For the entire problem set 01 = 30FG . Update the script so that the angle

of the throw �. can be entered by the user. By using the code repeatedly, and guessing on the value of

the throw angle, determine what throw gives the longest straight distance on the hill for each of the

following angles of hills.

�/�HH Guesses you tried, and x ‘visually’

read on the plot: angle (max x)

�.I��J for maximum

distance (best guess)

(extra credit – determine

graphically)

Max Distance (meters)

5° 20° (44.5m), 30° (68m), 45° (83m),

50° (83m), 60° (76m), so it’s between

45° and 60°… 55° (80.92m), 50°

(83.715m), 45° (83.7144m), 53°

(82.3727)

50 sqrt(83.715^2+7.324^2) =

84.0348

25°

30°

45°

Figure 7. Practicing the “re-usability” aspect of a program on a physics application.

Later in the semester, students learn the theoretical process to derive then solve these systems of

equations in Physics I and Calculus I. Having solved the problem graphically using MATLAB

provides students with the increased confidence in their ability to solve problems

mathematically.

Assessments & Results

To assess the impact of the SLC on student’s learning, assessments were made through two

satisfaction surveys (Hybrid Survey (Appendix C), and Social Media Integration Survey

(Appendix D)) and grade analysis. Both surveys were created by the author. The Social Media

Integration Survey has been used every semester since Fall 2012. All students in SLC and

non-SLC sections were given surveys at the end of the semester. Some of the results are

presented here.

Height (m)

distance (m)

Height travelled vs. distance

max distance �.

Page 24.920.8

The results of the surveys and the grade analysis are dependent on whether the student attended

classes continuously. The surveys were done in class on the very last day. While most students

were present, not only had some students withdrawn or stopped attending during the semester

but others were simply absent the last day. The overall class enrollment progression is shown in

Table 3.

Table 3: Enrollment statistics

Enrolled First

Day

Withdrew

or

Enrolled but no longer

attending classes

or

Removed from campus

roster

Students

active at end

of semester

Absent on

day surveys

administered

Non-SLC 52 7 (13%) 45 6

SLC 37 4 (11%) 33 2

For question 12 of the Hybrid Survey, “To what extent would you use MATLAB to solve a

mathematical or physics problem?”, more students from the non-SLC, 31% (non-SLC) vs. 23%

(SLC) would absolutely program a solution regardless of the level of complexity (Figure 8). This

may be due to the fact the non-SLC was not controlled for class level. It is nice to notice that

regardless of the complexity of the problem, 87% of students (non-SLC) and 97% (SLC) would

venture to program the solution (Table 4). One student from the SLC wrote that he would use

MATLAB only “If I had to re run the numbers more than twice”, which is exactly what has been

emphasized all semester: one major benefit of a program is its re-usability.

Figure 8. Will of students (non-SLC and SLC) to use programming for

mathematical or physics problems.

57

14

1

12

1

8

13

2

7

It would never come

to mind

Possibly, if the

problem was simple

Possibly, whether the

problem is simple or

complicated

Absolutely, if the

problem was simple

Absolutely, whether

the problem was

simple or

complicated

To what extent would you use MATLAB to solve a mathematical or physics

problem?

non-SLC (S=39) SLC (S=31)

Page 24.920.9

Table 4: Percentage of students would possibly or absolutely use programming

No Possibly Absolutely (Possibly & Absolutely)

Non-SLC (S=39) 13% 54% 33% 87%

SLC (S=31) 3% 68% 29% 97%

Questions 2, 3 and 4 of the same Hybrid Survey were given to only the SLC students to evaluate

the overall program success and identify the areas for improvement. An overwhelming majority

(85%) enjoyed being part of the SLC. However, while still a majority, a smaller amount felt it

helped learn better (67%), and enjoy their first semester at Embry-Riddle Aeronautical

University more than if they had not been in a SLC (70%) (Figures 9, 10, and 11).

Figure 9. Did students enjoy being part of the SLC?

Figure 10. Learning impact of being in the SLC.

Figure 11. Impact of being in the SLC on the aspect of enjoying college life.

1216

40 1

Strongly agree Agree Neither yes or

no

Disagree Strongly

disagree

You enjoyed being part of the Small Learning

Community (S = 33)

9

13

8

2 1

Strongly agree Agree Neither yes or

no

Disagree Strongly

disagree

I believe being part of the learning community

helped me learn better in class (S = 33)

914

8

0 2

Strongly agree Agree Neither yes or

no

Disagree Strongly

disagree

I believe being part of the Small Learning

Community made me enjoy my first semester better

than if I had not been part of a community. (S = 33)

Page 24.920.10

All students were also given a Social Media Integration survey. The highest number of

matriculated freshman occurs during the fall semester; the past two fall semesters were used to

measure the level of social integration of students. In the Fall of 2012, the SLC was not

available.

Students were asked on a Likert scale of 1 to 4 (1=not at all, 2=a little, 3=integrated, 4= very

well integrated), how much they felt part of both the Embry-Riddle Aeronautical University

community and the engineering community. Students in the Fall 2013 semester felt a higher

level of social integration in both categories (see Table 5). This may be due to the SLC students

bonding quicker with each other due to their multiple shared classes. Unfortunately, this survey

did not allow filtering the SLC from the non-SLC students.

Table 5: Level of integration (Fall 2012 and Fall 2013), with and without SLC experience

To what extend do you feel part

of the Embry-Riddle

Community?

To what extend do you feel

part of the ENGINEERING

Community?

Fall 2012 (without SLC)

(S=93) 2.75 (s.d.= 0.85) 2.37 (s.d.= 0.81)

Fall 2013 (with SLC)

(S=72) 2.82 (s.d.= 0.77) 2.49 (s.d.= 0.85)

Additional Findings

Collaborative Environment: The students in the SLC sections were more comfortable with each

other and were collaborative while working the in-class problems. They helped each other and

were more at ease asking for help from their fellow classmates in solving the problems. Students

in the non-SLC tended to solve the problems on their own and some of them were very reluctant

to ask for help or to form groups.

Increased Persistence: Students in the SLC completed 13% more assignments than non-SLC

students and they performed better across the major grade categories of the class as shown in

Table 6. It is believed the increased sense of community in the SLC section directly impacted

student performance. While students in the SLC may have been more apt of working together, no

more excessive collaboration (cheating) was discovered in the SLC classes. However, students

encouraged each other to complete assignments ahead of time thus giving them more time to

improve and do better on each assignment by over 10% (Table 7).

Table 6: Completion rates in major categories of the class for the MATLAB class

Averages Assignments Mini-Projects Quizzes Exams Final Projects

Non-SLC (S=50) 80% 71% 87% 96% 84%

SLC (S=35) 93% 79% 93% 99% 90%

Page 24.920.11

Table 7: Averages in major categories of the MATLAB class

Averages

(weight)

Assignments

(20%)

Quizzes

(10%)

Exams

(40%)

Final Projects

(20%)

Non-SLC (S=50) 76% 76% 74% 60%

SLC (S=35) 89% 84% 78% 69%

Increased Class Participation: As the students of the SLC were more familiar with each other,

they asked and answered more questions in class than the non-SLC. This made the course more

enjoyable both from the student’s point of view but also from the faculty perspective. Due to the

more outspoken, interactive, and energetic environment of the SLC students, stronger classroom

management was required. Only the confident students in the non-SLC sections were

comfortable enough to ask questions. However these were infrequent and often done outside of

class.

Increased Faculty Satisfaction: All three faculty observed that it was more enjoyable to teach the

SLC sections, as the students related well with others. They did not hesitate to interact with

professors in discussions beyond the scope of the class. Some students opened up about their

families, their interests, and their weekend activities. Some also asked about internships, and

future work opportunities. While this did happen in the non-SLC sections, it was much more

frequent with the SLC students.

Grade Distribution

At Embry-Riddle Aeronautical University, Early-Alert (third week) and Mid-Term (seventh

week) evaluations are completed to identify students who received satisfactory (S),

unsatisfactory (U), or unsatisfactory with excessive absence (UX) grades. Final semester grades

between the SLC and the non-SLC group were also compared to measure the impact of the

program.

During the week of Early-Alert, 51 students were still enrolled in the non-SLC sections, and 37

were enrolled in the SLC. One student who had withdrawn from the non-SLC section was no

longer enrolled and had left the school for personal reasons. A significantly higher number of the

SLC students had a Satisfactory evaluation as compared to the non-SLC (Table 8). In this

MATLAB class, this represented a current grade above or equal to 75%.

By the week of Mid-Term, two students withdrew from the SLC and from the University for

personal reasons. In order to get a satisfactory at the Mid-Term in the MATLAB class, students

needed a current average greater or equal to 70% and a grade on exam2 greater than or equal to

70%. The material taught had increased in complexity, thus lowering the threshold at 70% vs.

75% in the Early-Alert. Table 8 shows that still more SLC students were doing satisfactory in the

class than in the non-SLC. However, the overall Satisfactory percentage fell similarly in both

SLC and non-SLC.

Page 24.920.12

Table 8: Early-alert and Mid-term comparison in the MATLAB programming class

Early-Alert S U UX Withdrew

Non-SLC (S=52) Early-Alert 77% 21% 0% 2%

Mid-Term 65% 29% 4% 2%

SLC (S=37) Early-Alert 87% 8% 5% 0%

Mid-Term 76% 19% 0% 5%

The MATLAB non-SLC sections included students already in upper level math and physics.

Only 14 students (27%) in the non-SLC were also taking Calculus I and Physics I in separate

sections. In Table 9, it is interesting to compare the Early-Alert for those 14 students with the

SLC students, and note a 22% difference in Satisfactory. Possible reasons may be different

alignment of course content with faculty teaching non-SLC sections of Calculus I and Physics I,

or the lack of bonding that motivates students to study and progress together. However, if

comparing only the controlled non-SLC with the SLC, Table 9 shows an increase of Satisfactory

in the controlled non-SLC to the point of being very similar to the SLC results. By this time,

students have been at school for seven weeks, thus the bonding of all students might be reflected

here.

Table 9: Early-Alert and Mid-Term for the SLC and controlled non-SLC

Early-Alert S U UX Withdrew

Controlled Non-SLC (S=14)

(Calculus I and Physic I)

Early-Alert 64% 36% 0% 0%

Mid-Term 79% 21% 0% 0%

SLC (S=37) Early-Alert 87% 8% 5% 0%

Mid-Term 76% 19% 0% 6%

The comparison final grade distribution in Table 10 shows a significant reduction in failure. The

high failure rate in the non-SLC section is due to students who were enrolled but chose to no

longer attend class mid-way through the semester, and currently 5 students (10%) who have

Incompletes (I) due to on-going academic integrity procedures. While the number of A’s is not

significantly different, it is interesting to note the increase in B’s and C’s in the SLC students.

Table 10: Grade distribution in the MATLAB class

A B C D/F/I/W

Non-SLC (S=52) 15% 15% 14% 56%

Controlled Non-SLC (S=14)

(Calculus I and Physics I) 22% 7% 14% 57%

SLC (S=37) 19% 35% 19% 27%

Page 24.920.13

At the end of the semester, one student had withdrawn from the university (no GPA available)

both in the SLC and non-SLC, while one student had withdrawn from the SLC from the

MATLAB course but remained at the university. The GPA comparison shows a semester GPA

higher by 0.31 for the SLC sections compared to the non-SLC (Table 11). There is an even

greater difference between the SLC and the Controlled Non-SLC.

Table 11: End of semester GPA comparison of all groups

Semester GPA Average

(out of 4)

Non-SLC (S=51) 2.23 (s.d. = 1.01)

Controlled Non-SLC (S=14)

(Calculus I and Physics I)

2.17 (s.d. = 0.95)

SLC (S=36) 2.54 (s.d. = 0.84)

Challenges

Several challenges repeatedly appear in all sections. The lack of pre-requisite knowledge for

Calculus I is a significant challenge. Although students do take a math placement test, it is clear

that some pre-requisite are lacking. While the students are considered to be “Calculus I ready”,

they are not. An actual Calculus I ready class should benefit even more from a Calculus I,

Physics I and programming community environment.

Although the SLC section showed great ease and comfort in relating to each other, it is not sure

that the community spirit was shared by all of them. There were identifiably about four students

who chose to be outside the circle and participated in class only upon faculty insistence. More

discussion with all participating faculty on addressing such students is needed. Some students

will self-isolate, and determining how to successfully handle these students continues to be a

challenge.

Future Improvements

To continue improving the SLC experience, several points are considered.

Additional interdisciplinary mini-projects will be developed collaboratively with all three faculty

members. The collaboration in the work, the cross-referencing of the topics, and the delivery

timing during the semester is crucial for the students to fully gain the advantage of this teaching

method.

Page 24.920.14

The surveys at the end of the semester need to be able to filter the SLC from the non-SLC, but

also the control for math and physics experience for the non-SLC. This will allow for a more

meaningful comparison of the results.

If possible, the non-SLC needs to be a true control group. These non-SLC students should also

only be enrolled in Calculus I and Physics I. This is a challenge for registration. At the same

time, a better advertising of the SLC opportunity is required, with possibly a simple letter sent to

the students during registration process before the semester starts.

Longitudinal math, physics, and statics data will be collected for the students who participated in

the STEM SLC and compared to students who did not to see potential long term impact.

Conclusion

The STEM SLC students significantly performed better in the MATLAB class as the passing rate

is 73% vs. 44% in the non-SLC. The fact that the students in the SLC met daily together in their

classes created not only a bond of friendship, but of work ethic as well. They motivated each

other on a daily basis in addition to the faculty reminding them of their work daily. This

impacted their attendance, their participation, and the completion rate of the overall work.

The association of all topics across all three classes made the classes more connected. Students

did not feel they had three segregated classes, but possibly saw it as one class only. The mini-

projects, although specific to each faculty, connected the topics from all three faculty

simultaneously. Students in the SLC participated well in all mini-projects and considered all

three faculty when asking for help regardless of the problem.

The Spring 2014 will continue to introduce mini-projects in all three classes and the monitoring

of the current SLC and future SLC sections will take place.

1. Goris, T. V., & Dyrenfurth, M. J. “Students’ Misconceptions in Science, Technology and Engineering”, in ASEE

Illinois/Indiana Section Conference proceeding, Purdue University, West Lafayette, IN, 2010.

2. Rebello, S, and L. Cui. “Retention and Transfer of Learning from Math to Physics to Engineering” Proceedings

of the 2008 American Society for Engineering Education Annual Conference & Exposition, Pittsburgh, PA, June

22-25, 2008.

3. Rencis, J.J. and Grandin, H.T., “Mechanics of Materials: an Introductory Course with Integration of Theory,

Analysis, Verification and Design,” 2005 American Society for Engineering Education Annual Conference &

Exposition, Portland, OR, June 12-15, 2005.

Page 24.920.15

4. Pembridge, J., and Verleger, M., “First-Year Math and Physics Courses and their Role in Predicting Academic

Success in Subsequent Courses”, in ASEE Annual Conference and Exposition, Atlanta, GA, June 23-26, 2013.

5. Herniter, Marc E., Scott, David R., Pagasa, Rakesh, “Teaching Programming Skills with MatLab”, Computers in

Education Journal, 2001.

Page 24.920.16

Appendix A: Mini-Project #1

Name: _______________________________________ Section: _____ Practice for Exam1/Extra Credit

Assignment

Topics: MATLAB, variables, scripts, vectors, plotting, input/output

Take 3 full minutes to read the ENTIRE cover sheet first.

SUBMIT script file (NO ZIP) before the end of the class time. Turn in cover sheet.

A weight W (in Newton) is attached to the ceiling by the mean of two cables, as shown here. Calculate

the tension �� and �� (in Newton) using graphical analysis only.

Don’t panic: the equations have been solved for you, and therefore the problem can be solved

graphically. By solving the physics, �� can be expressed as a function of �� by two equations. These

equations are linear equations of the form ��� = ∗ � + ":

Equation 1: ����� =#$%&'�

#$%&(�∗ ��

Equation 2: ����� = −%)*&'�

%)*&(�∗ �� +

+

%)*&(�

Assuming both angles and the weight are known by the user, develop a program that can solve the

tensions for any similar setup by plotting both equations above and reading ��, ��� on the intersection

of these lines. The cable used can handle a maximum tension of 62N. Will it break? When complete, fill

in the table (5pts):

Angle 1

(degrees)

Angle 2

(degrees)

W (Newton) T1 (Newton)

2 decimals

T2 (Newton)

2 decimals

Break?

45 37 90

30 60 70

Using the full 7 steps taught in this class, and only the material taught in this class at this time, develop a

program that is easily reusable to solve the problem.

Step1(5pts):

Step2:

�� ��

�

�� ��

Page 24.920.17

Step3: (Equations given already)

Step4: (Assume values from scenario1 (line 1 in the table))

Step5: (solve graphically – hence no step5 needed)

Step6: not applicable

Step7a (comments) and 7b (place directly on the script file).

Requirements for the program itself:

- (12pts) prompt the user for the values of ��, ��, �.

- (15pts) define all vectors that can plot equation1 and 2

- (10pts) plot correctly, using colors, markers and line specifications AS SHOWN in the videos.

- (15pts) label the plot properly and fully

(7pts – other random errors!)

Within script:

name/section/description (3pts)

commands to clean up previous execution of MATLAB codes (3pts)

comments (which is considered the algorithm) (5pts)

spacing of code (5pts)

appropriate variable names (no single letters) (5pts)

semi-colon hiding intermediate calcuations (5pts)

Step7c (5pts): Verify mathematically your solution seems accurate.

(T1, T2)?

��M�

��M�

Page 24.920.18

Appendix B: Mini Project #2

Name:

Section:

Lab04: Vectors and Plotting

Code. Zip. Submit. 11:59pm Print. Staple in order. Bring to next lab.

Problem1 (name your file aircraftWind.m)

The path of an aircraft is changed due to winds. The pilot had travelled 50km west, then 35km south-

west, then an additional unknown straight distance. However, the pilot came back to the original

straight-line path, 200km from the original spot. Calculate the vector’s components for the missing

straight distance using vector analysis.

Complete Step1 to Step3 to completely understand the different vectors involved, one for each

distance. Step2 should be to scale. In the script file, define each vector separately by hardcoding their

component. Then solve for the components of the missing distance.

Problem2 (name your file projectileHillImpact.m) – no step needed, most are done for you anyways!

A projectile is thrown on a hill (see figure). Knowing the two angles (angle of throw �. and angle of the

hill �/� and the initial velocity 01 of the projectile, solve graphically for the coordinates (x, y) of the

impact.

Equations: Both height and distances are function of time.

ℎ345ℎ66� = 016748�.� −1

29.816^2

=476>8?36� = 016 cos�.�

The time interval that should be studied is from 0 seconds to �

@.A�01sin�.� seconds.

Requirements of the code:

- Hardcode the 3 givens as separate variables.

�. �/

�, ��?

height (m)

distance (m)

height travelled vs. distance

Page 24.920.19

- The equation of the line for the hill should be calculated within the script, based on the angle of

the hill.

- Plots should be as complete as on the tutorial video. (title, grid, labels, legend)

Just like in Lab2, reuse your code by changing the hardcoded values to answer the following questions:

Scenario # Angle Hill (degrees) Angle Throw

(degrees)

Initial Velocity

(m/s)

(x,y) impact?

1 30 45 20

2 10 50 20

3 45 60 20

Rubric:

Cover sheet complete & stapled properly: 10pts

Problems: 30pts + 15pts for correct results

Reminder: make sure to have within the script file, in order:

1. (2pts) first and last name

2. (2pts) section number

3. (4pts) description of the problem (10 words maximum)

4. (2pts) the two commands that erase the command window and the workspace

5. (5pts) comments throughout the code

6. (5pts) spacing (skipping lines between major paragraphs)

7. (5pts) variables names that are WORDS that describe the content. Absolutely do not

use single letter.

8. (5pts) semi-colons hiding all intermediate calculations; only the final result counts!

Page 24.920.20

Appendix C: Hybrid Survey

Page 24.920.21

Page 24.920.22

Appendix D: Social Media Integration

Page 24.920.23