Using the Computer as a Tool Across the Curriculum

An introductory course in mathematical tools is a common freshmen engineering course. Students are exposed to various mathematical and computer tools which should strengthen their ability to solve engineering problems in future courses. Examples of these tools would be MATLAB and Excel. In a review of the current curriculum at a 4 year institution, it was revealed that no current course in the sophomore year specifically utilized these tools. The students were at liberty to apply their skills with the tools, but were not required to use them. A concerted effort is being made to adapt the sophomore curriculum to include the use of these tools working from the basis that the students have garnered some mastery of them. This also puts the tools into context more than the introductory course was able to accomplish. Specifically, a sophomore level Thermodynamics course is being modified to develop several homework assignments that require the use of the computer as a tool. This modification will also address the ABET Program Outcomes that requires graduates to possess an ability to use the techniques, skills, and modern engineering tools necessary for engineering practice and a recognition of the need for and the ability to engage in life-long learning. This paper presents the different specific tasks that the students were asked to accomplish in the context of Thermodynamics with the described tools. The students were pre surveyed with regards to their knowledge base with the described tools and their application. Resource implications for teaching a course in such a fashion are discussed. Finally, student feedback to this approach is provided. Introduction A sophomore level course such as Thermodynamics seems the appropriate vehicle to reinforce the concept of the computer as an engineering tool. In this particular curriculum in the College of Engineering, the Thermodynamics course is required for mechanical engineering majors as well as being utilized as a service course for 3 other majors in the College of Engineering: Civil Engineering, Electrical Engineering and Applied Engineering Science. This is the first course in the curriculum that focuses on energy and energy related concepts. As noted in the appendix, the course learning objectives clearly place the emphasis on the basics of Thermodynamics and energy related topics. Beginning in the Fall of 2009, all of these majors are required to take the introductory course in mathematical tools utilizing MATLAB. There was an optional opportunity to enroll in the changed curriculum in the Fall 2008. The purpose of incorporating these tools in an engineering course is to showcase the uses of MATLAB in the context of engineering applications. Learning objectives were developed for the introduction of MATLAB to the course. In courses focused on learning the tool, rather then the application, students can become muddled in the nuances of the tool rather then its overall usefulness to the discipline. This is the impetus for adding this component to a required class in the sophomore level. Students were informed on the syllabus that certain assignments would be computer intensive and the point value for these problems would reflect the amount of expected effort. It was also noted on the homework assignments which problems were considered to be computer intensive. P ge 22642.2 In regards to previous work, considerable software has been developed for thermodynamic applications. These include property evaluation, power plant analysis, turbomachinery, cylinder-piston engines, and diesel engines. MATLAB has also been used to carry out projects in thermal/fluid courses. There have been some attempts to more fully integrate MATLAB into mechanical engineering courses and these include the efforts at Alabama A&M and Florida A&M University and Florida State University. Students Pre-knowledge In the first week of the semester the students were surveyed as to their knowledge and comfort level with MATLAB. The students were asked when they had taken the MATLAB course, who the instructor was and then a series of questions concerning specific functions and operations to determine immediate recall of the information. The most telling question was for the students was to assess their own comfort level with the material based on the 0-4.0 scale that is used for grading in the 4-year institution where this is being instituted. Table 1 gives the raw data sorted by comfort level selection Table 1 Students Comfort level with MATLAB Mapped to Grading Scale Level of comfort 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.0 Number of students 3 7 9 10 13 3 7 4 The average comfort level was 2.25 with the median being 2.5 of the 56 students surveyed. It is not unusual for non ME majors to be taking this 200 level course in a year different then their traditional sophomore year. The requirement at the college level for the freshmen level course in MATLAB is only 2 academic years old, replacing a more traditional programming course: 7 students fell into this category of not having taken the MATLAB course. Of the remaining students, 9 were either transfer students from another university or in a major that had given them credit for the freshmen level MATLAB course with other courses in their curriculum. The results of this survey clearly indicated that time would need to be spent on the use of MATLAB to solve problems; however, the course content in the basics of property evaluation and energy analysis could not be comprised. The key was to determine a balance where the students were benefiting from the computer as a tool and not a hindrance to their mastering of the energy related concepts. The latter being the true objective of the course. Examples of Assignments To begin the introduction of the computer as a tool, the students were given 26 temperatures in various units and asked to present the data in table form in all 4 units of temperature. This reinforces the relationship between the relative and absolute temperature scales and illustrates that large amounts of data which are tedious to work with by hand can be easily conquered with the use of the computer. Several students approached the problem by first converting the temperatures to one scale and then creating a vector in MATLAB to convert to the remaining scales. The table was then created in Excel or MATLAB. Students were required to verify that P ge 22642.3 they used the appropriate computer application by printing the workspace window from MATLAB. A second example of a computer intensive homework assignment is to have the students produce an ideal gas phase diagram for Nitrogen, N2. This is a P-v diagram for 6 values of temperature and includes lines of constant enthalpy. This diagram is created with a for loop in MATLAB filling a two dimensional pressure array for a range of specific volumes and one given temperature. These are then plotted in MATLAB creating a legend indicating lines of constant temperature and enthalpy. The values for enthalpy are taken from the ideal gas charts in the required textbook for the course. In thermodynamics, this introduces a simple phase diagram for a substance reinforcing the relationship between pressure and volume and for an ideal gas illustrating that enthalpy is a function of temperature only. In lecture, this assignment is supplemented with discussion of the solution being ‘far, far’ from the vapor dome for the particular substance making the ideal gas model valid. The graph produced is superimposed over the actual phase diagram showing the validity of the ideal gas model. A third example of a computer intensive homework assignment would be giving the students a set of P-V data to accompany the introduction of boundary work as part of the 1 law of thermodynamics. The students learn the functional relations for integrating boundary work for a given process, such as isobaric, isothermal, or isentropic. The presentation of the P-V data in table form requires that the students generate a plot of the data and perform the numerical integration. This is done in a MATLAB script file written by the students where the area under the curve can be determined by several different estimations. This topic is revisited when cycles are introduced and class discussion focuses on indicator diagrams for Internal Combustion engines. Further MATLAB work was done allowing the students to use complied script files for property evaluation in cycle analysis for homework assignments only. This was useful in illustrating the cycle concepts without the students being bogged down in the tedious nature of property evaluation with traditional tables. Property evaluation is emphasized in the beginning portion of the course utilizing the tables. Problem statements for computer intensive portions of the homework assignments are available in the Appendix, assignments not discussed in detail are also included. Homework Assessment On the described computer homework assignments, the average grades were 80.7%, 72.1%, 70.5%, 81% and 85%. The overall homework assignments average for all assignments was 79.5% with a range of 64% to 91.6%. The students did not seem to be overly burdened by the computer intensive assignments nor were their grades adversely impacted. It would appear by a visual inspection of the tabulated data (not included) that certain students choose not to do the more intensive portion of the assignments though benefited from using the complied script files for property evaluation in cycle analysis. Anecdotally, students were using Excel and MATLAB simultaneously to verify calculations and set up of problem solutions. This is a very useful technique for problem solving and P ge 22642.4 development of intrinsic verification of calculations. To go hand and hand with this, solutions to the assignments were presented using both Excel and MATLAB. Further anecdotal evidence presented itself early in the semester with a strong resistance to incl