Mathematica Laboratory for Upper-Level Science and Engineering Students

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In the past 6 years, the Department of Mechanical Engineering has developed a set of six upper-division undergraduate courses in applied mathematics. These courses combine training in traditional mathematics with strong and frequent connections to engineering and scientific problems. The courses meet a major need and have grown to a combined yearly enrollment of about 265 students. They are taken to satisfy degree requirements in Mechanical Engineering, Geomechanics, Physics, and Optics and as electives for some majors in Electrical Engineering, Chemical Engineering, and Mathematics. The objective of this project is to add a Mathematica Computational Laboratory to all of these courses. This laboratory can also be used in the Mechanical Systems course and other traditional engineering courses that feature a strong mathematical component. The numerical and graphical capabilities in Mathematica allow for the weekly assigning of more interesting problems and more realistic term projects. The symbolic capabilities of Mathematica allow extensions of traditional analytical techniques. The notebook interface makes it possible to supply each group of students with material of exactly the right level. Beginning students can simply execute notebooks with various parameter choices, whereas more advanced students can be asked to extend the given notebooks to handle more complex problems. This Mathematica Laboratory can be used by several hundred students a year. These students can gain greater insight into the use of mathematics in visualizing and analyzing physical processes. The students can also acquire skills in Mathematica, a mode of computing now essential in science and engineering.