Comparative Computational Mechanics / Engineering Science

If you had to design a course of the title: "Comparative Computational Mechanics" or "Comparative Methods of Computational Engineering Science and/or Mechanics", what would its contents be like?

Feel free to assume an appropriate level of preparation on the part of the course students (e.g. undergraduate/graduate/training of experienced engineers). Feel free to give concrete details (points to be taught) or a general outline as you wish. Feel free to note down what methods of computational mechanics, in your opinion, should be given more weightage in the overall course. If you can think of good illustrative examples that may better help the cause of a *comparative* analysis, please note down the same too.

One final point: Note the word "comparative." Humanities departments often have such courses: comparative literature/philosophy etc. But in sciences and engineering we tend not to have. Yet, there also are quite a few computational methods these days available as commercial packages and several more are at the research stage. So, the existence of such a course is amply justified.

So, if you had to deliver this course, what material would you base your course on? What its contents be like?

You may assume a course of a typical length, say a 3 credit-hour semester-long course.

Thanks in advance for all your replies.