Mechanical Engineering, Indian Institute of Science, Bangalore 560 012, India
Optimization hinders evolution!
ME256 Variational methods and structural optimization May-Jun., 2006
Instructor: G. K. Ananthasuresh, Room 106, ME Building, suresh at mecheng.iisc.ernet.in
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Homework #1
Assigned: May 1st, 2006
Due: May 15th, 2006
Points: 30

  1. 10 points
    Understanding what a functional is crucial to the study of calculus of variations. We can reinforce our understanding by formulating functionals pertaining to practical or hypothetical situations. Suggest such a functional, give its background and write its mathemtical form. If you come up with a new or an unfamiliar one, you will be given extra points. If you take up well known problems from books, you will be given less than full points.
  2. 10 points
    Verify that the four examples given for a normed function space in the notes on page 5 satisfy the four properties of the norm given on page 4.
  3. 10 points
    Compute the Gateaux variation of the functional for the Brachostochrone problem as well as any other problem of your choice.