Mechanical Engineering, Indian Institute of Science, Bangalore 560 012, India
Optimization hinders evolution!
ME256 Variational methods and structural optimization Jan.-May, 2007
Instructor: G. K. Ananthasuresh, Room 106, ME Building, suresh at mecheng.iisc.ernet.in
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Homework #1
Assigned: Jan. 4th, 2007
Due: Jan. 11th, 2007
Points: 20

  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
    Numerically solve the classical problems of brachistochrone and the shape of a chain hanging under the gravity using the Optimization Toolbox in Matlab. Plot your solution and the analytical solution in the same graph so that you can compare them. If you also solve some other classical problems of calculus of variation, you will be given extra points. Please submit your Matlab code and the plot.