Mechanical Engineering, Indian Institute of Science, Bangalore 560 012, India
Optimization hinders evolution!
ME256 Variational Methods and Structural Optimization Jan.-May. 2019
Instructor: G. K. Ananthasuresh , Room 106, ME Building, suresh at iisc.ac.in
Lectures: Tu, Th: 08:30 AM - 09:55 AM; Venue: ME Lecture Hall

Reference books

Textbook
There is no prescribed textbook for this course. The principal course material will be the notes taken during the lecture. Some handouts will be given. Papers from the contemporary literature will be provided. Some reference books are listed below.

Primary reference books

  1. Robert Weinstock "Calculus of Variations with Applications to Physics and Engineering", now in Dover publications in paperback form.
    It is a comprehensive book with an optimum balance between rigour, conceptual understanding, and emphasis on applications.
  2. A. S. Gupta, "Calculus of Variations with Applications", Prentice-Hall of India Pvt. Ltd., New Delhi, 2008.
    A very accessible book from the viewpoints of subject mattter and price. Among other things, it contains a good discussion of the sufficient conditions for the calculus of variations problems.
    I. M. Gelfand and S. V. Fomin "Calculus of Variations", now in Dover publications in paperback form.
    It is one of the classical books on calculus of variations. It starts from the very basics and goes to an advanced level. It is even suitable for self-study.
    This book is kept on reserve in the J. R. D. Tata library in the reference section so that you all can refer to it in the library and may borrow it for over-night study as per the rules of the library.
  3. Smith, D. R., "Variational Methods in Optimization," Dover Publications, 1998.
    It gives a comprehensive treatment of calculus of variations starting from the basics. Many examples are included. Although it is written by a mathematician, it is rich in applications. It also gives sufficient insight into the mathematical concepts.
    This book is kept on reserve in the J. R. D. Tata library in the reference section so that you all can refer to it in the library and may borrow it for over-night study as per the rules of the library.
  4. Haftka, R. T. and Gurdal, Z., "Elements of Structural Optimization," Kluwer Academic Publishers, 1992.
    The book gives a nice exposition of classical structural optimization. It has some examples that use variational methods approach. It also included numerical optimization techniques.
  5. Bendsoe, M. P. and Sigmund, O., "Topology Optimization: Theory, Methods, and Applications," Springer, 2003.
    A contemporary book on topology optimization. It is rich in methods and includes some examples. Its bibliography is very useful as well.
Other reference books
  1. David G. Luenberger, "Optimization by Vector Space Methods," John-Wiley & Sons, 1969.
    This is an excellent book for getting a rigorous and intuitive understanding of vector spaces and functionals. It gives a lucid treatment of such important concepts as Hahn-Banach theorem, etc.
  2. P. Y. Papalambros and D. J. Wilde "Principles of Optimal Design," Cambridge University Press, 2000.
    This is a great book if someone wants to learn about optimal design, optimization theory, and applications all from a single book. The monotonicity analysis presented in this book makes it extra special.
  3. Herman H. Goldstein, "A History of the Calculus of Variations: from the 17th through 19th century," Springer-Verlag, 1980.
    An authoratative exposition of the history of calculus of varitions from Fermat/Galileo to Wierstrass and Du Bois Raymond and others.