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ME 7100: March-April 2016 (Website only for the second half of the course)
Advanced Topics in Mathematical Tools
Department of Mechanical & Aerospace Engineering
IIT Hyderabad

Instructors: Harish Dixit
Lectures: Every Tuesday (12:00 to 1:30) and Friday (12:30-2:00)
Venue: Room 111
TA's: Anjishnu Choudhury
Office: Room 416, E-Block
Phone: 040-23017119
Email: hdixit(at)iith.ac.in

GRADING and EXAMS: Grading will be based on your performance in the assignments and the final exam for this part of the course.

Goals of the course

  • Expose you to fundamental techniques in perturbation methods and nonlinear dynamics
  • Learn to use symbolic packages such as Maple or Mathematica to obtain analytical solutions
  • Learn to obtain numerical solutions to simple ODE's with Matlab
  • Learn to represent your results pictorially (graphs, phase-plots, etc.)

    List of topics to be covered: Perturbation techniques for algebraic equations (regular & singular), Regular and singular (boundary-layer type) perturbation techniques for ODE's, multiple-scale analysis (nonlinear oscillators, limit cycles, etc.), Deterministic chaos in forced nonlinear oscillators, Logistic equation, Lorentz attractor, Poincare maps.

    Some useful references:
  • Carl M. Bender and Steven A. Orszag, "Advanced Mathematical Methods for Scientists and Engineers", Springer
  • E. J. Hinch, "Perturbation Methods", Cambridge Texts in Applied Mathematics
  • R. H. Rand, "Lecture Notes on Nonlinear Vibrations", Cornell University (you download the pdf from google)

    Useful suggestions and course policies:
    You are strongly advised to sincerely work out all the details of your class notes again at home. You use the same mantra for your assignments as well. If you don't take your assignments seriously, you are very likely to face great difficulty in solving final exam problems.

    Leave: You are fully responsible for taking all the necessary notes during class. I cannot promise to provide you with any hand-outs.

    Assignment: Assignments are to be submitted before the class begins on the due date. Failing to submit an assignment will normally result in a mark of zero. Exceptions may be granted in two cases: prior consent of the instructor or a medical emergency. In the latter case, the instructor must be notified as soon as possible (preferably before the day of submission), and presented with a doctor's note immediately upon the student's return to IITH.