Differential Equations and Boundary Value Problems

 

Four one-hour lectures per week: 8 credits

Class Timing: 16:00-17:55, Monday; 16:00-16:55, Tuesday; 15:00-15:55, Wednesday; (back-up slot:14:00-14:55, Thursday).

Room Number: 1103

First Day of Instruction: Tuesday, July 30, 2013

Last day of Instruction: Thursday, November 21, 2013

Course Instructor: Swaroop Nandan Bora (First half) and Durga Charan Dalal (Second half)

Office: E-306/E-206

Phone 2604/2615

Email: swaroop@iitg.ernet.in/durga@iitg.ernet.in

 

Classes with Friday Time-table   

 

Classes with Wednesday Time-table                  

August 20, 2013, Tuesday

 

 October 15,  2013, Tuesday

 

Holidays/No Classes during scheduled slots: August 15, Thursday (Independence Day);  September 23,24,25,26 (Mid Sem exam); October 2, Wednesday (Gandhi Jayanti);  October 14, Monday (Dussehra); October 16, Wednesday (Idul Zuha), November 14 (Muharram).

 

Course Contents:  

 
MA751 Differential Equations and Boundary-Value Problems [4-0-0-8]

Existence and uniqueness of solutions of ODEs, power series solution, singular points, some special functions. Nonlinear system of ODE : Preliminary concepts and definitions, the fundamental existence-uniqueness results, dependence on initial conditions and parameters, the maximum interval of existence, linearlization, stability and Liapunov functions, saddle, nodes, foci and centers, normal form theory and Hamiltonian systems. Boundary value problems : Green's function method, Sturm-Liouville problem.

First-order PDEs, Cauchy problem, method of characteristics, Second-order PDEs, classification, characteristics and canonical forms. Elliptic boundary value problems : Maximum principle, Green's function, Sobolev spaces, variational formulations, weak solutions, Lax-Milgram theorem, trace theorem, Poincarénequality, energy estimates, Fredholm alternative, regularity estimates, system of conservation laws, entropy criteria.

Texts/References:
  1. L. Perko, Differential Equations and Dynamical Systems, Springer, 2001.
  2. J. Guckenheimer, P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer-Verlag, New York, 1983.
  3. S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer-Verlag, New York, 1990
  4. Lawrence C. Evans, Partial Differential Equations, Graduate Studies in Mathematics, Vol. 19, American Mathematical Society, Providence, 1998
  5. Robert C. McOwen, Partial Differential Equations - Methods and Applications, Pearson Education Inc., Indian Reprint 2004.
  6. S.J. Farlow, Partial Differential Equations for Scientists and Engineers, Dover Publications,New York, 1982.

 

Plan of the course:

 

  1. Two quizzes: 20 marks.
  2. Mid semester examination: 30 marks.
  3. End semester examination: 50 marks.

 

Important Dates:

 

Quiz I:Monday, September 2, 2013

Mid Semester Exam: 2-4 PM, September 23

Quiz II: Friday, November 1, 2013

End Semester Exam:  1-4 PM, November 25