MA 542 Differential Equations LTPC 4-0-0-8

(M.Sc. (Mathematics and Computing)  2nd semester

Instructor: Dr. Swaroop Nandan Bora

Office: E-306 (Old Block)

Contact: 361 258 2604, Email: swaroop@iitg.ac.inswaroop@iitg.ac.in

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Class slots: Monday 11:00-11:55, Wednesday 8:00-8:55, Thursday 9:00-9:55, Friday 10:00-10:55

First Day of Instruction: January 6, Tuesday; Last day of Instruction: April 30

Holidays (excluding weekends): January 14, Monday; January 26, Monday; March 31, Tuesday, April 3, Friday; April 14, Tuesday; April 15, Wednesday

Additional no class days (excluding exam days): January 29, Friday (Alcheringa), February 27, Friday (pre-exam)

Time-table Change: 29 January, Thursday -> Monday; 24 February, Tuesday -> Friday; April 2, Wednesday -> Friday; April 13, Monday -> Tuesday

Evaluation:

Quiz 1: February 9, Monday, 11:00-11:55 (12 Marks)

Quiz 2: February 23, Monday, 11:05-11:50 (10 Marks)

Mid Semester Exam: March 5, 9:00-11:00 (28 Marks)

Quiz 3: April 6, Monday, 11:00-11:55 (12 Marks)

End Semester Exam: May 7, 9:00-12:00 (38 Marks)

(The quiz dates are tentative.)

Problem Dsicussion:

This course does not have a tutorial component. However, for the benefit of students, a number of problem discussion classes (4/5) will be taken. The tentative dates are January 23, February 6, February 20, March 23, April 17.

Course Outline:

Review of fundamentals of Differential equations (ODEs); Existence and uniqueness theorems, Power series solutions, Systems of Linear ODEs, Stability of linear systems.

First order linear and quasi-linear partial differential equations (PDEs), Cauchy problem, Classification of second order PDEs, characteristics, Well-posed problems, Solutions of hyperbolic, parabolic and elliptic equations, Dirichlet and Neumann problems, Maximum principles, Green's functions.

Textbooks:

1. E. A. Coddington and N. Levinson, Theory of Ordinary Differential Equations, Tata McGraw Hill, 1990.
2. S. L. Ross, Differential Equations, 3rd Edn., Wiley India, 1984.
3. I. N. Sneddon, Elements of Partial Differential Equations, Dover Publications, 2006.
4. F. John, Partial Differential Equations, Springer, 1982.

References:

1. S. J. Farlow, Partial Differential Equations for Scientists and Engineers, Dover Publications, 1993.
2. E. L. Ince, Ordinary Differential Equations, Dover Publications, 1958.
3. F. Brauer and J. A. Nohel, The Qualitative Theory of Ordinary Differential Equations: An Introduction, Dover Publications, 1969.