MA 542 Differential Equations (M.Sc. (Mathematics and Computing) 2nd Semester)

(L-T-P-C 4-0-0-8)

Jan-May 2025 semester

Instructor:

Dr. Swaroop Nandan Bora

Office: E-306, Department of Mathematics

Contact: swaroop@iitg.ac.in, 361 258 2604 (Office Phone) 

Room No.: 1G1

Class Timing: C-Slot - Monday 1000-1055, Tuesday 1100-1155, Thursday 0800-0855, Friday 0900-0955

First Day of Instruction: January 2, Thursday; Last Day of Instruction: April 25, Friday

No Class (as per time table for this course): January 14, January 31, February 24-28, March 14, March 31, April 10, April 14-15, April 18

Class Adjustment:  January 16, Thursday with Tuesday time table; March 19, Wednesday with Friday time table; April 5, Saturday with Monday time table

Evaluation: (As it stands now)

Four Tests: 30 Marks, Mid Sem Exam: 30 Marks, End Sem Exam: 40 Marks

Dates:

Test 1: January 20, Monday, 1005-1050

Test 2: February 14, Friday, 0905-0950 or February 17, Monday, 1005-1050

Mid Semester Exam: February 25, 0900-1100

Test 3: March 21, Friday, 0905-0950

Test 4: April 11, Friday, 0905-0950 or April 17, Thursday, 0800-0850

End Semester Exam: April 29, Tuesday, 0900-1200

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.

Texts:

  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.

More information, as required, will be added from time to time.