MA 542, Differential Equations (M.Sc. 2nd Semester)

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

Jan-May 2022 semester

(Scroll  down to the bottom of the page for the lecture slides)

Instructor:

Dr. Swaroop Nandan Bora

Office: E-306, Department of Mathematics

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

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

As of now, all lectures will be held live on MS Teams as per the class timing. In addition, slides will be uploaded on this site. No video lecture will be uploaded unless some lecture is missed by the Instructor.

From March 21, all classes and evaluation will take place offline.

Microsoft Team: MA542-2022

First Day of Instruction: January 6, Thursday; Last Day of Instruction: May 2, Monday

No Class (as per time table for this course): January 14, January 21, February 28-March 6, March 14-18, April 14-15, May 3

Class Adjustment:  Feb 19, Saturday with Friday time table; April 30, Saturday with Thursday time table; May 2, Monday with Friday time table

Evaluation: (As it stands now)

Two Tests: 2X12=24 Marks, Mid Sem Exam: 26 Marks, End Sem Exam: 38 Marks, Viva (after mid sem exam): 12 Marks

Dates:

Test 1: January 31, Monday, 1100-1145 (Lectures 1-11) - Online

Mid Semester exam: March 3, 0900-1100 (Lectures 1-25)- Online

Viva 1: Mach 15-16, Tuesday-Wednesday (Lectures 1-25) - Offline

Test 2: April 11, Monday, 1105-1150 (Lectures 26-35) - Offline (Seminar Hall)

Viva 2: May 1, Sunday (cancelled)

End Semester exam: May 7, Saturday, 0900-1200 (Lectures 26-last lecture) - Offline

The evaluation procedure has partially changed since the conventional teaching has started.

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 will be added from time to time.

Lecture Slides