Ordinary Differential Equations

Core course for B.Sc. (Research) Mathematics.

Credits (Lec:Tut:Lab)= 3:1:0 (3 lectures and 1 tutorial weekly)

Prerequisites: MAT 101 Calculus I or MAT 103 Mathematical Methods II

Overview: Ordinary Differential Equations are fundamental to many areas of science. In this course we learn how to solve large classes of them, how to establish that solutions exist in others, and to find numerical approximations when exact solutions can’t be achieved. Further, many phenomena which undergo changes with respect to time or space can be studied using differential equations. In this course, we will also see many examples of mathematical modeling using differential equations.

Detailed Syllabus:

1. First Order ODEs: Modelling, Geometrical Meaning, Solution techniques
2. Second and Higher Order Linear ODEs: Modelling, Geometrical Meaning, Solution techniques
3. Numerical Techniques
4. Existence of Solutions of Differential Equations
5. Systems of ODEs: Phase Plane and Qualitative Methods
6. Laplace Transforms
7. Series Solutions

References:

1. Erwin Kreyszig, Advanced Engineering Mathematics, 9^th edition, Wiley India, 2012.
2. G.F. Simmons and S. Krantz, Differential Equations: Theory, Technique, and Practice, McGraw Hill Publishing Company, 2006.
3. J. Polking, D. Arnold, A. Boggess, Differential Equations, Pearson, 2005.
4. C. Henry Edwards and David E. Penney, Differential Equations and Boundary Value Problems: Computing And Modeling, 3^rd edition, Pearson, 2010.
5. Hirsch, Morris W., Stephen Smale, and Robert L. Devaney, Differential Equations, Dynamical Systems, and an Introduction to Chaos. Academic Press, 2012.

Past Instructors: Ajit Kumar