Course content:

  •  Introduction to ODE with illustrative examples, concept of solution, equivalence of IVP and solution of integral equation
  •  Picard’s iteration, existence theorem, Lipschitz continuity, uniqueness theorem
  •  Continuation of solution,
  •  General theory of linear ordinary differential equations
  •  Methods for solving linear non-homogeneous equation
  •  Cauchy-Euler equation
  •  Series solution
  •  Legendre equation, Bessel equation
  •  System of Linear ordinary differential equations
  •  Stability theory for system of linear ordinary differential equations
  •  Phase portraits for system of two linear equations
  •  Boundary value problems, Strum-Liouville theory
  •  Green’s function

Suggested Textbooks:

1. S. L. Ross, Introduction to Ordinary Differential Equations, Wiley, 1980.
2. G. Simmons, Differential Equations with Applications and Historical Notes, McGraw-Hill Higher Education, 1991.
3. W. E. Boyce, R. C. DiPrima, Elementary Differential Equations, Wiley, 2008.

Distribution/Weightage of Marks:

Quiz (20) + Mid Sem (30) + End Sem (50)