# MTH421A - Ordinary Differential Equations

### 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.

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)