Department of Mathematics

IIT Bombay

Mumbai, 400076, INDIA

IIT Bombay

Mumbai, 400076, INDIA

e-mail: `siva@math.iitb.ac.in`

Phone:

- (+91-22) 2576 7476 (Office)
- (+91-22) 2572 3480 (Fax)

Office:

210B Mathematics Building

## Lecture Notes

- Solutions
- First order equations: Variable-separable method, linear equations
- Existence and Uniqueness (partially complete).
- Continuation of solutions
- Second order equations: fundamental pairs of solutions, VoP revisited, MUC.
- Boundary value problems for second order equations.
- Sturm-Liouville Eigenvalue problems
- Sturm's separation, comparison theorems
- Cauchy-Lipschitz-Picard existence theorem
- Global existence, Continuous dependence theorems
- Stability theory, Linear 2x2 systems
- Bibliography

## Instructions

You must pay attention to solving exercises given in notes as well as problems from books of Coddington and Myint-U. It is important.