A basic outline of the syllabus for the course can be found at this link under Math 417.
Schedule: The class meets twice a week, Tuesday/Friday 3.30 - 5 pm.
Notes:
1. Criterion of real analyticity
2. Linear ODE with real analytic coefficients
References:
There is no one book that will be linearly followed. However, most of the material covered in class should be found in some guise in the following:
(A) Teschl, Gerald. Ordinary differential equations and dynamical systems. Grad. Stud. Math., 140, American Mathematical Society, Providence, RI, 2012. xii+356 pp
Thanks: I am generally indebted to my friends and colleagues Saikat Mazumdar and Debanjana Mitra for allowing me to blatantly steal much of the material from earlier iterations that they taught.
Contact information:
Email: mathmukherjee@gmail.com or mukherjee@math.iitb.ac.in
Office: G3 -E, Math Department (ground floor from the corridor entrance, first floor from the front entrance)
General advice: It is highly recommended that you consult other standard texts in the field, to appreciate different tastes in selection of materials, or differing slants on the same material.