Where can one find the 1st year syllabus of IIEST, Shibpur?

The syllabus of IIEST, Shibpur has remained pretty much the same over the years. At http://www.iiests.ac.in/images/all pdf/1-5STRUCTURES.pdf, you can find the structure for the 1st year.

The professor reveals the syllabus when the course begins (exact names of topics that will be covered in that semester). This syllabus keeps changing each year. Maybe it's not the same syllabus students had earlier. 

The professor either gives the paper directly after the course begins, or others do not have a habit of not giving it. You can feel free to ask your professor to give you the syllabus document in such a situation.