I am taking a second course in calculus and came across sequences defined inductively, as in recursively. My teacher told the class that a general formula for the $n$th term can be obtained using a tool called "Difference Equations". Embarassingly enough I've never heard of the term before. Now, recursion also comes up in a second Differential Equations class I'm taking in Power series solutions.
I did not find any reference-request questions on the subject in general. If this is a duplicate, I apologise and please point me towards the original. This could also be a classical case of a gaping hole in my prior education but here goes.
Can someone please recommend a good introductory text on"Difference Equations" and "Recurrance Relations"? What are the pre-requisites to tackle such a book?
A difference equation is an equation that contains sequence differences. For a good start, read the notes available at http://www.math.utah.edu/mathcircle/notes/earnshaw.pdf. See also the following books: http://www.amazon.com/Introduction-Difference-Equations-Dover-Mathematics/dp/0486650847, and http://www.springer.com/mathematics/dynamical+systems/book/978-0-387-23059-7.
For recurrence relations, see http://en.wikipedia.org/wiki/Recurrence_relation for an introduction. I do not know of any book on recurrence relations only, but I can recommend you the notes available at http://euler.slu.edu/~bart/08-135discrete/Section7-1and7-2.pdf, and as is said in an answer at https://mathoverflow.net/questions/124851/books-request-on-nonlinear-recurrence-relations, maybe http://www.amazon.com/Finite-Difference-Equations-Dover-Mathematics/dp/0486672603 is a good book.