The official textbook for the course is:
Lorenzo Peccati, Sandro Salsa, Annamaria Squellati, Mathematics for economics and business.
It covers all of the main subjects of the course, with some added details.  However it does not have very many exercises or examples of applications, so it is a good place to start (especially if you are unable to follow the lectures) but you may want to supplement it with other resources.  

I am aware of a number of other books which correspond less closely to the course program but are still useful:

The OpenStax Calculus series (https://openstax.org/subjects/math#Calculus) is a high-quality free online textbook, and I recommend it as a source of additional exercises and examples.  It is designed for a multi-semester sequence of courses, so only the following sections are relevant for this course:
Volume 1: all chapters
Volume 2: chapter 3, section 1 and chapter 5, sections 1 and 2 (chapters 1-2 are repeated from volume 1)
Volume 3 chapter 2, sections 1-3 and 4; Chapter 4, sections 1-4 and 7
Unfortunately, unlike the other books listed here, this series does not cover linear algebra (matrices).

Knut Sydsæter, Peter Hammond, Arne Strøm, Essential Mathematics for Economic Analysis has many exercises and examples, many of them drawn from economic theory.  It includes a considerable amount of more advanced material (especially related to linear algebra and optimization) but the discussion of limits and sequences is quite limited, and does not discuss series (infinite sums).

Carl P. Simon, Lawrence Blume, Mathematics for Economists also covers most of the material needed for this course, generally in a more detailed  and more abstract way than the other books.  It may be useful if you want a more advanced book to carry on studying beyond this course.