I've just finished my first year studying mathematics at the ANU, also originally from NSW, and completed MATH1115 earlier this year. The lecture notes that are provided by the lecturers would definitely suffice to do well in the course, but they do recommend buying the two prescribed textbooks for the linear algebra and calculus halves of the course. The linear algebra textbook (Elementary Linear Algebra - Anton and Rorres) is probably more essential to get instead of the calculus textbook (Essential Calculus - Stewart) as MATH1115 assumes quite a bit of linear algebra knowledge that isn't covered in the HSC in NSW, and the lecturer required us to read certain chapters from this textbook before starting the course. However, both textbooks are more for practicing computational examples related to concepts in linear algebra and calculus, which is not the aim of the course as MATH1115 is very proof heavy, unlike maths at the HSC which is why the lecture notes are generally better study aids compared to the textbooks. But I recommend getting the linear algebra textbook (assuming they don't change the prescribed texts for next year) as NSW students have much less experience with linear algebra compared to ACT students.
The lecture notes are free and given out by the lecturers gradually throughout the semester, so everyone gets them. A lot of the calculus half of the course is introducing real analysis in a rigorous theorem-proof way and goes into even more detail in MATH1116 in second semester, which isn't generally found in other first year courses at universities in NSW
Ok, thanks. Is there any reason then why getting a real analysis textbook wouldn't be a good idea? Do you think it could perhaps complement the subject better for the proofs and knowledge, than Stewart's calculus (as you suggested it's more useful for computational exercise)?
It would definitely be a good idea to look at Trench's 'Introduction to Real Analysis' which you can get for free online here: http://ramanujan.math.trinity.edu/wtrench/misc/index.shtml - this was a recommended text for MATH1116.
The first four chapters of Trench would be useful for 1115 and the last four chapters are useful for 1116. If you read through and do some of the harder exercises in the text, then you would definitely be on track to do well in the Calculus halves of both courses