I'm an undergraduate physics student at the University of Bremen,
Germany. Our lecturers in theoretical physics always expect a great
deal of mathematical knowledge from us in order to understand the
lesson. However, much of this knowledge is provided in other lessons
with a delay, or not provided at all. I in my first year of studying I
have spent a great amount of time on searching for books to find the
corresponding mathematical basics.
I believe that I know the German books on mathematics or mathematical
methods for physicists/engineers well, and I wanted to extend my scope
to English books. I was hoping to find books which teach mathematical
basics for theoretical physics and leave lots of space for practice,
like examples, exercises, and (if available) solutions. I have found
many English books similar to Arfken/Weber or Riley/Hobson/Bence, but
these compendium-like books are not very helpful to me because they
are too compressed.
So I would like to know which books for the purpose of teaching
mathematical skills are used for undergraduate students or beginner
students in physics at your Universities? I would be very grateful if
you could recommend me several books which choose a simple approach
and leave much room for examples/practice.