In order to successfully pass the modules offered in theoretical physics, a considerable amount of maths knowledge is required. For this reason, we are increasingly focussing on basic knowledge, such as "What is a derivative", particularly in the entrance exams for Bachelor's modules.
If you still have deficits in this respect, we refer you to the lectures "Advanced Mathematics for Scientists I+II", which cover the following topics:
- Elementary logic, sets, complex numbers
- Sequences and series
- Limits and continuity of real functions
- Differential calculus in one variable
- Integral calculus in one variable
- Linear algebra 1: Vector spaces, linear mappings + systems of equations, determinants, matrix calculus, esp. scalar and cross products (!)
- Linear algebra 2: Geometric transformations, orthogonal matrices, eigenvalue problems, diagonalization of matrices, change of basis
- Ordinary differential equations, initial value problems, types of differential equations, solution methods for 1st and 2nd order differential equations with const. coefficients
- Integral and differential calculus in several variables
- An overview of the knowledge imparted
- Exercises incl. solutions for HM1 and HM2
- Mathematica Demonstrations for HM
Good basic literature, some of it even written specifically for physicists:
- S. Großmann: Mathematischer Einführungskurs für die Physik (ub, amzn)
- H. Korsch: Mathematische Ergänzungen zur Einführung in die Physik (amzn)
- P. Furlan: Das gelbe Rechenbuch (ub, amzn)
- T. Arens: Mathematics (ub, amzn)
These books also cover the field of vector analysis in more detail.
A compilation of all important "mathematical" formulae for theoretical physics will be published here shortly.
If you have explicit questions or problems, you are also welcome to contact the relevant course instructor.