After successful completion of the course, students are able to...

• correctly use the terms vector space, linear dependency and basis,
• understand the meaning and use of an inner product and a norm,
• understand the relation between linear functions and matrices,
• perform calculations with matrices, in particular to invert matrices and perform a change of basis,
• recognize linear systems of equations and efficiently determine and interpret the set of solutions,
• determine and interpret determinant, eigenvalues and eigenvectors,
• differentiate real functions in several variables, expand them in Taylor series and determine their local extrema,
• parametrize basic paths and surfaces and determine and interpret integrals over those paths and surfaces,
• calculculate and interpret divergence, gradient and curl of vector resp. scalar fields and represent them using nabla,
• solve linear and exact differential equations as well as linear systems of differential equations,
• construct simple probability spaces and calculate (conditional) probabilities,
• calculate expectation value and variance of random variables,
• to recognize the applicability of the law of large numbers and the central limit theorem.

Linear algebra, ordinary differential equations, systems of linear differential equations, differential calculus, multiple integrals, basic concepts of vector analysis, introduction to statistics and probability theory.

Solving preassigned problems. Discussion of questions in the online forum and in the weekly plenum.

Midterm exams (70%), pop-up exams (30%) and weekly problem assignments (bonus points)

Mathematics 1 für CE, i.e. elements of mathematical logic, real and complex numbers, real functions and calculus in one dimension.