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

• correctly use the terms vector space, linear dependency and basis,
• describe the properties of an inner product and a norm and to apply them in specific computations,
• explain the relation between linear functions and matrices,
• perform calculations with matrices, in particular to invert matrices and perform a change of basis,
• identify 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,
• describe 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, linear partial differential equations.

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)

Das positive Absolvieren der Übung Mathematik 1 für BI ist dringend empfohlen!