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.

The first session (including the first pop-up quiz) will be on Tuesday 16 March.

Introductory Meeting on March 9, 2021 at 13PM on Zoom

Midterm exams (60%), pop-up exams (40%) and weekly problem assignments.

Until further notice, the performance reviews will take place in online format. The following requirements must be met for this:

• Internet-capable terminal with camera and microphone as well as smartphone
• generally stable internet access.
• Access to a room that can be used alone during the exam period.
• Willingness to ensure that there are no avoidable disruptions (telephone/visits, etc.) during the examination period

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