After successfully attending the class students are familiar with the basic concepts related to the differential and integral calculus of functionsof several real variables.

Presentation at blackboardwith computer support.

1 Fields and vector differential operators•                 Vectorsin 3-dimensional Euclidean space•                 Scalarfields, vector fields and curves•                 Vectordifferential operators•                 Vectordifferential identities•                 Specialvector fields and potentials•                 Totalderivatives of curves•                 Chainrule for fields and curves•                 Taylor'stheorem•                 Extremalvalues2 Vector integration•                 Lineintegrals•                 Multipleintegrals•                 Specialcoordinate systems3 Green's, Gauß's and Stokes' theorems•                 Green'stheorem•                 Gauß'stheorem•                 Stokes'theorem4 Ordinary differential equations

Analysis 1 for Engineers, firm understanding of school mathematics.

M. Brokate, P. Manchanda,A. Hassan Siddiqi: Calculus for Scientists and Engineers, Industrial andApplied Mathematics, Springer, 2019K. Burg, H. Haf, F. Wille,A. Meister: Höhere Mathematik für Ingenieure Band I, Analysis,  Teubner-Ingenieurmathematik, Vieweg+Teubner, Wiesbaden, 2011 (Standardreference for german speaking students)

Written exam that can allow boththeoretical questions and the solution of the particular problems.Allowed aids: lecture notes with handwritten notes, no electronicaids (tablets, smartphones, etc.)

The contents of the lecture.

•     50% of the points in the final exam are sufficient to pass