After successfully attending the class students are familiar with the basic concepts related to the differential and integral calculus of multivariable calculus. Moreover, they have basic knowledge on Fourier series, as well as Fourier and Laplace transforms. 

Blackboard or computer presentations

0 Fourier series, Fourier and Laplace transforms1 Fields and vector differential operatorsVectors in 3-dimensional Euclidean spaceScalar fields, vector fields and curvesVector differential operatorsVector differential identitiesSpecial vector fields and potentialsTotal derivatives of curvesChain rule for fields and curvesNewton's methodTaylor's theoremExtremal values2 Vector integrationLine integralsMultiple integralsSpecial coordinate systems3 Green's, Gauß's and Stokes' theoremsGreen's theoremGauß's theoremStokes' theorem4 Ordinary differential equations

Analysis 1 for Engineers, interest in mathematics

Large parts of the course are based on the lecture notes "Vector Calculus" by Andrea Moiola (https://mate.unipv.it/moiola/ReaDG/VC2016/VectorCalculus_LectureNotes_2016.pdf)M. Brokate, P. Manchanda, A. Hassan Siddiqi: Calculus for Scientists and Engineers, Industrial and Applied Mathematics, Springer, 2019K. Burg, H. Haf, F. Wille, A. Meister: Höhere Mathematik für Ingenieure Band I, Analysis,   Teubner-Ingenieurmathematik, Vieweg+Teubner, Wiesbaden, 2011 (Standard reference for german speaking students)

written exam in the last week of the courseallowed aids: lecture notes with handwritten notes, no electronic aids (tablets, smartphones, etc.)

Contents of the class

50% of the obtained points in the exam are sufficient to pass