260402 PVU STEOP 2: Introduction to Calculus (2021W)

Aims:
Acquirement, understanding and refreshment of the basic mathematical skills in the context of analytical computational methods which are required in the initial phase of physics studies.
Application of the knowledge acquired in the lecture in mathematical examples and physical problems (solving of mathematical problems, discussion of different solutions), deepening of the lecture material.

Contents:
The most important functions and their properties, coordinate systems and vector algebra, differentiation rules, differentiation of functions and vectors, partial differentiation, integration rules, rotational bodies, calculation of arc lengths, multiple integrals, complex numbers (Cartesian representation, exponential form), differentiation of fields (grad, div and rot), integration of fields (curve and surface integrals) as well as ordinary differential equations 1st and 2nd order (linear homogeneous and inhomogeneous differential equations in the physical context, existence and uniqueness of solutions).

Method:
In the lecture part, the concepts and methods are deepened and directly applied by means of representative examples.
The exercise part of the PVU takes place in groups. Students work on calculation examples in groups (teamwork). Several teachers and a tutor are present to support the students in solving the problems in digital breakout rooms.