Mathematical Convergence Course

• The students know the notation and combination of sets of numbers and intervals, and they master the application of arithmetic laws up to the third level (powers, logarithms).
• They can solve equations (linear, quadratic, root equations, fractional equations, as well as exponential and logarithmic equations) by transforming expressions; they know the solution behavior of linear systems of equations and can interpret it geometrically.
• They can solve inequalities and absolute value equations by using case distinctions.
• They know the most important properties of the following classes of functions: power functions, exponential and logarithmic functions, trigonometric functions and their inverse functions; they understand the effects of transformations (translation, scaling) on basic functions and can describe such transformations using function equations.
• They can apply trigonometric functions for general triangle calculations and solve simple geometric equations using inverse trigonometric functions.
• The students can represent directional information with vectors and calculate ratios of division; they can perform calculations with vectors in component form and decompose vectors into components.

To analyze and model a wide range of processes, a solid foundation in mathematics is essential. The convergence course aims to provide students with the mathematical knowledge and skills at the level of the vocational baccalaureate in a technical field.

• Numbers, sets, arithmetic laws: set relations, intervals; basic arithmetic operations, exponentiation, logarithms; hierarchy of arithmetic operations
• Equations, expressions, bracket rules: solution methods for linear equations and systems of equations and their geometric interpretation; quadratic equations, root and fractional equations that lead to such forms; inequalities and absolute value equations
• Functions: domain and range, symmetry, monotonicity, periodicity, continuity; transformation of functions; power functions with arbitrary exponents, exponential and logarithmic functions, inverse functions
• Trigonometry: calculations in right-angled triangles; trigonometric functions and inverse trigonometric functions; sine and cosine laws and their application in oblique triangles; addition theorems and simple trigonometric equations
• Vectors: coordinate-free representation of directional information; vectors in Cartesian coordinate systems; vector calculus up to the scalar product