The basics
If you fulfil the initial requirements, you should be able to follow the lecture Mathematics, offered during the Autumn Term of the Assessment Year, without too many difficulties. The required subject areas are listed in detail below.
You should be familiar with these concepts and be comfortable with applying the corresponding mathematical tools in practice. In addition, elementary algebraic skills - in particular basic algebraic operations and dealing with fractions - are essential.
1. Arithmetic and algebra
- Power with rational exponents (including calculation rules)
- Basic rules for inequalities
- Solution of linear systems of equations with a maximum of three variables
- Solution of quadratic equations with one variable
- Specific terms and the fundamental associated relationships: absolute value, sigma sign, factorial, binomial coefficients, notation of elementary set theory
2. Functions
- Polynomial functions
- Simple rational functions
- Root functions
- Exponential functions, including properties and calculation rules, and the Euler number
- Logarithmic functions, including properties and calculation rules
- Trigonometric functions (degrees, radians, definition in the unit circle), included addition theorems for cosine and sine
- Domain and range of functions
- Inverse function with concrete examples
The ability to produce graphs and recognise functions based on their graphical representation are also a requirement. When handling exponential and logarithmic functions, as well as trigonometric functions, knowledge of the most important function values is a necessity.
3. Calculus
- Limits
- Continuity of functions of a real variable in the graphical sense
- Derivatives of function of a real variable
- Geometric meaning of the first derivative
- Meaning of the first derivative in applications (growth behaviour of functions)
- Derivatives for basic functions e.g., xʳ, cos, sin, tan, exp, ln
- Rules of derivation (product, quotient rule and chain rule)
- Determination of extreme points of functions of a real variable
- Calculation of integrals (integration by parts and integration by substitution)
References
For further information on the above mentioned terms and concepts, please refer to the following books:
- De Giorgi, Enrico (2019): Mathematics, University of St. Gallen
(see www.enricodegiorgi.com).
- Sydsaeter, Knut, Peter Hammond, and Arne Strom (2012): Essential Mathematics for Economic Analysis (4th Edition), Prentice Hall, Chapter 1-9.