Contents of the lecture: Mathematical Methods
Introduction/ Repetition of school knowledge
- motivation
- functions in economics
- recap of school knowledge
- important sets
- sigma sign
- fractional arithmetic
- percentage calculation
- roots, powers, logarithms
- absolute values
- transforming equations, p-q formula, factorising
- transforming inequations
- functions, inverse functions
- numerical sequences
- limits of sequences and functions, l'Hôpital's rule
- composite functions
- continuity
Combinatorics
- permutations
- combinations
- variations
Functions of one variable
- differentiability
- tangent function
- differential
- elasticity
Fundamentals of Financial Mathematics
- geometric series
- interests
- present values
- loans, annuities, credit periods
Linear Algebra
- matrices and vectors
- basic matrix algebra
- inverse matrix
- linear independence
- rank of a matrix
- linear map
- solving linear equations
Differentiable functions of several variables
- graphic representation, level curves
- continuity
- partial differentiability
- partial elasticity
- partial differential
- total differentiability
- gradient
- tangent function
- total differential
- homogeneous functions, Euler's theorem
- vector-valued function, Jacobi matrix
- derivative rules, theorem of total derivative, chain rule
- implicit functions and their derivatives
- marginal rate of substitution
- elasticity of substitution
- higher order partial derivatives, Hessian matrix
Extrema of functions of several variables
- relative extrema
- convexity und concavity
- global extrema
- extrema at the boundary
- extrema under constraints:
- method of elimination
- method of Lagrange multipliers
- envelope theorem
Integral Calculus
- basics and economic examples
- integration by parts
- integration by substitution
- improper integrals
- integral calculus for functions of two variables
- integral calculus in the calculus of probability
Differential and difference equations (only until summer term 2018)
- applications in economics
- homogeneous and inhomogenous linear differential equations of order one
- separable differential equations
- linear difference equations