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## Syllabus

EN IT

### Prerequisites

Being able to solve first and second order equations, inequalities, fractional inequalities, exponential, logarithmic and trigonometric inequalities.

Basic knowledge of properties of exponential, logarithmic and trigonometric functions.

### Program

Basic properties of functions.
Set theory. Set Operations: union, intersection, difference, complement. Intuitive construction of number sets.
Real valued functions.
Linear, quadratic and polynomial functions. Exponential, Logarithmic and Trigonometric functions. Domain, Range of a function. Increasing, decreasing and monotonic functions.
Injective, surjective functions. The inverse function. Sequences.
Definition of limit of a sequence, uniqueness of the limit of a sequence (with proof), monotonic sequences. Existence of the limit of a monotonic and bounded sequence.
Comparison Theorem (with proof). Notable limits. Series.
Definition and examples. Conditions for convergence of geometric series (with proof).
Limit of real functions of one real variable.
Definition. Uniqueness of the limit. Comparison Theorem.
Continuity: definition and main theorems. Characterization of the discontinuity points of a function: jumps and removable and essential discontinuities.
Derivative of a real functions of one real variable.
Necessary condition for differentiability (with proof).
Maxima and minima of a function: necessary and sufficient conditions.
Tangent line and 1st order Taylor approximation.
Convex and concave functions. Second-order conditions for maxima and minima.

### Books

Knut Sydsæter, Peter Hammond, Arne StrØm, Essential Mathematics for Economic Analysis
Carl P. Simon, Lawrence Blume, Mathematics for Economists

### Teaching methods

Theoretical lectures and exercise classes

### Exam Rules

Written test with exercises and theoretical questions