**PART A**

- Structure of the number system
- Algebraic simplifications
- Square and cubic roots, absolute values, powers, logarithms and trigonometric relationships
- Elementary functions with inverse functions and their graphs
- Quadratic curves
- Inequalities
- Equations with absolute values, polynomial, exponential, power, logarithmic and trigonometric equations
- Trigonometric identities
- Complex number sets, Argand diagram and complex planes
- Conjugate to a complex number
- Complex numbers in Cartesian, Polar and Exponential form
- Loci and regions of the complex plane
- De Moivre’s theorem
- Equations with non-real roots and equations with complex coefficients

**PART B**

- Vector space
- Addition and subtraction of vectors, multiplication between vectors, the length of a vector
- Distance in the plane and in the space
- Dot product and Cross product of vectors
- Line equation in the plane and in the space
- Distance, angle and possibly intersections between lines in the plane and space
- Equation for a plane in space
- Distance, angle and possibly intersection between lines and plane or plane and plane in the space
- Area for triangle and parallelogram in the plane and in the space, the volume of a parallelepiped.
- Addition, subtraction and multiplication of matrices
- Matrix equations
- Unit matrix and invert matrices of order 2 and 3
- Linear equation systems with Gauss' elimination method and Jacobi's method
- Least square method for curve fitting
- Matlab as a mathematical analysis tool

**PART C**

- Arithmetic and geometric sequences and their economic and scientific applications
- Functional concepts, real, compound, monotonic, inverse and arcus functions
- Limit values
- Sequence of numbers as n goes towards infinity
- L´Hospital's rule for evaluating limits
- Conditions for continuous functions
- The derivative's definition and derivation of the derivative to the elementary functions
- Linear approximation
- Chain, product and quota rule when deriving
- Logarithmic derivation, implicit derivation
- Numerical equation solution with Newton's method
- Application of the derivative in curve construction, in calculating rates and in optimization problems
- Primitive functions to elementary functions, integration by parts, substitution, integrals of rational functions
- Numeric integration with Trapezoidal and Simpson's method
- Definite and improper integrals
- Application of integrals in area calculation, volume calculation and calculation of arc length
- Curves in polar form
- Volume calculation with double integral
- Numerical solution of differential equations with Euler's method with Excel
- Separate differential equations, use of integrative factor to solve first-order equations
- First- and second order linear homogeneous differential equations
- Maclaurin series for elementary functions.
- Application of Maclaurin series in integral calculation and limit value calculations