1. 
Selected topics in algebra (allowance 16/16) 

a. 
Vectors 
b. 
Matrix calculus 
c. 
Systems of linear equations 
d. 
Algebraic equations, complex numbers 

2. 
Real functions (allowance 8/8) 

a. 
Real functions and their properties 
b. 
Elementary functions 
c. 
Infinite sequences and their limits 
d. 
Limit and continuity of function 

3. 
Diferential calculus of real functions of one variable (allowance 12/12) 

a. 
The derivative, geometric and physical meaning 
b. 
Properties of functions with derivation, application in optimization 
c. 
Polynomial approximation of function, Taylor polynomial 
d. 
Parametric curves and functions 

4. 
Integral calculus of real functions of one variable (allowance 16/16) 

a. 
Primitive function, indefinite integral, basic formulas 
b. 
Integration by substitution 
c. 
Integration by parts 
d. 
Integration of rational functions, application of tables 
e. 
Definite integral 
f. 
Basic properties and methods for computing 
g. 
Applications of definite integral in geometry, chemistry and physics 
