Mathematics 1 (FSI-Z1M)

Conditions for awarding the course-unit credit (0-100 points, minimum 50 points):

• two written tests (each maximum 50 points); students who fail to score 50 points in total will be allowed to resit the test during the first week of the examination period.

Conditions for passing the exam (0-100 points, minimum 50 points):

• written test (maximum 85 points),
• discussion about the test and the oral part of the exam (maximum 15 points),
• maximum 100 points, the overall classification is given by ECTS grade scale.

Lecture: Attendance at lectures is obligatory and checked, only one unexpected absence is allowed, absence may be compensated for based on an agreement with the teacher.

Seminar: Attendance in seminars is obligatory and checked, only one unexpected absence is allowed, absence may be compensated for based on an agreement with the teacher.

• Basis of mathematical logic (premise, logical connective, quantifiers).


• Complex numbers (algebraic and trigonometric forms, operations with complex numbers, Euler’s identity).


• Vector, Cartesian coordinate system (free and bound vector, operations with vectors, scalar and vector products, magnitude of the vector).


• Matrices (matrix, operations with matrices, determinant, inverse of a matrix, system of linear algebraic equations).


• Analytic geometry (problems involving straight lines and planes in 2D and 3D spaces, e.g., intersection, distance, angle, etc.).


• Functions of one real variable (notion of a function, graph, basic properties, basic elementary functions, vector function).


• Differential calculus of functions of one variable (limit, L´Hospital rule, continuity, derivative, differential, linear and quadratic approximations, Taylor polynomial).


• Behaviour of functions of one variable (monotonous functions, convex and concave functions, inflection points, local and global extremes, asymptotes).


• Integral calculus of functions of one variable (Riemann integral, antiderivative, Newton-Leibnitz formula, indefinite integral, basic techniques of integration).

• Operations with vectors, scalar and vector products, examples of a possible use in geometry and solid mechanics.


• Properties of matrices, operations with matrices, solving of systems of linear algebraic equations.


• Problems involving straight lines and planes in 2D and 3D spaces.


• Basic properties of functions of one real variable, vector function, examples of a possible use in geometry and kinematic.


• Evaluation of basic limits of functions of one variable, derivatives of functions of one variable, linear and quadratic approximations, examples of a possible use in geometry and kinematic.


• Behaviour of functions of one variable, local and global extremes, examples of a possible use in problems of strength analysis.


• Evaluation of indefinite and definite integrals of functions of one variable, geometrical and physical applications, examples of a possible use in evaluation of line integrals.