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Course detail
FP-mae1PAcad. year: 2026/2027
The subject is part of the theoretical basis of the field. Learning outcomes of the course unit The aim of the course is to unify and supplement the students' knowledge in the areas of further teaching of basic mathematical concepts and to teach students the comprehension of using the linear algebra system to solve the linear equations and the differential functions of one variable (including basic applications in economic disciplines).
Language of instruction
Number of ECTS credits
Assignment to study programme types
Mode of study
Guarantor
Department
Entry knowledge
Knowledge of high school mathematics.
Rules for evaluation and completion of the course
Requirements for awarding credit:Passing control tests and achieving at least 55% of points or completing a comprehensive written work and achieving at least 55% of points.Awarding credit is a necessary condition for taking the exam.
Exam requirements:The exam is written.For all tasks in the written part, a calculation must be written, or the procedure must be described, or the result must be justified verbally. The examples are divided into thematic groups. If the student does not achieve at least 50% of the total number of achievable points in each thematic group of examples, the written part and the entire exam are graded "F" (unsatisfactory).If the student does not achieve at least 55% of the total number of achievable points in the written work, the written part and the entire exam are graded "F" (unsatisfactory).Completion of the course for students with individual study:Passing the comprehensive control test and achieving at least 55% of points.Awarding credit is a necessary condition for taking the exam.Exam requirements:The exam is written.For all tasks in the written part, a calculation must be written, or the procedure must be described, or the result must be justified verbally. The examples are divided into thematic groups. If the student does not achieve at least 50% of the total number of achievable points in each thematic group of examples, the written part and the entire exam are evaluated with a grade of "F" (unsatisfactory).If the student does not achieve at least 55% of the total number of achievable points in the written work, the written part and the entire exam are evaluated with a grade of "F" (unsatisfactory).
Participation in seminars is checked.
Students studying under the ISP take one comprehensive test, which includes all topics covered in the exercises and can be scored from 0-60 points.
Aims
The aim is to master the solution of systems of linear equations and detailed analysis of processes described by a real function of one real variable, including the implementation of necessary calculations in general and in economic applications (also with regard to the use of computer technology).
Study aids
Prerequisites and corequisites
Basic literature
Recommended reading
Classification of course in study plans
specialization BAK-EAM-UAD , 1 year of study, winter semester, compulsory, fundamental theoretical courses of the profile corespecialization BAK-EAM-EP , 1 year of study, winter semester, compulsory, fundamental theoretical courses of the profile core
Lecture
Teacher / Lecturer
Syllabus
1. Mathematical notation, quantifiers, set theory (Venn diagrams)2. Cartesian product, relations (relations between sets and on sets, properties)3. Matrices (types, matrix operations, rank)4. Determinants (properties, rules and calculation of determinants)5. Systems of linear equations (solvability, GEM)6. Functions of one variable (characteristics, properties, operations with functions, elementary functions)7. Polynomials (roots of a polynomial and their determination, Horner scheme)8. Summary (sets, relations, linear algebra)9. Limit of a function (proper and improper limit at a proper and improper point, rules for calculation)10. Continuity of a function (continuity at a point and on an interval, properties and rules for calculating continuous functions)11. First-order derivatives (meaning, basic properties and rules, derivatives of elementary functions)12. Summary (properties of functions, polynomials, limit and continuity of functions)13. Higher order derivatives, review for the entire semester.
Exercise
Review of basic concepts2. Mathematical notation, quantifiers, set theory (Venn diagrams)3. Cartesian product, relations (relations between sets and on sets, properties)4. Matrices (types, matrix operations)5. Determinants (properties, rules and calculation of determinants)6. Systems of linear equations 1. (matrix rank, solvability)7. Systems of linear equations 2. (GEM)8. Functions of one variable 1. (characteristics, properties, operations with functions, elementary functions)9. Functions of one variable 2. (characteristics, properties, operations with functions, elementary functions)10. Polynomials (roots of a polynomial and their determination, Horner's scheme)11. Limit of a function (proper and improper limit at an eigen and improper point, rules for calculation)12. First-order derivatives (meaning, basic properties and rules, derivatives of elementary functions)13. Higher order derivatives, repetitionLearning outcomes:Professional knowledgeThe student knows the principles of solving systems of linear equations and differential calculus of functions of one variable, including their applications.Professional competencesThe student can analyze the properties of functions, choose an appropriate calculation procedure and interpret the results in the context of a practical problem.Professional skillsThe student is able to solve systems of equations and perform derivatives of functions, including the use of computer technology, and apply calculations to real situations.
Self-study
Individual preparation for an ending of the course