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Course detail
FP-mae1PAcad. year: 2025/2026
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
Mode of study
Guarantor
Department
Entry knowledge
Knowledge of high school mathematics.
Rules for evaluation and completion of the course
Credit requirements:
Passing control tests and achieving at least 55% points or passing a comprehensive written work and achieving at least 55% points.Awarding credit is a necessary condition for taking the exam.
Exam requirements:
The exam has a written and an oral part, with the focus of the exam being the oral part.
For all tasks in the written part, the calculation must be written down, 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) and the student does not proceed to the oral part.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) and the student does not proceed to the oral part.The oral part, focused on knowledge of the theory, follows the written part, and also serves to resolve any ambiguities in the written part.
Completion of the subject for students with individual study:Passing the comprehensive control test and achieving at least 55% points.Awarding credit is a necessary condition for taking the exam.The exam has a written and an oral part, with the focus of the exam being the oral part.For all tasks in the written part, the calculation must be written down, 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) and the student does not proceed to the oral part.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) and the student does not proceed to the oral part.The oral part, focused on knowledge of the theory, follows the written part, and also serves to resolve any ambiguities in the written part.
Participation in exercises is controlled.
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, compulsoryspecialization BAK-EAM-EP , 1 year of study, winter semester, compulsory
Lecture
Teacher / Lecturer
Syllabus
Fundamentals of logic and set theory (Propositional logic, sets, Venn diagrams)Relations (between sets and on sets, properties, tolerance, equivalence, ordering)Matrices (properties, matrix operations, rank calculation and inverse matrices)Determinants (properties, rules and determinant calculation)Systems of linear equations (solvability, GEM and Cramer's rule)Functions of one variable (basic characteristics of functions, properties, rational operations with functions, properties)Elementary functions, constructions and graph shiftsPolynomials (roots of a polynomial and their determination, Horner's scheme)Summary (linear algebra, basic properties of functions)Limit and continuity of a function1st-order derivative (meaning, basic properties and rules, derivatives of elementary functions)Summary (properties of functions, polynomials, limit and continuity of a function, derivatives)Higher-order derivatives, l'Hospital's rule, differential
Exercise
Review of basic conceptsFundamentals of logic and set theory (Propositional logic, sets, Venn diagrams)Relations (between sets and on sets, properties, tolerance, equivalence, ordering)Matrices (properties, matrix operations, rank calculation and inverse matrix)Determinants (properties, rules and determinant calculation)Systems of linear equations (solvability, GEM and Cramer's rule)Functions of one variable (basic characteristics of functions, properties, rational operations with functions, properties)Elementary functions, constructions and shifts of graphsPolynomials (roots of a polynomial and their determination, Horner's scheme)Summary (linear algebra, basic properties of functions)Limit and continuity of a function1st-order derivative (meaning, basic properties and rules, derivatives of elementary functions)Summary (properties of functions, polynomials, limit and continuity of a function, derivatives)Learning 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.
Individual preparation for an ending of the course
Self-study