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Course detail
FP-mae2PAcad. year: 2025/2026
Not applicable.
Language of instruction
Number of ECTS credits
Mode of study
Guarantor
Department
Entry knowledge
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 of the course is to build up mathematical tools necessary for the instruction of specialized courses.Acquired knowledge and practical mathematical skills will be an important starting point for mastering new knowledge in the follow-up courses of mathematical character; they will also be essential for acquiring knowledge in courses on economy and for the correct use of mathematical software.
Study aids
See basic and recommended literature
Prerequisites and corequisites
Basic literature
Recommended reading
Classification of course in study plans
specialization BAK-EAM-UAD , 1 year of study, summer semester, compulsoryspecialization BAK-EAM-EP , 1 year of study, summer semester, compulsory
Lecture
Teacher / Lecturer
Syllabus
Course of a function I (monotonicity, local and absolute extrema of a function, convexity and concavity)Course of a function II (asymptotes of a function, complete description of the behavior of a function)Indefinite integral (meaning, properties, basic rules for calculation)Integration methods I (method per partes and substitution)Integration methods II (decomposition into partial fractions, integration of rational fractional functions)Definite integral (meaning, properties, rules for calculation, applications)Functions of several variables and partial derivatives (graph and its sections, partial derivatives, differential)Summary (course of a function, indefinite integral of a function)Extrema of functions of several variables (partial derivatives of higher orders, local extrema and on compact sets)Boundary extrema (Lagrange's method)Introduction to graph theory (graph skeleton, traversal of a graph)Summary (definite integral, functions of several variables, Venn diagrams) diagrams, relations)Applications
Exercise
Higher-order derivatives, l'Hospital's rule, differentialFunction curve I (monotonicity, local and absolute extrema of a function, convexity and concavity)Function curve II (asymptotes of a function, complete description of the behavior of a function)Indefinite integral (meaning, properties, basic rules for calculation)Integration methods I (method per partes and substitution)Integration methods II (decomposition into partial fractions, integration of rational fractional functions)Definite integral (meaning, properties, rules for calculation, applications)Functions of several variables and partial derivatives (graph and its sections, partial derivatives, differential)Summary (function curve, indefinite integral of a function)Extrema of functions of several variables (partial derivatives of higher orders, local and compact extrema)Boundary extrema (Lagrange's method)Introduction to graph theory (graph skeleton, passage graph)Summary (definite integral, functions of several variables, Venn diagrams, relations)
Learning outcomes:Professional knowledgeThe student knows the methods of integral calculus and differential calculus of functions of several variables and their practical use.Professional competencesThe student can choose and apply appropriate mathematical methods for solving models of real processes and interpret the results in the context of the application.Professional skillsThe student can calculate integrals and extrema of functions of several variables and interpret the results in practice.
Individual preparation for an ending of the course
Self-study