Course detail
Mathematics 2
FP-MA2_MAcad. year: 2024/2025
This course follows Mathematics I course. Content is linear algebra, differential calculus of several variables, differential and difference equations (mainly linear) and instruments for their only solution - power series and Fourier series and selected integral transformation.
Language of instruction
Number of ECTS credits
Mode of study
Guarantor
Department
Entry knowledge
Rules for evaluation and completion of the course
Conditions for awarding course-unit credits:
-active participation in the seminars where the attendance is compulsory,
-fulfilment of individual tasks and successful completion of written assignments,
-working out of a semester project marked with at least “E”,
-completion of partial written exams marked more than 55% points
The exam has a written and an oral part with the written part being more important.
Attendance at exercises (seminars) is controlled.
Aims
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
Viz. literature
Prerequisites and corequisites
Basic literature
MEZNÍK, I. Základy matematiky pro ekonomii a management. Základy matematiky pro ekonomii a management. 2017. s. 5-443. ISBN: 978-80-214-5522-1. (CS)
Mezník,I.: Matematika II.FP VUT v Brně, Brno 2009 (CS)
Recommended reading
Elearning
Classification of course in study plans
- Programme BAK-MIn Bachelor's 1 year of study, summer semester, compulsory
Type of course unit
Lecture
Teacher / Lecturer
Syllabus
- Course of function I (monotonicity, local and absolute extrema of the function,convexity and concavity)
- Course of the function II (asymptotes of the function, complete description of the behavior of the function)
- Indefinite integral (meaning, properties, basic rules for calculation)
- Integration methods I (per partes and substitution method)
- Methods of integration II (decomposition into partial fractions, integration of rational fractional functions)
- Definite integral (meaning, properties, calculation rules, applications, improper integral)
Summary (function progression, function integral) - Functions of several variables and partial derivatives (graph and its sections, partial derivatives, differential)
- Extrema of functions of several variables (partial derivatives of higher orders, local extrema and on compact sets)
- Bound extrema (Lagrange method)
- Differential equation of the 1st order (with separated variables, linear)
- Summary (definite integral, differential equation, introduction to functions of several variables)
- Linear differential equation of the 2nd order (with constant coefficients)
Exercise
Teacher / Lecturer
Syllabus
- Differential and derivatives of higher orders (differential and its use, derivatives of higher orders, l'Hospital's rule)
- Course of function I (monotonicity, local and absolute extrema of the function)
- Course of the function II (convexity and concavity; asymptotes of the function, complete description of the behavior of the function)
- Indefinite integral (meaning, properties, basic rules for calculation)
- Integration methods I (per partes and substitution method)
- Methods of integration II (decomposition into partial fractions, integration of rational fractional functions)
- Definite integral (meaning, properties, rules for calculation)
- Definite integral (application)
- Functions of multiple variables and partial derivatives (graph, partial derivatives, differential)
- Extrema of functions of several variables (partial derivatives of higher orders, local extrema and on compact sets)
- Extrema of functions of several variables
Differential equation of the 1st order (with separated variables, linear) - Linear differential equation of the 2nd order (with constant coefficients)
Elearning