Course detail
Mathematics 1
FEKT-BKC-MA1Acad. year: 2018/2019
Vectors spaces, linear combination, linear dependence, basis and dimension of vector space. Matrices and systems of linear equations. Limit, continuity, derivative, l´Hospital's rule, Taylor polynomial, behavior of function. Antiderivative, indefinite integral. Definite integral and its applications. Improper integral. Number series, power series, Taylor series.
Language of instruction
Number of ECTS credits
Mode of study
Guarantor
Department
Learning outcomes of the course unit
- decide whether vectors are linearly independent and whether they form a basis of a vector space;
- add and multiply matrices, and compute the determinant and the inverse of a square matrix;
- solve a system of linear equations;
- differentiate and find the tangent to the graph of a function;
- sketch the graph of a function including extrema, points of inflection and asymptotes;
- integrate using basic formulas including integration by parts;
- evaluate a definite integral using the Fundamental Theorem of Calculus;
- compute the area of a region using the definite integral;
- discuss the convergence of a number series.
Prerequisites
Co-requisites
Planned learning activities and teaching methods
Assesment methods and criteria linked to learning outcomes
Course curriculum
2. Vectors, combination, dependence and independence of vectors, basis and dimension of vector space.
3. Matrices and determinants.
4. Systems of linear equations and their solutions.
5. Differential calculus of one variable, limit, continuity, derivative.
6. Derivatives of higher orders, Taylor polynomial.
7. L'Hospital's rule, behaviour of function.
8. Integral calculus of one variable, antiderivative, indefinite integral.
9. Integration by parts, substitution method, integration of some elementary functions.
10. Definite integral and its applications.
11. Improper integral
12. Number series, convergence tests.
13. Power series, Taylor series.
Work placements
Aims
Specification of controlled education, way of implementation and compensation for absences
Recommended optional programme components
Prerequisites and corequisites
Basic literature
Recommended reading
Classification of course in study plans
- Programme BKC-MET Bachelor's 1 year of study, winter semester, compulsory
- Programme BKC-TLI Bachelor's 1 year of study, winter semester, compulsory
- Programme BKC-EKT Bachelor's 1 year of study, winter semester, compulsory
- Programme EEKR-CZV lifelong learning
branch EE-FLE , 1 year of study, winter semester, compulsory