Course detail
Mathematics 1
FEKT-CMA1Acad. year: 2010/2011
Basic mathematical notions, functions and sequences. Vector spaces, linear combination of vectors, linear dependence and independence of vectors vectors, basis and dimension of vector space. Matrices and determinants. Systems of linear equations and their solutions.
Limit, continuity and derivative of function of one variable, derivatives of higher orders, Taylor polynomial, behavior of function, l´Hospital rule. Antiderivatives, indefinite integral of fuction of one variable, integration by parts, substitution method, integration of some elementary functions. Definite integral and its applications. Improper integral. Number series, power series, Taylor series. Limit, continuity and derivatives of function of several variables, gradient, derivatives of higher orders, total differential, Taylor polynomial, local extrema of functions of several variables.
Language of instruction
Number of ECTS credits
Mode of study
Guarantor
Department
Learning outcomes of the course unit
Prerequisites
Co-requisites
Planned learning activities and teaching methods
Assesment methods and criteria linked to learning outcomes
Course curriculum
2. Determinant, inverse matrix.
3. Function, limit, continuity.
4. Derivative -- physical and mathematical meaning of the concept. Rules for creating derivatives.
5. Graph of function -- intervals with f(x) increasing, local extremal points.
6. Graph of function II -- intervals with f(x) convex, asymptote of the graph.
7. Integration -- relation between definite and indefinite integral, basic integration methods.
8. Definite integration.
9. Application of definite integral. Improper integral.
10. Infinite number series, criteria of convergence.
11. Infinite power series, radius of convergence.
12. Taylor polynomial, Taylor series.
Work placements
Aims
Specification of controlled education, way of implementation and compensation for absences
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Prerequisites and corequisites
Basic literature
Recommended reading
Classification of course in study plans
- Programme EECC Bc. Bachelor's
branch BC-AMT , 1 year of study, winter semester, compulsory
branch BC-SEE , 1 year of study, winter semester, compulsory
branch BC-MET , 1 year of study, winter semester, compulsory
branch BC-EST , 1 year of study, winter semester, compulsory
branch BC-TLI , 1 year of study, winter semester, compulsory
Type of course unit
Lecture
Teacher / Lecturer
Syllabus
2. Vectors, combination, dependence and independence of vectors, basis and dimension of vector space.
3. Matrices and determinants, systems of linear equations and their solutions.
4. Differential calculus of one variable, limit, continuity, derivative.
5. Derivatives of higher orders, Taylor polynomial, l'Hospital rule, behaviour of function.
6. Integral calculus of one variable, antiderivative, indefinite integral.
7. Integration by parts, substitution method, integration of some elementary functions.
8. Definite integral and its applications.
9. Improper integral.
10. Number series, criterions of convergence.
11. Power series, Taylor series.
12. Differential calculus of more variables, limit, continuity, partial derivatives, gradient.
13. Derivatives of higher orders, total differential, Taylor polynomial, local extrema of functions of several variables.