Course detail
Mathematics 1
FEKT-BMA1Acad. year: 2012/2013
Basic mathematical notions. Sets, operations with sets, concept of a function, inverse function, sequences.
Linear algebra and geometry. Vector spaces, basic notions,linear combination of vectors, linear dependence, independence vectors, base, dimension of a vector space. Matrices and determinants. Systems of linear equations and their solution.
Differential calculus of one variable, limit, continuity, derivative of a function. Derivatives of higher orders, l´Hospital rule, behavior of a function. Integral calculus of fuctions of one variable, antiderivatives, indefinite integral. Methods of a direct integration. Integration by parts, substitution methods, integration of some elementary functions. Definite integral and its applications. Improper integral. Infinite number series, convergence criteria. Power series, Taylor theorem, Taylor series.
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. Vectors and matrices.
3. Determinants, systems of linear equations.
4. Limits and the continuity of the functions of one variable.
5. The derivative of the functions of one variable.
6. The Taylor polynom and the l'Hospitalovo rule.
7. Graphing a function.
8. Antiderivatives, the per partes method and the substitution technic.
9. Integration of the rational functions.
10. Definite integral.
11. The aplications of the definite integral and the improper integral.
12. Series.
13. Power series and 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
Small, D.B., Hosack, J.M., Calculus (An Integrated Approach), Mc Graw-Hill Publ. Comp., 1990. (EN)
Švarc, S. a kol., Matematická analýza I, PC DIR, Brno, 1997. (CS)
Classification of course in study plans
- Programme ZRZT-J Bachelor's
branch J-ZRT , 1 year of study, winter semester, compulsory
- Programme EECC Bc. Bachelor's
branch B-AMT , 1 year of study, winter semester, compulsory
branch B-MET , 1 year of study, winter semester, compulsory
branch B-TLI , 1 year of study, winter semester, compulsory
branch B-SEE , 1 year of study, winter semester, compulsory
branch B-EST , 1 year of study, winter semester, compulsory - Programme EEKR-CZV lifelong learning
branch EE-FLE , 1 year of study, winter semester, compulsory
Type of course unit
Lecture
Teacher / Lecturer
Syllabus
2. Vector - combination, dependence and independence of vectors, base and dimension of a vector space.
3. Matrices and determinants.
4. Systems of linear equations and their solution.
5. Differential calculus of one variable. Limit, continuity, derivative of a function.
6. Derivatives of higher order, Taylor theorem.
7. L'Hospital rule, behaviour of a function.
8. Integral calculus of functions of one variable, primitive function, indefinite integral. Methods of direct integration.
9. Per partes method and substitution method. Integration of some elementary functions.
10. Definite integral and its applications.
11. Improper integral.
12. Infinite number series, convergence criteria.
13. Power series, Taylor theorem, Taylor series.
Exercise in computer lab
Teacher / Lecturer
Syllabus
2. Matrices, determinants.
3. Solving a system of linear equations.
4. Derivative of a function of one variable.
5. Behaviour of a function.
6. Calculation of indefinite and definite integrals.
7. Series.