Course detail
Mathematical Analysis
FIT-IMAAcad. year: 2017/2018
Limit and continuity, derivative of a function. Partial derivatives. Basic differentiation rules. Elementary functions. Extrema for functions (of one and of several variables). Indefinite integral. Techniques of integration. The Riemann (definite) integral. Multiple integrals. Applications of integrals. Infinite sequences and infinite series. Taylor polynomials.
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
- Syllabus of lectures:
- Function of one variable, limit, continuity.
- Differential calculus of functions of one variable I: derivative, differential, Taylor theorem.
- Differential calculus of functions of one variable II: maximum, minimum, behaviour of the function.
- Integral calculus of functions of one variable I: indefinite integral, basic methods of integration.
- Integral calculus of functions of one variable II: definite Riemann integral and its application.
- Infinite number and power series.
- Taylor series.
- Functions of two and three variables, geometry and mappings in three-dimensional space.
- Differential calculus of functions of more variables I: directional and partial derivatives, Taylor theorem.
- Differential calculus of functions of more variables II: funcional extrema, absolute and bound extrema.
- Integral calculus of functions of more variables I: two and three-dimensional integrals.
- Integral calculus of functions of more variables II: method of substitution in two and three-dimensional integrals.
- Limit, continuity and derivative of a function. Partial derivative. Derivative of a composite function.
- Differential of function of one and several variables. L'Hospital's rule. Behaviour of continuous and differentiable function. Extrema of functions of one and several variables.
- Primitive function and undefinite integral. Basic methods of integration. Definite one-dimensional and multidimensional integral.
- Methods for solution of definite integrals (Newton-Leibnitz formula, Fubini theorem).
- Indefinite number series. Convergence of series. Sequences and series of functions. Taylor theorem. Power series.
Syllabus of numerical exercises:
The class work is prepared in accordance with the lecture.
Syllabus of computer exercises:
Trained tasks are prepared to follow and complete study matter from lectures and seminar practice.
Syllabus - others, projects and individual work of students:
Work placements
Aims
Specification of controlled education, way of implementation and compensation for absences
Homeworks: 30 points.
Semestral examination: 60 points.
Recommended optional programme components
Prerequisites and corequisites
Basic literature
Recommended reading
Classification of course in study plans
Type of course unit
Lecture
Teacher / Lecturer
Syllabus
- Function of one variable, limit, continuity.
- Differential calculus of functions of one variable I: derivative, differential, Taylor theorem.
- Differential calculus of functions of one variable II: maximum, minimum, behaviour of the function.
- Integral calculus of functions of one variable I: indefinite integral, basic methods of integration.
- Integral calculus of functions of one variable II: definite Riemann integral and its application.
- Infinite number and power series.
- Taylor series.
- Functions of two and three variables, geometry and mappings in three-dimensional space.
- Differential calculus of functions of more variables I: directional and partial derivatives, Taylor theorem.
- Differential calculus of functions of more variables II: funcional extrema, absolute and bound extrema.
- Integral calculus of functions of more variables I: two and three-dimensional integrals.
- Integral calculus of functions of more variables II: method of substitution in two and three-dimensional integrals.
Fundamentals seminar
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Syllabus
Exercise in computer lab
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Syllabus