Course detail
Mathematics
FAST-AA01Acad. year: 2014/2015
Basics of linear algebra (matrices, determinants, systems of linear algebraic equations). Some notions of vector algebra and their use in analytic geometry. Function of one variable, limit, continuous functionst, derivative of a function. Some elementary functions, Taylor polynomial. Basics of calculus. Probability. Random varibles, laws of distribution, numeric charakteristics. Sampling, processing statistical data.
Language of instruction
Czech
Number of ECTS credits
3
Mode of study
Not applicable.
Guarantor
Department
Institute of Mathematics and Descriptive Geometry (MAT)
Learning outcomes of the course unit
Operations with matrices.
Algebra of vectors.
Differential and integral calculus of functions of one variable.
Differential calculus of functions of several variables.
Probability and statistics.
Algebra of vectors.
Differential and integral calculus of functions of one variable.
Differential calculus of functions of several variables.
Probability and statistics.
Prerequisites
Basics of mathematics as taugth at secondary schools. Graphs of elementary functions (powers and roots, quadratic function, direct and indirect proportion, absolute value, trigonometric functions) and basic properties of such functions. Simplification of algebraic expression, geometric vector and basics of analytic geometry in E3.
Co-requisites
Not applicable.
Planned learning activities and teaching methods
Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations – lectures, seminars.
Assesment methods and criteria linked to learning outcomes
Abilities leading to successful solution of some typical classes of differential equations as well as necessary theoretical knowledge and its application will be positively estimated.
The final evaluation (examination) depends on assigned points (0-100 points), 30 points is maximum points which can be assigned during seminars. Final examination is in written form (estimated by 0-70 points ).
The final evaluation (examination) depends on assigned points (0-100 points), 30 points is maximum points which can be assigned during seminars. Final examination is in written form (estimated by 0-70 points ).
Course curriculum
1. Matrices, basic operations.
2. Systems of linear algebraic equations, Gauss elimination method.
3. Basics of vector algebra, dot, cross, and scalar triple product.
4. Functions of one variable. Limit, continuity and derivative of a function.
5. Some elementary functions, their properties, approximation by Taylor polynomial.
6. Antiderivative and indefinite integral, Newton integral.
7. Riemann’s integral and its calculation, some applications in geometry and physics.
8. Numeric calculation of a definite integral.
9. Two- and more-functions, partial derivative and its use.
10. Probability, random variables.
11. Numerical characteritics of a random variable.
12. Basic distributions.
13. Random sampling, statistics
2. Systems of linear algebraic equations, Gauss elimination method.
3. Basics of vector algebra, dot, cross, and scalar triple product.
4. Functions of one variable. Limit, continuity and derivative of a function.
5. Some elementary functions, their properties, approximation by Taylor polynomial.
6. Antiderivative and indefinite integral, Newton integral.
7. Riemann’s integral and its calculation, some applications in geometry and physics.
8. Numeric calculation of a definite integral.
9. Two- and more-functions, partial derivative and its use.
10. Probability, random variables.
11. Numerical characteritics of a random variable.
12. Basic distributions.
13. Random sampling, statistics
Work placements
Not applicable.
Aims
The students should learn about the basics of linear algebra, solutions to systems of linear algebraic equations, calculus, theory of probability and statistics.
Specification of controlled education, way of implementation and compensation for absences
Extent and forms are specified by guarantor’s regulation updated for every academic year.
Recommended optional programme components
Not applicable.
Prerequisites and corequisites
Not applicable.
Basic literature
Daněček, J., Dlouhý, O., Přibyl, O.: Neurčitý integrál. FAST - studijní opora v intranetu, 2007. (CS)
Daněček, J., Dlouhý, O., Přibyl, O.: Určitý integrál. FAST - studijní opora v intranetu, 2007. (CS)
Dlouhý, O., Tryhuk, V.: Reálná funkce dvou a více proměnných. FAST - studijní opora v intranetu, 2005. (CS)
Dlouhý, O., Tryhuk, V.: Reálná funkce jedné reálné proměnné. FAST - studijní opora v intranetu, 2008. (CS)
Larson R., Hostetler R.P., Edwards B.H.: Calculus (with analytic geometry). Brooks Cole, 2005. (EN)
Novotný, J.: Základy lineární algebry. FAST - studijní opora v intranetu, 2005. (CS)
Tryhuk, V., Dlouhý, O.: Vektorový počet a jeho aplikace. FAST - studijní opora v intranetu, 2007. (CS)
Daněček, J., Dlouhý, O., Přibyl, O.: Určitý integrál. FAST - studijní opora v intranetu, 2007. (CS)
Dlouhý, O., Tryhuk, V.: Reálná funkce dvou a více proměnných. FAST - studijní opora v intranetu, 2005. (CS)
Dlouhý, O., Tryhuk, V.: Reálná funkce jedné reálné proměnné. FAST - studijní opora v intranetu, 2008. (CS)
Larson R., Hostetler R.P., Edwards B.H.: Calculus (with analytic geometry). Brooks Cole, 2005. (EN)
Novotný, J.: Základy lineární algebry. FAST - studijní opora v intranetu, 2005. (CS)
Tryhuk, V., Dlouhý, O.: Vektorový počet a jeho aplikace. FAST - studijní opora v intranetu, 2007. (CS)
Recommended reading
Daněček: Sbírka příkladů z matematiky I. CERM Brno, 2006. (CS)
Koutková, H., Dlouhý, O.: Sbírka příkladů z pravděpodobnosti a matematické statistiky. CERM Brno, 2008. (CS)
Koutková, H., Moll, I.: Základy pravděpodobnosti. CERM, 2008. (CS)
Koutková, H., Dlouhý, O.: Sbírka příkladů z pravděpodobnosti a matematické statistiky. CERM Brno, 2008. (CS)
Koutková, H., Moll, I.: Základy pravděpodobnosti. CERM, 2008. (CS)
Classification of course in study plans
Type of course unit
Lecture
26 hod., optionally
Teacher / Lecturer
Syllabus
1. Matrices, basic operations.
2. Systems of linear algebraic equations, Gauss elimination method.
3. Basics of vector algebra, dot, cross, and scalar triple product.
4. Functions of one variable. Limit, continuity and derivative of a function.
5. Some elementary functions, their properties, approximation by Taylor polynomial.
6. Antiderivative and indefinite integral, Newton integral.
7. Riemann’s integral and its calculation, some applications in geometry and physics.
8. Numeric calculation of a definite integral.
9. Two- and more-functions, partial derivative and its use.
10. Probability, random variables.
11. Numerical characteritics of a random variable.
12. Basic distributions.
13. Random sampling, statistics
2. Systems of linear algebraic equations, Gauss elimination method.
3. Basics of vector algebra, dot, cross, and scalar triple product.
4. Functions of one variable. Limit, continuity and derivative of a function.
5. Some elementary functions, their properties, approximation by Taylor polynomial.
6. Antiderivative and indefinite integral, Newton integral.
7. Riemann’s integral and its calculation, some applications in geometry and physics.
8. Numeric calculation of a definite integral.
9. Two- and more-functions, partial derivative and its use.
10. Probability, random variables.
11. Numerical characteritics of a random variable.
12. Basic distributions.
13. Random sampling, statistics
Exercise
13 hod., compulsory
Teacher / Lecturer
Syllabus
1. Matrices, basic operations.
2. Systems of linear algebraic equations, Gauss elimination method.
3. Basics of vector algebra, dot, cross, and scalar triple product.
4. Functions of one variable. Limit, continuity and derivative of a function.
5. Some elementary functions, their properties, approximation by Taylor polynomial.
6. Antiderivative and indefinite integral, Newton integral.
7. Riemann’s integral and its calculation, some applications in geometry and physics.
8. Numeric calculation of a definite integral.
9. Two- and more-functions, partial derivative and its use.
10. Probability, random variables.
11. Numerical characteritics of a random variable.
12. Basic distributions.
13. Random sampling, statistics
2. Systems of linear algebraic equations, Gauss elimination method.
3. Basics of vector algebra, dot, cross, and scalar triple product.
4. Functions of one variable. Limit, continuity and derivative of a function.
5. Some elementary functions, their properties, approximation by Taylor polynomial.
6. Antiderivative and indefinite integral, Newton integral.
7. Riemann’s integral and its calculation, some applications in geometry and physics.
8. Numeric calculation of a definite integral.
9. Two- and more-functions, partial derivative and its use.
10. Probability, random variables.
11. Numerical characteritics of a random variable.
12. Basic distributions.
13. Random sampling, statistics