Course Details
Mathematics
Academic Year 2024/25
BAA014 course is part of 1 study plan
BPC-APS Winter Semester 1st year
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.
Credits
3 credits
Language of instruction
Czech
Semester
winter
Course Guarantor
Institute
Forms and criteria of assessment
course-unit credit and examination
Entry Knowledge
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.
Aims
The students should learn about the basics of linear algebra, solutions to systems of linear algebraic equations, calculus, theory of probability and statistics.
Students will have a short overview on methods of higher mathematics(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).
Students will have a short overview on methods of higher mathematics(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).
Basic Literature
LARSON, Ron, HOSTETLER, Rober, EDWARDS Bruce: Calculus With Analytic Geometry, 8th edition, Brooks Cole, 2005. ISBN: 978-0618502981 (en)
NOVOTNÝ, Jiří: Matematika I, Modul 1, Základy lineární algebry, Akademické nakladatelství CERM, s.r.o., Brno 2004. ISBN: 978-80-7204-748-2 (cs)
TRYHUK, Václav, DLOUHÝ, Oldřich: Matematika I, Modul GA01–M01, Vybrané části a aplikace vektorového počtu, Akademické nakladatelství CERM, s.r.o., Brno 2004. ISBN: 978-80-7204-526-6 (cs)
DLOUHÝ, Oldřich, TRYHUK, Václav: Matematika I, Diferenciální počet funkce jedné reálné proměnné}, Akademické nakladatelství CERM, s.r.o., Brno 2008. ISBN: 978-80-7204-982-0 (cs)
DANĚČEK, Josef, DLOUHÝ, Oldřich, PŘIBYL, Oto: Matematika I, Modul 7, Neurčitý integrál, Fakulta stavební VUT, Akademické nakladatelství CERM, Brno 2007. ISBN: 978-80-7204-524-2 (cs)
DANĚČEK, Josef, DLOUHÝ, Oldřich, PŘIBYL, Oto: Matematika I, Modul 8, Určitý integrál, Fakulta stavební VUT, Akademické nakladatelství CERM, Brno 2007. ISBN: 978-80-7204-525-9 (cs)
TRYHUK, Václav, DLOUHÝ, Oldřich: Matematika I, Diferenciální počet funkcí více reálných proměnných, Akademické nakladatelství CERM, s.r.o., Brno 2004. ISBN: 80-214-2776-0 (cs)
KOUTKOVÁ, Helena, Mill, Ivo: Základy pravděpodobnosti, Akademické nakladatelství CERM, s.r.o., Brno 2008. ISBN: 978-80-7204-574-7 (cs)
NOVOTNÝ, Jiří: Matematika I, Modul 1, Základy lineární algebry, Akademické nakladatelství CERM, s.r.o., Brno 2004. ISBN: 978-80-7204-748-2 (cs)
TRYHUK, Václav, DLOUHÝ, Oldřich: Matematika I, Modul GA01–M01, Vybrané části a aplikace vektorového počtu, Akademické nakladatelství CERM, s.r.o., Brno 2004. ISBN: 978-80-7204-526-6 (cs)
DLOUHÝ, Oldřich, TRYHUK, Václav: Matematika I, Diferenciální počet funkce jedné reálné proměnné}, Akademické nakladatelství CERM, s.r.o., Brno 2008. ISBN: 978-80-7204-982-0 (cs)
DANĚČEK, Josef, DLOUHÝ, Oldřich, PŘIBYL, Oto: Matematika I, Modul 7, Neurčitý integrál, Fakulta stavební VUT, Akademické nakladatelství CERM, Brno 2007. ISBN: 978-80-7204-524-2 (cs)
DANĚČEK, Josef, DLOUHÝ, Oldřich, PŘIBYL, Oto: Matematika I, Modul 8, Určitý integrál, Fakulta stavební VUT, Akademické nakladatelství CERM, Brno 2007. ISBN: 978-80-7204-525-9 (cs)
TRYHUK, Václav, DLOUHÝ, Oldřich: Matematika I, Diferenciální počet funkcí více reálných proměnných, Akademické nakladatelství CERM, s.r.o., Brno 2004. ISBN: 80-214-2776-0 (cs)
KOUTKOVÁ, Helena, Mill, Ivo: Základy pravděpodobnosti, Akademické nakladatelství CERM, s.r.o., Brno 2008. ISBN: 978-80-7204-574-7 (cs)
Offered to foreign students
Not to offer
Course on BUT site
Lecture
13 weeks, 2 hours/week, elective
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
Exercise
13 weeks, 1 hours/week, compulsory
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