Course Details

Mathematics 1

Academic Year 2026/27

BAA021 course is part of 1 study plan

​ BPC-SIS / SI Winter Semester 1st year

Credits

6 credits

Language of instruction

Czech

Semester

winter

Course Guarantor

doc. Mgr. Irena Hinterleitner, Ph.D.

Institute

Institute of Mathematics and Descriptive Geometry

Forms and criteria of assessment

course-unit credit and examination

Basic Literature

BUDÍNSKÝ, B. - CHARVÁT, J.: Matematika I. Praha, SNTL, 1987. (cs)
STEIN, S. K: Calculus and analytic geometry. New York, 1989. (en)
LARSON, R.- HOSTETLER, R.P.- EDWARDS, B.H.: Calculus (with Analytic Geometry). Brooks Cole, 2005. (en)

Recommended Reading

DANĚČEK, J. a kolektiv: Sbírka příkladů z matematiky I. CERM, 2003. (cs)
RYHUK, V. - DLOUHÝ, O.: Modul GA01_M01 studijních opor předmětu GA01. FAST VUT, Brno, 2004. [https://intranet.fce.vutbr.cz/pedagog/predmety/opory.asp] (cs)
NOVOTNÝ, J.: Základy lineární algebry. CERM, 2004. (cs)
DLOUHÝ, O., TRYHUK, V.: Diferenciální počet I. CERM, 2009. (cs)
DANĚČEK, J., DLOUHÝ, O., PŘIBYL, O.: Matematika I. Modul 7 Neurčitý integrál. CERM, 2007. (cs)
SLOVAK, J., PANÁK, M., BULANT, M.: Matematika drsně a svižně. MU Brno, 2013. (cs)
BHUNIA, S. C., PAL, S.: Engineering Mathematics. Oxford University Press, 2015. (en)

Offered to foreign students

Not to offer

Course on BUT site

https://www.vut.cz/en/students/courses/detail/298850

Lecture

13 weeks, 2 hours/week, elective

Syllabus

  1. Basics of matrix calculus, elementary transformations of a matrix, rank of a matrix.
  2. Determinants (cross rule, Sarrus' rule, Laplace expansion), rules for calculation with determinants.
  3. Vector calculus (operations with vectors, dot, cross, and mixed products of vectors). Real linear space, linear combination and independent bases and dimension of a linear space.
  4. Solutions to systems of linear algebraic equations by Gauss elimination method, Frobenius theorem.
  5. Inverse to a matrix, matrix equations. Eigenvalues and eigenvectors of a matrix.
  6. Real function of one real variable and its basic properties, explicit and parametric definition of a function. Composite function and inverse to a function. Some elementary functions (inverse trigonometric functions). 
  7. Polynomial and the basic properties of its roots, decomposition of a polynomial in the field of real and complex numbers. Rational functions and their decomposition into partial fractions.
  8. Limit of a function, continuous functions, basic theorems.
  9.  Derivative of a function, its geometric and physical applications, rules of differentiation. 
  10.  Differential of a function. Higher-order derivatives, higher-order differentials. Taylor polynomial and Taylor's theorem.
  11. L'Hospital's rule, asymptotes of the graph of a function. Sketching the graph of a function.
  12. Anti-derivative, indefinite integral and its properties. Integration by parts and substitution methods in calculating integrals.
  13. Integration of selected functions (rational, trigonometric, irrational).

Exercise

13 weeks, 3 hours/week, compulsory

Syllabus

  1. High school repetition.
  2. Basic operations with matrices. Elementary transformations of a matrix, rank of a matrix.
  3. Determinants (cross rule, Sarrus' rule, Laplace expansion), rules for calculation with determinants.
  4. Vector calculus (operations with vectors, dot, cross, and mixed products of vectors).
  5. Solutions to systems of linear algebraic equations by Gauss elimination method.
  6. Inverse to a matrix, matrix equations. Eigenvalues and eigenvectors of a matrix.
  7. Test 1. Some elementary functions (inverse trigonometric functions). Composite function and inverse to a function.
  8. Polynomial and the basic properties of its roots, decomposition of a polynomial in the field of real and complex numbers.
  9. Rational functions and their decomposition into partial fractions. Limit of a function, continuous functions. Derivative of a function, its geometric and physical applications, rules of differentiation.
  10. Differential of a function. Higher-order derivatives, higher-order differentials. Taylor polynomial.
  11. Test 2. L'Hospital's rule, asymptotes of the graph of a function. Sketching the graph of a function.
  12. Anti-derivative, indefinite integral and their properties. Integration by parts and substitution methods in calculating integrals.
  13. Integration of selected functions (rational, trigonometric, irrational).

Self-study

39 weeks, 1 hours/week

Individual preparation for an ending of the course

52 weeks, 1 hours/week