Course Details

Mathematics 1

Academic Year 2025/26

BAA012 course is part of 1 study plan

​ BPC-EVB Winter Semester 1st year

Course Guarantor

doc. Mgr. Irena Hinterleitner, Ph.D.

Institute

Institute of Mathematics and Descriptive Geometry

Language of instruction

Czech

Credits

5 credits

Semester

winter

Forms and criteria of assessment

course-unit credit and examination

Offered to foreign students

Not to offer

Course on BUT site

https://www.vut.cz/en/students/courses/detail/289981

Lecture

13 weeks, 2 hours/week, elective

Syllabus

  • 1. Real function of one real variable, explicit and parametric definition of a function. Composite function and inverse to a function.
  • 2. Some elementary functions, inverse trigonometric functions. Hyperbolic functions. Polynomial and the basic properties of its roots, decomposition of a polynomial in the field of real numbers.
  • 3. Rational functions. Sequence and its limit.
  • 4. Limit of a function, continuous functions, basic theorems. Derivative of a function, its geometric and physical applications, differentiating rules.
  • 5. Derivatives of composite and inverse functions. Differential of a function. Rolle and Lagrange theorem.
  • 6. Higher-order derivatives, higher-order differentials. Taylor theorem.
  • 7. L`Hospital's rule. Asymptotes of the graph of a function. Sketching the graph of a function.
  • 8. Basics of matrix calculus, elementary transformations of a matrix, rank of a matrix. Solutions to systems of linear algebraic equations by Gauss elimination method.
  • 9. Second-order determinants. Higher-order determinants calculated by Laplace expansion. Rules for calculating with determinants. Cramer's rule of solving a system of linear algebraic equations.
  • 10. Inverse to a matrix. Jordan's method of calculation. Matrix equations. Real linear space, base and dimension of a linear space. Linear spaces of arithmetic and geometric vectors.
  • 11. Eigenvalues and eigenvectors of a matrix. Coordinates of a vector. Dot and cross product of vectors, calculating with coordinates.
  • 12. Mixed product of vectors. Plane and straight line in 3D, positional problems.
  • 13. Metric problems. Surfaces.

Exercise

13 weeks, 2 hours/week, compulsory

Syllabus

  • 1. Absolute value of a function. Quadratic equations in complex field. Conics. Graphs of selected elementary functions. Basic properties of functions.
  • 2. Composite function and inverse to a function (inverse trigonometric functions, logarithmic functions).
  • 3. Polynomial, sign of a polynomial.
  • 4. Rational function, sign of a rational function, decomposition into partial fractions.
  • 5. Limit of a function. Derivative of a function (basic calculation) and its geometric applications, basic formulas and rules for differentiating.
  • 6. Derivative of an inverse function. Basic differentiation formulas and rules.
  • 7. Test I. Higher-order derivatives. Taylor theorem. L` Hospital's rule.
  • 8. Asymptotes of the graph of a function. Sketching the graph of a function.
  • 9. Basic operations with matrices. Elementary transformations of a matrix, rank of a matrix, solutions to systems of linear algebraic equations by Gauss elimination method.
  • 10. Calculating determinants using Laplace expansion and rules for calculating with determinants. Calculating the inverse to a matrix using Jordan's method.
  • 11. Test II. Matrix equations. Eigenvalues and eigenvectors of a matrix.
  • 12. Using dot and cross products in solving problems in 3D analytic geometry.
  • 13. Mixed product. Seminar evaluation.