Course Details

Mathematics 1 (G)

Academic Year 2025/26

BAA008 course is part of 1 study plan

​ BPC-GK Winter Semester 1st year

Course Guarantor

doc. Mgr. Irena Hinterleitner, Ph.D.

Institute

Institute of Mathematics and Descriptive Geometry

Language of instruction

Czech

Credits

8 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/289942

Lecture

13 weeks, 3 hours/week, elective

Syllabus

  • 1. Matrices, systems of linear algebraic equations, Gaussian elimination method.
  • 2. Inverse matrix, determinants.
  • 3. Geometrical vectors in three dimensional Euclidean space, operations with vectors.
  • 4. Applications of vector calculus in spherical trigonometry.
  • 5. Vector space, basis, dimension, coordinates of a vector.
  • 6. Eigenvalues and eigenvectors of a matrix.
  • 7. Application of vector calculus in analytic geometry.
  • 8. Real function of one real variable, explicit and parametric expression of a function. Basic properties of functions. Composite fuction and inverse function. Elementary functions (including inverse trigonometric functions and hyperbolic functions).
  • 9. Polynomials and rational functions.
  • 10. Sequences and their limits, limit and continuity of a function.
  • 11. Derivative of a function, its geometrical and physical meaning, derivation rules. Derivative of a composite function and of an inverse function. Derivatives of elementary functions.
  • 12. Derivatives of higher order, geometrical meaning of first order and second order derivatives for sketching the graph of a function, l Hospital's rule, asymptotes.
  • 13. Properties of functions continuous on an interval. Basic theorems of differential calculus (the Rolle and Lagrange theorems). Differential of a function. Taylor's theorem. Derivative of a function given in a parametric form.

Exercise

13 weeks, 3 hours/week, compulsory

Syllabus

  • 1. Geometrical vectors in E3, operations with vectors.
  • 2. Applications of vector calculus in spherical trigonometry.
  • 3. Vector space, base, dimension, coordinates of a vector.
  • 4. Application of vector calculus in analytic geometry.
  • 5. Matrices, systems of linear algebraic equations, Gaussian elimination method.
  • 6. Inverse matrix, determinants.
  • 7. Eigenvalues and eigenvectors of a matrix.
  • 8. Real function of a one real variable, explicit and parametric expression of a function. Basic properties of functions. Composite and inverse functions. Elementary functions.
  • 9. Polynomials and rational functions.
  • 10. Sequences and theirs limits, limit and continuity of a function.
  • 11. Derivative of a function, its geometrical and physical meaning, derivation rules. Derivative of a composite function and of an inverse function. Derivatives of elementary functions.
  • 12. Derivatives of higher order, geometrical meaning of first and second order derivatives for investigation of behavior of a function, l`Hospitals rule, asymptotes.
  • 13. Properties of function, continuous on an interval. Basic theorems of differential calculus. Differential of a function. Taylor’s theorem. Derivative of a function given in a parametric form. Primitive function, Newtons integral, its properties and computation. Riemann’s integral. Integration methods for indefinite and definite integrals.