Course Details
Mathematics 1
Academic Year 2025/26
BAA001 course is part of 4 study plans
BPA-SI Winter Semester 1st year
BPC-SI / VS Winter Semester 1st year
BPC-MI Winter Semester 1st year
BKC-SI Winter Semester 1st year
Course Guarantor
Institute
Language of instruction
Czech, English
Credits
7 credits
Semester
winter
Forms and criteria of assessment
course-unit credit and examination
Offered to foreign students
To offer to students of all faculties
Course on BUT site
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, 3 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). Numerical solutions of equations by bisection and regula falsi method.
- 3. Polynomial, sign of a polynomial. Lagrange and Newton interpolation 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. Numerical differentiation.
- 7. Test I. Higher-order derivatives. Taylor theorem. L` Hospital's rule. Approximation of solutions of one equation in one variable by the Newton method.
- 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. Numerical solutions of systems of linear equations.
- 10. Calculating determinants using Laplace expansion and rules for calculating with determinants. Calculating the inverse to a matrix using Jordan's method. Solutions of systems of linear equations by iteration.
- 11. Test II. Matrix equations. The discrete least square method. Eigenvalues and eigenvectors of a matrix.
- 12. Using dot and cross products in solving problems in 3D analytic geometry.
- 13. Mixed product. Seminar evaluation.