Course Details

# Mathematics 1

BAA001 course is part of 4 study plans

BPC-SI / VS Winter Semester 1st year

BPC-MI Winter Semester 1st year

BKC-SI Winter Semester 1st year

BPA-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.