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FAST-BA001Acad. year: 2022/2023
Real function of one real variable. Sequences, limit of a function, continuous functions. Derivative of a function, its geometric and physical applications, basic theorems on derivatives, higher-order derivatives, differential of a function, Taylor expansion of a function, sketching the graph of a function. Linear algebra (basics of the matrix calculus, rank of a matrix, Gauss elimination method, inverse to a matrix, determinants and their applications). Eigenvalues and eigenvectors of a matrix. Basics of vectors, vector spaces. Linear spaces. Analytic geometry (dot, cross and mixed product of vectors, affine and metric problems for linear bodies in 3D).The basic problems in numerical mathematics (interpolation, solving nonlinear equation and systems of linear equations, numerical differentiation).
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Specification of controlled education, way of implementation and compensation for absences
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branch VS , 1 year of study, winter semester, compulsory
branch MI , 1 year of study, winter semester, compulsory
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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.