Mathematics 1

Course Description

COURSE CONTENT

1. Theory of matrix. Matrix inversion. Matrix equations. Matrix notation of a linear system. Matrix rank. Kronecker-Capelli's theorem.
2. The term of eigenvalues and eigenvectors. Determination of eigenvalues and eigenvector. Applications.
3. The concept of a sequence. Monotony of sequence and sequence constraint. Convergence of sequence. Number e.
4. Polynomials, rational functions, irrational functions. Exponential and logarithmic function. Trigonometric and arcus functions. Graphs of elementary functions.
5. Second order curves. Polar coordinates. Examples of curves which are given implicit or parametric.
6. The limit value of functions and their continuity of. Indefinite forms.
7. Concept of derivation. The concept of differential. Derivability and differentiability. Derivations of elementary functions. Properties of derivation. Higher order derivations and higher order differentials.
8. The terms of local and global extremes. Fermat’s, Rolle’s, Lagrange’s, Cauchy’s and Taylor's theorem. Taylor polynomial.
9. Necessary and sufficient conditions for local extremes. Criteria for monotony, concavity and convexity. Inflection points. L'Hospital's rule. Asymptote of curve. Qualitative graph of function. Linear and square approximation.

LEARNING OUTCOMES

• solve the matrix equation, and the system of linear equations using the Gauss algorithm
• determine eigenvalues and eigenvectors for square matrices of order 2
• recognize and draft graphs of basic functions, determine the domain of complex functions, and identify the basic curves which are given implicit or parametric
• calculate the limit values of the sequences and functions, and recognize the sequences and functions connected with the number e
• calculate the derivation of functions, and approximate the function values
• apply a differential calculus for various problems connected with the study of functions and their graphs