Mathematics 1
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Course Description
COURSE CONTENT
- Theory of matrix. Matrix inversion. Matrix equations. Matrix notation of a linear system. Matrix rank. Kronecker-Capelli's theorem.
- The term of eigenvalues and eigenvectors. Determination of eigenvalues and eigenvector. Applications.
- The concept of a sequence. Monotony of sequence and sequence constraint. Convergence of sequence. Number e.
- Polynomials, rational functions, irrational functions. Exponential and logarithmic function. Trigonometric and arcus functions. Graphs of elementary functions.
- Second order curves. Polar coordinates. Examples of curves which are given implicit or parametric.
- The limit value of functions and their continuity of. Indefinite forms.
- Concept of derivation. The concept of differential. Derivability and differentiability. Derivations of elementary functions. Properties of derivation. Higher order derivations and higher order differentials.
- The terms of local and global extremes. Fermat’s, Rolle’s, Lagrange’s, Cauchy’s and Taylor's theorem. Taylor polynomial.
- 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