Mathematics
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Course informations
| Study program level |
Undergraduate |
| Study program |
Computer Science |
| Study program direction |
Software Engineering |
| Course year |
1. |
| Course semester |
I |
| Course status |
Core |
| ECTS |
6 |
| Lectures (h) |
30 |
| Excercises (h) |
30 |
| Seminars (h) |
- |
Course objectives
Acquiring knowledge and skills required for independent work and successful continuation of education. To clarify the basic tenants of the course and to encourage the application of certain units on the relevant areas. To develop logical thinking and deducing, to analyze a real problem and to create an appropriate mathematical model and to critically review the obtained results. Initial stages of algorithmic thinking. To emphasize the importance of fields in programming. Students become acquainted with the basic terms of differential and integral accounts and their applications.
Course outcomes
- To cite the basic operations of mathematical logic. To apply those basic operations on sets and to present those sets with Venn diagrams.
- To define the sets of natural, whole, rational, real and complex numbers. To apply the basic operations on the field of real and complex numbers. To apply De Moivre’s formulas. To draw the position of a complex number on the Gaussian plane.
- To calculate the sum of position vectors, and their scalar, vectorial, and mixed products of multiplication, and to interpret the obtained results.
- To calculate the sum, difference and product of real matrices, and the inverse of regular matrices. To solve the matrix equation of the form A∙X=B. To solve the system of linear equations using one of the methods.
- To define functions, compositions of functions, and inverse functions. To classify functions (even/odd). To classify elementary functions.
- To calculate the marginal values of sequences and real functions of one real variable.
- To define the rules of elementary deriving and to know to apply them on the derivations of complex functions, implicitly assigned functions.
- To develop a real function in a Taylor series around an arbitrary point from its natural field of definition.
- To define the basic properties of an indefinite integral.
- To use the method of substitution and partial integration while solving tasks. To define a definite integral and to apply the Newton-Leibnitz formula. To apply the definite integer while calculating the surface under a curve.
Course content
Syllogism, set, basics of mathematical logic. Number sets.Vectors, vector operations, vector application in analytical geometry of space. Matrix, determinant, equation systems. System of Linear Equations (Cramer Rule, Gauss-Jordan Elimination Procedure). Functions, elementary functions. Sequences, limes sequences, limes functions, continuity of functions. Derivation of functions, derivation of complex functions, derivation application, graph function. Function rows, power rows, Taylor and MacLaur's rows. An indefinite integral. Tabular integrals, solving the unspecified integral by the substitution method, the partial integration method and the indefinite integral rational functions. Integral application.
