Mathematics 2
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Course informations
| Study program level |
Undergraduate |
| Study program |
Electrical Engineering |
| Study program direction |
Telecommunications and informatics |
| Course year |
1. |
| Course semester |
II |
| 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. Students are introduce to differential equations and their applications, and the basic terms of combinatorial equations and graph theory.
Course outcomes
- To solve a differential equation of the first and second order.
- To apply the methods of numerical solution of differential equations.
- To differentiate the criteria and choose which convergence order criteria to use with positive members in solving tasks.
- To differentiate the basic principles of enumeration.
- To differentiate and apply permutations and combinations of sets and multisets in problem tasks.
- To analyze, model and to solve the problems of recursive relations.
- To define and connect basic terms and problems from graph theory.
Course content
Techniques that lead to the use of differential equations. The concept and basic properties of differential equations. Differential equation solution. Theorem of the existence of a solution. The method of separating variables. Homogeneous differential equation. Linear differential equation of the first order. Linear differential equations of the second order with constant coefficients. Application of differential equations to professional problems.
Numerical integration. Numerical solution of differential equations. Concept and convergence of a row. Convergence criteria with positive members. Alternating rows and Leibniz Criteria. Functions rows. Convergence. Potentials. Convergence Interval. Combinatorics. Final sets. Product sets. Counting Techniques. Permutations. Combinations. Variations. Recursive relationships. Fibonacci's sequence. Sterling’s number. Linear recursive formulas.
Graph definition and basic graph properties. Top level, multiple bridges, pseudo graph. Subgraph. Special graphs. Regular graphs. Euler's proposition. Euler's tour as closed Euler's path and Euler's graph. Related graphs. Weight charts and applications. The problem of a travelling salesperson. Directed graph (digraph). Tournament: Definition and Properties. Networks and critical paths.
