Academic year/semester: 2025/26/2

ECTS Credits: 4

Available for: All OU students

Lecture hours: 1
Seminarium:0
Practice: 2
Laboratory: 0
Consultation: 0

Prerequisites: Mathematics I.

Course Leader: Dr. habil. Katalin Gambár

Faculty: Kandó Kálmán Faculty of Electrical Engineering, 1084 Budapest, Tavaszmező utca 17.

Course Description:
Algebraic basics: Introduction, properties and illustrating complex numbers. Properties, coordinate-wise definition and application of spatial (3D) vectors. Introduction, properties and application of matrices, operations on matrices, quadratic matrices. Concept, properties and application of determinants. Computing determinants. (30 hours)

Basics of probability theory: concept and properties of probability. Discrete and continuous probability variables. Notable distributions. (12 hours)

Competences:
Tasks and problems related to the field are solved, with which we contribute to the development of the student\'s conceptualization and problem-solving abilities. Development of practical problem-solving skills of basic mathematical knowledge required for technical sciences. The student is able to make independent decisions in the processes appearing in his field of expertise and carry them out responsibly.

Topics:
1. Trigonometric functions, trigonometric identities, angle sum, and difference identities. Definition of complex numbers, algebraic form. Conjugate and the absolute value of a complex number.
2. Operations on the algebraic form of the complex number: addition, subtraction, multiplication by a constant, multiplication, and division.
3. Illustration of complex numbers, the Gaussian complex plane. The trigonometric and exponential forms of complex numbers. Euler’s theorem. Transitions between different forms.
4. Operations on trigonometric and exponential forms of the complex number: multiplication, division, integer power, and integer root.
5. Concept of spatial (3D) vector. Coordinates of a vector. Operations on vectors: addition, subtraction, multiplication by a real number.
6. Test 1
7. Definition of the dot (scalar), cross (vector), and mixed products of vectors. Operations on coordinates of vectors. The connection between orthogonality and dot product. Application of dot and cross products. Systems of equations of a straight line, equation of a plane, equation of a sphere.
8. Concept of the matrix, special matrices, operations (addition, multiplying by a scalar, transposing matrices, multiplication of matrices)
9. Concept of determinant, computing second-order and third-order determinants. Application of determinants, solving systems of linear equations. Cramer’s rule.
10. Concept of probability and Kolgomorov’s axioms. Important properties of probability. Classical field of probability.
11. Conditional probability, independent events. Concept of probability variable. Expected value and standard deviation of discrete probability variable. Notable discrete probability distributions.
12. Continuous probability distributions. Density function, the cumulative distribution function of the continuous probability distribution. Notable continuous distributions. Expected value and standard deviation.
13. Test 2.
14. Make-up test

Assessment: The condition for obtaining a signature is successful writing of the mid-year papers) and successful submission of the homework(s).

Exam Types:

Written Exam

Compulsory bibliography: 1. Kovács, J., Schmidt, E., Szabó, L.A.: Mathematics, ÓE KVK 2103, Budapest, 2013 2. 2. Kovács, J., Schmidt, E.: Mathematics. Problem-Solving, E-learning 3. RA Adams

Recommended bibliography: 1. Ch Essex: Calculus: A Complete Course, Publisher: Toronto, Pearson Canada 2009, 973 pages, ISBN 9780321549280 4. 2. Elliott Mendelson: 3000 Solved Problems in Calculus, McGraw-Hill, New-York 2009, 455 pages, ISBN 9780071635349

Additional bibliography: -

Additional Information: -