Academic year/semester: 2025/26/1

ECTS Credits: 4

Available for: Only for the faculty’s students

Lecture hours: 2
Seminarium:2
Practice: -
Laboratory: -
Consultation: -

Prerequisites: Calculus I.

Course Leader: Dr. István VAJDA

Faculty: John von Neumann Faculty of Informatics, 1034 Budapest, Bécsi út 96/b

Course Description:
Learning the basic concepts and techniques of univariate and multivariate analysis based on the international trends and requirements of IT education. Creating a clear conceptual system, developing problem-solving skills, providing the student with mathematical tools for further studies.
Ordinary differential equations. Laplace-transform. Numeric series. Function series: Taylor and Fourier series. Multivariate functions.

Competences:
Learning the basic concepts and techniques of univariate and multivariate analysis based on the international trends and requirements of IT education. Creating a clear conceptual system, developing problem-solving skills, providing the student with mathematical tools for further studies.

Topics:
Lecture schedule
Education week
Topic
1.
The concept and applications of differential equations. Classification. Separable
differential equations.
2.
First order linear differential equations.
3.
Second order linear differential equations. Resonance.
4.
The Laplace-transform. (Concept and properties.) The Laplace-transform of
some well-known types of functions. Inverse Laplace-transform.
5.
Applications of Laplace-transform. Solving differential equations with Laplace-transform.
6.
Series of functions. Region of convergence. Pointwise and uniform convergence.
Operations with series of functions.
7.
Taylor-series and their applications. The Taylor-formula.
8.
Fourier-series.
9.
Multivariate functions. (Boundedness, extrema, continuity, limits.)
10.
Differential calculus of multivariate functions. Partial and total derivatives. Tangent
plane and normal line. Estimation of errors of calculations.
11.
Extrema of bivariate functions. Saddle points.
12.
Integration of bivariate functions on rectangles and normal regions.
13.
Integration of multivariate functions with substitution. Applications of integrals.
14.
Practice, preparing for the exam.

Assessment: Mid-term requirements Conditions for obtaining a mid-term grade/signature To get a signature students absence can be no more than 30% of the lessons, and they need to obtain at least 50% of the points accessible on the midterm test. Assessment schedule Education week Topic 6. Differential equations, Laplace-transform. 13. Series of functions. Multivariate functions. 14. Retake Method used to calculate the mid-term grade (to be filled out only for subjects with mid-term grades) Type of the replacement Type of the replacement of written test/mid-term grade/signature Students may retake only one of the midterm tests, namely the one with less points, or they can write a missing one on the 14th week. In the exam period there is a signature retake exam as well, however it can be written by only those, who have written both of their tests till the end of the last education week. On the signature retake exam there will be questions from the whole material of the semester. Type of the exam (to be filled out only for subjects with exams) It is a written exam, which can be completed by a short oral part if it is necessary. Calculation of the exam mark (to be filled only for subjects with exams) 30% of the accessible points comes from the midterm tests, another 30% from the theoretic questions, 40% from the calculation problems of the exam. Students need to achieve at least 50% from each to get a passing grade. ​​Final grade calculation methods:​ 0-49% Fail (1) 50-61% Pass (2) 62-73% Satisfactory (3) 74-85% Good (4) 86-100% Excellent

Exam Types:

Written Exam

Compulsory bibliography: J. Hass, M. D. Weir, G.B. Thomas: University Calculus Early Transcendentals, Addison-Wesley, 2007.

Recommended bibliography: -

Additional bibliography: Course materials in the Moodle system. (https://elearning.uni-obuda.hu/)

Additional Information: -