Academic year/semester: 2024/25/2

ECTS Credits: 4

Available for: All OU students

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

Prerequisites: -

Course Leader: Dr. Vajda István

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

Course Description:
Goal: The aim of the course is to develop students’ conceptualization and problem-solving abilities through the acquisition of the basic concepts of univariate mathematical analysis; as well as an introduction to the use of the Matlab program.
Course description: Convergence of series, continuity, and limit of functions. Differential calculus of univariate functions, derivation rules, applications, function analysis. Indefinite and
definite integral. Symbolic and numerical integration techniques, applications.

Competences:
-

Topics:
1. The concept of sequence of numbers. Monotonicity boundedness, convergence.
2. Limits and operations. Some often used types of sequences. Cauchy’s criteria.
3. Series of numbers and their convergence. Geometric and telescoping series.
4. Series with only positive terms. Alternating series.
5. Differentiability of functions, derivatives. Rules of differentiation.
6. Higher order derivatives. Derivatives of elementary functions.
7. Tangent of a curve. Osculation of curves, angle of curves. L’Hôpital’s rule. Rolle’s
theorem, mean value theorem.
8. Examining monotonicity, extrema, concavity, ... with derivatives. Analysing
functions.
9. The Riemann integral. Properties of integrals. Integral function.
10. Antiderivatives and indefinite integrals. Technics of integration.
11. Integration by parts, integration with substitution.
12. Integration of elementary functions. Numeric methods of integration.
13. Applications of integrals.
14. Improper integrals.

Assessment: Signature: It can be achieved 50-50 points at most on midterm test. (100 points altogether) Students can get their signature only if all the following conditions are fulfilled: They attend the lessons regularly (see study-and-examination-regulations-of-obuda-university.pdf). They don’t fail to hand in both midterm tests. The results of the midterm test are at least 30% (15 points) in both cases. Students achieve at least 50% (50 points) on the two tests altogether. The test are written in a classroom under the supervision of the teachers. They contain a theoretic part and a practical. 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. Without a signature students can not register for the exam. Students have to sit a written exam, which has a theoretic part and a practical. They can get at most 30 points for the theoretic part, 40 points for the practical. They need at least 50% on both part to pass the exam. If they fulfilled these conditions, we add to their achieved points 30% of the points they achieved on the midterm test, i.e., they can have at most 100 points. The grade of the exam is decided as the table shows: 0-49%: failed (1) 50-61%: satisfactory (2) 62-73%: average (3) 74-85%: good (4) 86-100%: excellent (5) If only online exams will be allowed, then there will be a written and an oral part of the exam managing through Moodle and Teams. Only those students can take the oral part, who achieved at least 50% percent on the written part. To get a passing grade you have to pass both the written and the oral part. More details will be announced, if its necessary.

Exam Types:

Mid Term Exam

Final Exam

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

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

Additional bibliography: -

Additional Information: Students have to sit a written exam, which has a theoretic part and a practical. They can get at most 30 points for the theoretic part, 40 points for the practical. They need at least 50% on both part to pass the exam. If they fulfilled these conditions, we add to their achieved points 30% of the points they achieved on the midterm test, i.e., they can have at most 100 points. The grade of the exam is decided as the table shows: 0-49%: failed (1). 50-61%: satisfactory (2) 62-73%: average (3) 74-85%: good (4) 86-100%: excellent (5) 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.