Public Syllabus

Learning time distribution

Total
Curriculum	Lecture	Practice	Total Weekly	Lecture	Practice
56	28	28	4	2	2
Exam hours
7
Individual Study	Bibliography study	Field study	Homework	Tutoring	Others
62	23	11	23	5	0
Overall
125

Learning outcomes

Knowledge

Fundamental knowledge of differential and integral calculus for real and vector functions of a single variable and for real and vector functions of n variables.

Skills

Acquisition of differential and integral calculus techniques used in solving logistical and real-world problems.
Awareness of the importance of differential and integral calculus tools in approaching the modeling and solving of real-world problems

Responsibility

Applying rules of rigorous and efficient work, demonstrating responsible attitudes towards the scientific and educational field, for the optimal and creative exploitation of one's own potential in specific situations.
Efficient and effective conduct of activities organized in a team.
Efficient use of information resources for communication and professional development.

Online platform

Google Classroom

Course content

Content	Methods	Obs
1. Introduction to single variable calculus. Topology in R1 . Sequences and series of real numbers. Convergence Rules.	Participatory lecture, debate, dialogue, presentation, problematization, demonstration, exemplification	2 hours
2. Properties of functions of one real variable (review): limits, continuity, differentiability.	Participatory lecture, debate, dialogue, presentation, problematization, demonstration, exemplification	2 hours
3. Sequences and series of functions. Power series. Taylor polynomials.	Participatory lecture, debate, dialogue, presentation, problematization, demonstration, exemplification	2 hours
4. The Riemann-Darboux integral. Properties of the Riemann-Darboux integral. Classes of Riemann-Darboux integrable functions. Mean value theorem. The fundamental theorem of calculus. Techniques to find primitives. Improper integrals.	Participatory lecture, debate, dialogue, presentation, problematization, demonstration, exemplification	2 hours
5. Fourier series. Applications	Participatory lecture, debate, dialogue, presentation, problematization, demonstration, exemplification	2 hours
6. Calculus with parametric curves. Curves defined by parametric equations. Introduction to differential geometry of curves in the plane. Polar coordinates.	Participatory lecture, debate, dialogue, presentation, problematization, demonstration, exemplification	2 hours
7. Vector functions and space curves. Geometry of curves in the space. Arc length and curvature. Motion in space: velocity and acceleration.	Participatory lecture, debate, dialogue, presentation, problematization, demonstration, exemplification	2 hours
8. Introduction to functions of several variables. Limits and continuity.	Participatory lecture, debate, dialogue, presentation, problematization, demonstration, exemplification	2 hours
9. Differentiability of functions of several variables. Partial derivatives and directional derivatives. Frenchet differentiability. Basic properties of differentiable functions.	Participatory lecture, debate, dialogue, presentation, problematization, demonstration, exemplification	2 hours
10. Higher order partial differentiability. Taylor's theorems. Classification theorem for local extrema. Conditional extrema. Lagrange multipliers.	Participatory lecture, debate, dialogue, presentation, problematization, demonstration, exemplification	2 hours
11. The Riemann-Darboux integral of functions of two variables. Integrable functions. Properties of the Riemann-Darboux integral. Riemann-Darboux integral calculus when A is rectangular. Riemann-Darboux integral calculus when A is not a rectangle.	Participatory lecture, debate, dialogue, presentation, problematization, demonstration, exemplification	2 hours
12. Line integrals. First and second type line integrals. Green’s theorem.	Participatory lecture, debate, dialogue, presentation, problematization, demonstration, exemplification	2 hours
13. Triple integrals. Spherical and cylindrical coordinates.	Participatory lecture, debate, dialogue, presentation, problematization, demonstration, exemplification	2 hours
14. Introduction to the geometry of elementary surfaces. Parametric surfaces and their area. Surface integrals. Divergence and curl. Stoke’s theorem.	Participatory lecture, debate, dialogue, presentation, problematization, demonstration, exemplification	2 hours

Course bibliography

[1] St. Balint, E. Kaslik, L. Tănasie, Calcul diferential si integral, Editura Universitatii de Vest Timisoara, 2010. [2] R. Haggarty, Fundamentals of Mathematical Analysis; Addison-Wesley, 1989, Oxford [3] A. B. Israel, R. Gilbert, Computer-Supported Calculus; Springer Wien New York, 2001, RISC Johannes Kepler University, Linz, Austria. [4] C. Lanczos, Applied Analysis; Sir Isaac Pitman, 1967, London. [5] F. Ayres, J. Cault, Differential and Integral Calculus in Simetric Units; Mc.Grow-Hill, 1988. [6] O. V. Manturov, N. M. Matveev, A course of higher mathematics; Mir, 1989. [7] C.H. Edwards, D.E. Penney: "Calculus - Early Transcendentals", Pearson Prentice Hall, 2008. [8] J. Stewart: Calculus – Early Transcendentals, 8th Edition, Cengage Learning, 2016.

Seminar content

Content	Methods	Obs
The seminars follow the taught course by solving exercises to reinforce the theoretical considerations taught in the course.	exercise, demonstration, exemplification, debate, project, case study, evaluation	2 hours / week
Bibliography: The same as for the course.

Seminar bibliography

The content of the discipline is correlated with the epistemic standards and methodological rigor specific to the academic community in mathematics and computer science, ensuring a coherent and systematic treatment of fundamental concepts of differential and integral calculus. The curriculum is structured in accordance with the competencies defined by the study programme and reflects the requirements formulated by professional associations and representative employers in the IT field. By developing analytical reasoning, abstraction capacity, quantitative modeling, and problem-solving skills, the discipline contributes to the formation of transversal and professional competencies necessary for advanced studies in computer science and for professional integration in domains that require mathematical foundation, algorithmic thinking, and the application of quantitative methods.

Corroboration

(none)

AI tools guidance

Generative AI tools (such as ChatGPT, Gemini, Copilot, or similar) may be used as learning aids, but not as substitutes for independent mathematical reasoning. Students may consult AI for clarifying concepts, checking intermediate steps, improving explanations, or assisting with programming tasks in projects, provided they first attempt the work on their own. AI may not be used to generate complete solutions, proofs, or derivations that the student cannot fully understand and reproduce. Any use of AI must be clearly declared at the beginning of the assignment, specifying the tool used, how it was used, and for which part of the work. Students remain fully responsible for the correctness and justification of all submitted material, and AI use is strictly prohibited during exams and in-class assessments.

Evaluation and delivery

Activity	Criteria	Methods	Percentage
C	- Correctness of the assimilated notions. - Logical coherence, degree of assimilation of the specialized language.	Written exam at the end of the semester.	40.0%
S	- Ability to work with abstract knowledge. - Ability to put into practice the studied notions.	- Written evaluation through periodic tests in seminars.- Oral evaluation (solving exercises at the whiteboard)- Evaluation of laboratory projects	60.0%

Performance standards

Minimum requirements for academic performance: operational knowledge of the fundamental results of differential and integral calculus presented in this discipline. Minimum requirements for seminar attendance: at least 70% of seminars, in accordance with the Code of Student Rights and Obligations.

Additional info