* Load is given in academic hour (1 academic hour = 45 minutes)
COURSE GOALS: Course goals are gaining operational knowledge about techniques of integration and understanding the related theoretical concepts.
LEARNING OUTCOMES AT THE LEVEL OF THE PROGRAMME:
Upon completing the degree, students will be able to:
2. APPLYING KNOWLEDGE AND UNDERSTANDING
2.1 identify the essentials of a process/situation and set up a working model of the same or recognize and use the existing models
2.3 apply standard methods of mathematical physics, in particular mathematical analysis and linear algebra and corresponding numerical methods
5. LEARNING SKILLS
5.1 search for and use physical and other technical literature, as well as any other sources of information relevant to research work and technical project development (good knowledge of technical English is required)
LEARNING OUTCOMES SPECIFIC FOR THE COURSE:
Upon passing the course Mathematical analysis 2, the student will be able to:
- demonstrate knowledge of basic concepts of mathematical analysis (integrals and its properties, series, Taylor series);
- apply basic integration rules for calculating known type of integrals;
- use Taylor series to approximate the functions of several variables;
- solve known type of double and triple integrals and use them to calculate areas and volumes;
- solve known type of line integrals and use them to calculate the arc length of the curve;
1. Riemann integral (1 week).
2. Indefinite integral and primitive function (1 week)
3. Integrability of monotone and continuous functions (1 week).
4. Newton-Leibniz formula. Integration methods (2 week).
5. Series of real numbers. Function series (2 weeks).
6. Functions of several variables. Taylor series (4 week).
7. Double and triple integral (2 weeks)
8. Line integrals (1 week)
REQUIREMENTS FOR STUDENTS:
Students are required to regularly attend lectures and exercises, and actively participate in solving problems during exercises. Furthermore, students are required to solve homework assignments and to pass two colloquiums during the semester by achieving at least 45% of the total number of points on them.
GRADING AND ASSESSING THE WORK OF STUDENTS:
The final score is established on final oral examination and represents the average value of grades obtained on two colloquiums and oral examination.
- B.Guljaš, Matematička analiza I & II, skripta,
- S. Kurepa, Matematička analiza 1 i 2, Tehnička knjiga, Zagreb
- B.P. Demidovič, Zadaci i riješeni primjeri iz više matematike, Tehnička knjiga, Zagreb
Mathematical Analysis 1