COURSE GOALS:
Course goals are to acquire knowledge of the basic mathematical notions, gaining operational knowledge about techniques of differentiation 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 1, the student will be able to:
- demonstrate knowledge of basic concepts of mathematical analysis (sequences, limits, derivation of a function, Taylor series and its properties);
- list all elementary functions and its properties and use them in practical computations;
- differentiate elementary functions;
- apply differentiation to identify properties and sketch the graph of a function;
- use Taylor series to approximate the functions;
COURSE DESCRIPTION:
1. Set, function, bijection and inverse function (2 weeks).
2. Natural numbers and principle of mathematical induction (0.5 week).
3. Real numbers, supremum (1 week).
4. Elementary functions (1.5 week).
5. Sequence and limit of a sequence (1 week).
6. Limit of a function at a point, continuous function defined on a segment (1 week)
7. Derivation of a function. Derivation rules. Derivatives of elementary functions (3 weeks)
8. Taylor's theorem (1 week)
9. Extreme values of a function. Investigating the properties of a function (3 weeks).
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.
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- S. Kurepa, Matematička analiza 1 i 2, Tehnička knjiga, Zagreb.
B.P. Demidovič, Zadatci i riješeni primjeri iz više matematike, Tehnička knjiga, Zagreb.
B.Guljaš, Matematička analiza I & II, skripta,
http://web.math.pmf.unizg.hr/~guljas/skripte/MATANALuR.pdf
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