Undergraduate study programme

Ak.g.2014./2015.2015./2016.2016./2017.2017./2018.

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Calculus III P301

ECTS 5 | P 30 | A 30 | L 0 | K 0 | ISVU 74045

Course groups

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Course lecturers

MAROŠEVIĆ TOMISLAV, Lecturer
MILETIĆ JOSIP (vanjski suradnik), Associate

Course description

Real functions of several real variables. Level curves and level surfaces. Limits and continuity. Partial derivatives and differential. Equation of tangent plane to a surface. Partial derivatives of composite functions and implicit functions. Partial derivatives and differentials of higher orders. Taylor's formula for functions of several variables. Extrema and conditional extrema of functions of several variables. Double and triple integrals - basic concepts, calculation and applications. Line integrals (of the first and of the second kind) – definition, properties, calculation and applications. Vector functions of several variables. Scalar and vector field. Gradient of a scalar field; divergence of a vector field; curl of a vector field; applications. Complex functions of a complex variable. Derivative. Cauchy-Riemann equations. Integral of function of a complex variable. Cauchy theorem and integral formula. Taylor and Laurent series. Singularities. Residues.

Knowledge and skills acquired

Students are introduced at the introductory level to basic ideas and methods of functions of several variables and functions of a complex variable, as a basis for other courses. Stress will be put on applications, and basic concepts are going to be analysed in an informal way. During exercises students should acquire certain techniques and be trained for solving concrete problems.

Teaching methods

Students are obliged to attend both lectures and exercises.

Student assessment

During the semester students can take several tests which replace the written examination. This ensures continuous assessment of students’ work and knowledge.

Obligatory literature

1. Javor, P. Matematička analiza II. Zagreb: Element, 2000.

2. Demidović, B.P. - Zadaci i riješeni primjeri iz više matematike s primjenom na tehničke nauke. Zagreb: Tehnička knjiga, 2003.

3. H. Kraljević, S. Kurepa, Matematička analiza 4/1 (funkcija kompleksne varijable), Tehnička knjiga, Zagreb, 1986.

Pretraži literaturu

Recommended additional literature

1. M. Krasnov et al., Mathematical Analysis for Engineers – Vol. 1, & ibid. Vol. 2, Mir Publishers, Moscow, 1990.

2. S. Kurepa, Matematička analiza 3 (funkcije više varijabli), Tehnička knjiga, Zagreb, 1979.

3. B.P. Demidovič, Zadaci i riješeni primjeri iz više matematike s primjenom na tehničke nauke, Tehnička knjiga, Zagreb, 1986.

4. R. Galić, Funkcije kompleksne varijable – za studente tehničkih fakulteta, Osijek, Elektrotehnički fakultet, 1994.

5. N. Elezović, D. Petrizio, Funkcije kompleksne varijable: zbirka zadataka, Element, Zagreb, 1994.

6. P. Javor, Matematička analiza II, Element, Zagreb, 2000.

ECTS credits

An ECTS credit value has been added according to calculation of time required for studying and successful course completion.

Examination methods

The final examination consists of the written and the oral part. Students can take the final examination after the completion of lectures and exercises. During the semester students can take several tests which replace the written examination.

Course assessment

During the semester students can take several tests which enables continuous assessment and stimulation of students' work. At the semester end an official questionnaire can be conducted pertaining to students' evaluation of course teaching and lecturers participating in course teaching.

Overview of course assesment

Learning outcomes
Upon successful completion of the course, students will be able to:

1. diskutirati funkcije više varijabli i grafički prikazati funkcije dvije varijable, te razumjeti pojam višedimenzionalnog prostora

2. izračunati parcijalne derivacije i diferencijale prvog i višeg reda za funkcije više varijabli

3. izračunati ekstreme funkcija više varijabli, te uvjetne ekstreme

4. definirati dvostruke i višestruke integrale, diskutirati o njima i izračunati konkretne primjere i primjene

5. izračunati krivuljne integrale prve i druge vrste, te ih koristiti u primjenama

6. koristiti se pojmovima skalarna i vektorska polja, te osnovnim vektorskim računom u inženjerskoj teoriji i primjenama; razumjeti pojam kompleksnih funkcija kompleksne varijable.



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Prvo unesite postotak evidencije nazočnosti!

Student's activity Workload ECTS (Workload/30) Learning outcomes
Upon successful completion of the course, students will be able to:
Teaching
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Assessment method Points
Attendance
Lectures, Auditory exercises

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Lectures, Auditory exercises Attendance register. Mandatory attendance percentage is:
%

This percentage defines the minimum workload for the activity. The maximum is defined by the study programme.
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Max

Oral exam Workload
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Oral exam Assessment of student's answers Min

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Σ Activities Σ Workload
0
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