Undergraduate study programme

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Calculus III P301

ECTS 5 | P 30 | A 30 | L 0 | K 0 | ISVU 74045 | Academic year: 2017./2018.

Course groups

Prikaži sve grupe na predmetu

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 to the basic ideas and methods of functions of several variables and functions of a complex variable as the basis for other courses. The emphasis will be put on applications and basic concepts will be analysed in an informal way. During exercises, students should acquire certain techniques and be trained for solving specific problems.

Teaching methods

Mandatory lectures and auditory exercises.

Student requirements

Definirano Okvirima kriterija ocjenjivanja studenata FERIT-a i stavkom 1.9

Monitoring of students

Definirano Okvirima kriterija ocjenjivanja studenata FERIT-a i stavkom 1.9

Student assessment

During the semester, students can take several revision exams which replace the written exam. This ensures a continuous assessment of students’ work and knowledge. The final exam consists of the written and oral part.

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 na:

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

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

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 assessment consists of both the written and oral exam upon completion of lectures and exercises. During the semester, students can take several revision exams replacing the written exam.

Course assessment

Provođenje sveučilišnih anketa o nastavnicima (pristup prema studentima, transparentnost kriterija, motivacija na
izvršavanje aktivnosti, jasnoća izlaganja, i sl.). Provođenje fakultetskih anketa o predmetima (nakon položenog predmeta
samoevaluacija studenata o usvojenim ishodima učenja, te o opterećenosti u usporedbi s ECTS-ima aktivnosti i predmeta
u cjelini).

Overview of course assesment

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

1. discuss functions of several variables and graphically illustrate the functions of two variables, and understand the concept of multidimensional space

2. calculate partial derivatives and differentials of the first and higher orders for functions of several variables

3. calculate function extrema of several variables and conditional extrema

4. define double and triple integrals, discuss them and calculate examples and applications

5. calculate curve integrals of the first and second kind and apply them in exercises

6. use concepts of scalar and vector fields, and basic vector calculus in engineering theory and application; understand the concept of complex functions of a complex variable



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

60
ECTS
2
- discuss functions of several variables and graphically illustrate the functions of two variables, and understand the concept of multidimensional space- calculate partial derivatives and differentials of the first and higher orders for functions of several variables- define double and triple integrals, discuss them and calculate examples and applicationsLectures, Auditory exercises Attendance register. Mandatory attendance percentage is:
70%

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

0
Max

0
Practice – problem solving Workload
40
ECTS

1.3
- calculate partial derivatives and differentials of the first and higher orders for functions of several variables- calculate function extrema of several variables and conditional extrema- define double and triple integrals, discuss them and calculate examples and applications- calculate curve integrals of the first and second kind and apply them in exercisesMidterm exam Evaluation of (written) exercises Min

20
Max

40
Oral exam Workload
40
ECTS

1.3
- discuss functions of several variables and graphically illustrate the functions of two variables, and understand the concept of multidimensional space- define double and triple integrals, discuss them and calculate examples and applications- use concepts of scalar and vector fields, and basic vector calculus in engineering theory and application; understand the concept of complex functions of a complex variableOral exam Assessment of student's answers Min

25
Max

50
Seminars Workload
11
ECTS

0.4
- calculate partial derivatives and differentials of the first and higher orders for functions of several variables- calculate function extrema of several variables and conditional extrema- calculate curve integrals of the first and second kind and apply them in exercises- use concepts of scalar and vector fields, and basic vector calculus in engineering theory and application; understand the concept of complex functions of a complex variableWriting a seminar paper on a given topic Grading a seminar paper Min

0
Max

10
Σ Activities Σ Workload
151
Σ ECTS
5
Σ Max
100