Undergraduate study programme

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Calculus I (Differential Calculus) P102

ECTS 5 | P 30 | A 30 | L 0 | K 0 | ISVU 74035 | Academic year: 2019./2020.

Course groups

Prikaži sve grupe na predmetu

Course lecturers

HREHOROVIĆ IVAN, Associate
RUDEC TOMISLAV, Lecturer
ŠTEKO ANJA, Associate

Course description

1. Preliminaries. Real numbers, infimum and supremum, absolute value, intervals. Complex numbers. 2. Functions. Definition of a function. Basic properties. Composition of functions. Inverse function. Elementary functions (polynomial, rational, exponential, logarithm, trigonometric, cyclometric, hyperbolic and area functions). 3. Sequences of real numbers. Concept of a sequence, properties and convergence. Number e. 11 4. Limits and continuity of functions. Concept and properties of the limits of the function. Asymptotes. Continuity of functions. 5. Differential calculus. The derivative and the tangent. The derivative as velocity. Concept of the derivative. Derivative rules. The chain rule and the derivative of the inverse function. The derivative of elementary functions. Implicit differentiation. Parametric differentiation. Mean value theorem. Higher derivatives. Taylor's theorem. 6. Application of the differential calculus. Differential. Newton’s method. L'Hôpital's rule. Examination of functions (monotonicity, minima and maxima, convexity, asymptotes). Sketching curves.

Knowledge and skills acquired

At the introductory level students should be introduced to fundamental ideas and methods of mathematical analysis, which represent the basis for many other courses. During lectures basic terminology would be explained in an informal way, their utility and applications would be illustrated. During exercises students should master an adequate technique and become trained for solving concrete problems.

Teaching methods

Mandatory lectures and exercises.

Student requirements

Defined by the Student evaluation criteria of the Faculty of Electrical Engineering, Computer Science and Information Technology Osijek and paragraph 1.9

Monitoring of students

Defined by the Student evaluation criteria of the Faculty of Electrical Engineering, Computer Science and Information Technology Osijek and paragraph 1.9

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. 1 Galić, A; D.Crnjac Milić; Galić, I;.Katić Matematika 1 Osijek: ETF Osijek, 2008.

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

3. 3 S. Kurepa Matematička analiza 1 (diferenciranje i integriranje) Tehnička knjiga, Zagreb, 1989.


Pretraži literaturu na:

Recommended additional literature

1. 1 S. Kurepa Matematička analiza 2 (funkcije jedne varijable) Tehnička knjiga, Zagreb, 1990.

2. 2 W. Rudin Principles of Mathematical Analysis McGraw-Hill, Book Company, 1964.

Examination methods

The final assessment consists of both the written and oral exam upon completion of lectures and exercises.

Course assessment

Conducting university questionnaires on teachers (student-teacher relationship, transparency of assessment criteria, motivation for teaching, teaching clarity, etc.). Conducting Faculty surveys on courses (upon passing the exam, student self-assessment of the adopted learning outcomes and student workload in relation to the number of ECTS credits allocated to activities and courses as a whole).

Overview of course assesment

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

1. discuss the properties of the given elementary function by knowing the properties and characteristic examples of elementary functions

2. construct a model for the decision on the convergence of the given sequence by knowing the properties and the characteristic examples of sequenceS

3. discuss the general characteristics of different elementary functions by comparing them

4. construct the form of a default function

5. construct a mathematical or physical problem model using differential calculus



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