||Wednesday from 13.30pm-15pm
||At the introductory level introduce students to the basic ideas and methods of mathematical analysis, which are the basis for many other courses. Lectures will be given in an informal manner, illustrating their utility and application. At exercises students learn the necessary techniques and apply them to solve real problems.
|Content (Course curriculum)
- Introductory section. Real numbers, infimum and supremum of a set, absolute value, intervals. Complex numbers.
- Functions. The concept of a function and basic properties. Elementary functions. Composition of functions. Bijection and inverse function.
- Sequences.of real numbers. The concept of a sequence, properties and convergence. The number e.
- Limits and continuity of functions. Limit of function. Properties of the limit. One-sided limits. Infinite limits and limits at infinity. Asymptote. Continuity and properties of continuous functions.
- Differential calculus. Problems of tangents and speed. The derivative. The derivative. Rules for finding the derivative. Derivatives of elementary functions. Derivatives of an implicit function. Derivatives of an parametric function. Lagrange’s mean value theorem. Higher derivatives. Taylor’s theorem.
- Applications of the differential calculus. The differentia. Newton’s tangent’s method. L’Hôpital’s rule. Testing functions (monotonicity, extrema, convexity, the asymptote).
- Rudin, Principles of Mathematical Analysis, Mc Graw-Hill, Book Company, 1964.
- D. Jukić, R. Scitovski, Matematika I, Department of Mathematics, University of Osijek, Osijek, 2000
- S. Kurepa, Matematička analiza 1 (diferenciranje i integriranje), Tehnička knjiga, Zagreb, 1989.
- S. Kurepa, Matematička analiza 2 (funkcije jedne varijable), Tehnička knjiga, Zagreb, 1990.
- B.P. Demidovič, Zadaci i riješeni primjeri iz više matematike s primjenom na tehničke nauke, Tehnička knjiga, Zagreb, 1986.
||Lectures and exercises are mandatory.
||The exam consists of a written and oral examination, which is taken after completion of lectures and exercises. During the semester, students can take three tests that replace the written examination.
|Quality control and successfulness follow up
||An anonymous questionnaire