||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)
- The Riemann integral. The problem of an area. Definition and properties of the Riemann integral. Integrability of monotone and continuous functions. The mean value theorem of integral calculus. Newton-Leibniz formula. Indefinite integral. Methods of integration. Basic techniques of integration. Application of integration: area between two curves, volumes of revolution, length of curve, work force, torque, center of mass. Improper integrals. Numerical integration (trapezoidal and Simpson’s rule).
- Series of real numbers. Infinite series and convergence. The convergence criteria.
- Series of functions. Rows function. Uniform convergence. Power series. Taylor series of elementary functions. Exponential and logarithmic functions.
- W. 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.
- M. Crnjac, D. Jukić, R. Scitovski, Matematika, Osijek, 1994.
- 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 two tests that replace the written examination.
|Quality control and successfulness follow up
||An anonymous questionnaire