||By arrangement or after class
||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)
- Field of real numbers, infimum, and supremum of a set, absolute value, intervals. Field of complex numbers. Principle of mathematical induction.
- Functions. Notion of a function. Properties of functions. Elementary functions (polynomials, rational functions, and irrational functions, exponential and logarithmic functions, trigonometric and inverse trigonometric functions). Composite function. Bijective function. Inverse function.
- Notion of sequence and subsequence, the main properties, and convergence. Number e.
- Limit and function continuity. Notion of function limit. Limits properties. One-sided limits. Infinite limits and limits in the infinity. Asymptotes. Continuity and continuous function properties.
- Differential calculus. The tangent and velocity problem. Notion of derivative. Differentiation rules. Derivatives of elementary functions. Implicit function derivative. Derivative of parametric function. Higher-order derivatives. The fundamental theorems of differential calculus.
- Differential calculus applications. Notion of differential. L’Hôspital’s rule. Function analysis (monotonicity, extremes, convexity, asymptotes).
- 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 part. After the completion of lectures and exercises, students can take the exam. Acceptable mid-term exam scores replace the written examination.
|Quality control and successfulness follow up
||An anonymous questionnaire