Course title Mathematics 1 (Differential calculus)
Code M101
Status Lectures(30), Exercises (45)
Level Basic course
Year 1. Semester 1.
ECTS 6 ECTS credits
Lecturer Antoaneta Klobučar, Full Professor; Ljiljana Primorac Gajčić, Assistant
Course objective To introduce students to the basic ideas and methods of mathematical analysis, which are the basis for many other courses and training students to apply knowledge for solving specific problems.
Prerequisites Knowledge of high school.
Learning outcomes: After successfully completed course, students will be able to:

  1. understand and replay the correct mathematical proof of the claims by applying the basic forms of reasoning and mathematical logic,
  2. understand and solve the problem of computing the derivatives, and the problem of testing functions
Teaching activity ECTS Learning outcome Students activity Methods of evaluation Points
min max
Class attendance Class attendance  Evidence list
Knowledge test (preliminary exam) 4,5 1-9 Preparation for written examination. Written  preliminary exam  0  300
Final exam Repetition of teaching materials. Oral exam (and written exam). 0 100
Total 6
Consultations Wednesday from 13.30pm-15pm
Gained competencies 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)
  1. Introductory section. Real numbers, infimum and supremum of a set, absolute value, intervals. Complex numbers.
  2. Functions. The concept of a function and basic properties. Elementary functions. Composition of functions. Bijection  and inverse function.
  3. Sequences.of real numbers. The concept of a sequence, properties and convergence. The number e.
  4. 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.
  5. 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.
  6. Applications of the differential calculus. The differentia. Newton’s tangent’s method. L’Hôpital’s rule. Testing functions (monotonicity, extrema, convexity, the asymptote).
Recommended reading
  1. Rudin, Principles of Mathematical Analysis, Mc Graw-Hill, Book Company, 1964.
  2. D. Jukić, R. Scitovski, Matematika I, Department of Mathematics, University of Osijek, Osijek, 2000
Additional reading
  1. S. Kurepa, Matematička analiza 1 (diferenciranje i integriranje), Tehnička knjiga, Zagreb, 1989.
  2. S. Kurepa, Matematička analiza 2 (funkcije jedne varijable), Tehnička knjiga, Zagreb, 1990.
  3. B.P. Demidovič, Zadaci i riješeni primjeri iz više matematike s primjenom na tehničke nauke, Tehnička   knjiga, Zagreb, 1986.
Instructional methods Lectures and exercises are mandatory.
Exam formats 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.
Language Croatian
Quality control and successfulness follow up An anonymous questionnaire
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