﻿ Mathematics 2- Integration calculus – Curriculum

# Curriculum.

 Course title Mathematics 2 (Integration calculus) Code M102 Status Lectures(30), Exercises (45) Level Basic course Year 1. Semester 2. 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 Differential calculus Learning outcomes: After successfully completed course, students will be able to: understand and replay the correct mathematical proof of the claims by applying the basic forms of reasoning and mathematical logic, 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) Preparation for written examination. Written  preliminary exam 0 300 Seminars Homework 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) 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. Recommended reading 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. Additional reading 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. 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