Josip Juraj Strossmayer University of Osijek, Department of Physics

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 Mihaela Ribičić Penava, Associate Professor; Jelena Jankov, 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:

  1. Differentiate between and give typical examples of integrable and non-integrable real functions of one variable, convergent and divergent series of real numbers.
  2. Apply the techniques for computing definite and indefinite integral of real functions of one variable.
  3. Interpret results of the application of definite integral to a simpler problem of calculating the area, volume rotation calculus and calculating the arc length.
  4. Apply the technique of function development in the power series and identify conditions on the function that could allow this.
  5. Understand and reproduce the correct mathematical proof of claim applying basic forms of mathematical and logical inference.
Teaching activity ECTS Learning outcome Students activity Methods of evaluation Points
min max
Class attendance 1 1-5 Class attendance  Evidence list 0 4
Knowledge test (preliminary exam) 2 1-5 Preparation for the written examination. Evaluation  25  48
Final exam 3 1-5 Repetition of teaching materials. Oral exam 25 48
Total 6 50 100
Consultations http://www.fizika.unios.hr/m2/en/
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. 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).
  2. Series of real numbers. Infinite series and convergence. The convergence criteria.
  3. Series of functions. Rows function. Uniform convergence. Power series. Taylor series of elementary functions. Exponential and logarithmic functions.
Recommended reading
  1. W. 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.
  3. M. Crnjac, D. Jukić, R. Scitovski, Matematika, Osijek, 1994.
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 two tests that replace the written examination.
Language Croatian
Quality control and successfulness follow up An anonymous questionnaire
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