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Calculus II (Integral Calculus -Differential Equations) P201

ECTS 6 | P 30 | A 30 | L 0 | K 0 | ISVU 37111 | Academic year: 2019./2020.

Course groups

Prikaži sve grupe na predmetu

Course lecturers

HREHOROVIĆ IVAN, Associate
KATIĆ ANITA, Lecturer
ŠTEKO ANJA, Associate

Course description

1. Riemann integral. The integral as an area. Concept and properties of the Riemann integral. Integrability of monotonic and continuous functions. The mean value theorem for integral of the continuous function. Newton-Leibniz formulae. 2. Indefinite integral. Basic methods and techniques of integration (the method of substitution, integration by parts, integration of rational functions and integration of functions boiling down to integrals of rational functions, Euler substitution, binomial integral) 3. Application of integration. Area between two curves, surface and volumes of revolution, length of curve, work of power, moments, centre of mass. Improper integral. Numerical integration (trapezium and Simpson’s rule). 4. Series of real numbers. Concept of series and convergence. Criteria of convergence. 5. Series of functions. Uniform convergence. Power series. Taylor series of elementary functions. Exponential and logarithm function. 6. Ordinary differential equations. Sources of ordinary differential equations. General and particular solution. Cauchy problem. Geometric point of view. Problem of sensitivity to a change of initial values. Some types of ordinary differential equations of the first order (exact, homogeneous, linear, Bernoulli equation). Examples and applications. 7. Ordinary differential equations of the second order. Some special types. Linear differential equation of the second order. Lagrange's method of variation of the constant. Linear differential equation of the second order with constant coefficients. Examples and applications (harmonic oscillator).

Knowledge and skills acquired

At the introductory level students should be introduced to fundamental ideas and methods of mathematical analysis, which represent the basis for many other courses. During lectures basic terminology would be explained in an informal way, their utility and applications would be illustrated. During exercises students should master an adequate technique and become trained for solving concrete problems.

Teaching methods

Mandatory lectures and exercises.

Student requirements

Defined by the Student evaluation criteria of the Faculty of Electrical Engineering, Computer Science and Information Technology Osijek and paragraph 1.9

Monitoring of students

Defined by the Student evaluation criteria of the Faculty of Electrical Engineering, Computer Science and Information Technology Osijek and paragraph 1.9

Student assessment

During the semester, students can take several revision exams which replace the written exam. This ensures a continuous assessment of students’ work and knowledge.

Obligatory literature

1. 1 Demidović, B.P. Zadaci i riješeni primjeri iz više matematike s primjenom na tehničke nauke Zagreb: Tehnička knjiga, 2003.

2. 2 D. Jukić, R. Scitovski Matematika I Odjel za matematiku, Osijek, 2000.

3. 3 I. Ivanšić Fourierovi redovi. Diferencijalne jednadžbe Odjel za matematiku, Osijek, 2000.


Pretraži literaturu na:

Recommended additional literature

1. 1 W. Rudin Principles of Mathematical Analysis McGraw-Hill, Book Company, New York, 1964.

2. 2 S. Kurepa Matematička analiza 1 (diferenciranje i integriranje) Tehnička knjiga, Zagreb, 1989.

3. 3 S. Kurepa Matematička analiza 2 (funkcije jedne varijable) Tehnička knjiga, Zagreb, 1990.

4. 4 G.F.Simmons, J.S.Robertson Differential Equations with Applications and Historical Notes, $2^{nd$ Ed McGraw-Hill, Inc., New York, 1991.

5. 5 Schaums outline series McGRAW-HILL, New York, 1991.

Examination methods

The final assessment consists of both the written and oral exam upon completion of lectures and exercises.

Course assessment

Conducting university questionnaires on teachers (student-teacher relationship, transparency of assessment criteria, motivation for teaching, teaching clarity, etc.). Conducting Faculty surveys on courses (upon passing the exam, student self-assessment of the adopted learning outcomes and student workload in relation to the number of ECTS credits allocated to activities and courses as a whole).

Overview of course assesment

Learning outcomes
Upon successful completion of the course, students will be able to:

1. explain the meaning and application of a definite integral

2. for a given mathematical problem, create an integral, solve it and interpret the solution

3. for a given series of real numbers and series of functions, create a statement of convergence decisions

4. for a given, specific problem in mathematics or physics, design a mathematical model using basic forms of differential equations



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