This course is graded through continuous assessment, consisting of homework (5%), two midterm exams (80%), the final written (15%) and oral exam. Some of the students who gain insufficient points for a passing grade, according to the Faculty statute, are allowed to take four written and oral exam at most. Students who did not get a total of 45 (out of 300) points through continuous assessment, can not take the written and oral exam. The students who fail, have to enroll the complete course again.

Methods of monitoring quality that ensure acquisition of exit competences:

Students actively participate and work in the classroom. In addition, their work will be monitored in the system for e-learning. The records of students will be shown at the end of the semester by tracking the given elements. Their knowledge and competence will be checked during the semester with exams and individual on-line assignments at home.

Upon successful completion of the course, students will be able to (learning outcomes):

After successfully completing the course, students will be able (know/can) to do the following: use integration techniques applied to the definite integral solve problems with improper integrals create mathematical models of first order differential equations and solve them present a geometrical approach to differential equations and their solutions solve second order linear differential equations with constant coefficients use the differential calculus of functions of several variables for approximate calculation and solving optimization problems apply techniques of multiple integration

Lectures

1. Definite integral

2. Fundamental theorem of calculus

3. Integration by substitution

4. Integration by parts

5. Applications of definite integrals

6. Applications of definite integrals 1st midterm exam

7. First order differential equations, separable equations, first order linear differential equations

8. Field of directions, orthogonal trajectories

9. Second order linear differential equations with constant coefficients

10. Autonomous differential equations and phase plane, 2st midterm exam

11. Functions of several variables

12. Partial derivatives, directional derivatives, gradient

13. Local extremum of a function of several variables

14. Global extremum of a function of several variables

15. Multiple integrals, 3nd midterm exam, final exam

Exercises

1. Definite integral

2. Fundamental theorem of calculus

3. Integration by substitution

4. Integration by parts

5. Applications of definite integrals

6. Applications of definite integrals 1st midterm exam

7. First order differential equations, separable equations, first order linear differential equations

8. Field of directions, orthogonal trajectories

9. Second order linear differential equations with constant coefficients

10. Autonomous differential equations and phase plane, 2st midterm exam

11. Functions of several variables

12. Partial derivatives, directional derivatives, gradient

13. Local extremum of a function of several variables

14. Global extremum of a function of several variables

15. Multiple integrals, 3nd midterm exam, final exam

Compulsory literature:

Zvonimir Šikić: "Diferencijalni i integralni račun", Profil, Zagreb, 2008.

- Zvonimir Šikić: Diferencijalne jednadžbe, Profil, Zagreb, 2006.

- Demidovič - "Zadaci i riješeni primjeri iz više matematike s primjenom na tehničke nauke", Tehnička knjiga, 1998.

- V.P. Minorski - "Zbirka zadataka iz više matematike", Tehnička knjiga, 1972.

- "Inženjerski priručnik iz matematike, Temelji inženjerskih znanja", Školska knjiga, Zagreb, 1996.

- Erwin Kreyszig - "Advanced Engineering Mathematics", Wiley and Sons

Recommended literature:

e-textbooks:

https: //www.fsb.unizg.hr/matematika/udzbenik

http: //lavica.fesb.hr/mat1/

http: //e-ucenje.fsb.hr/course/view.php?id=57