This course is graded through continuous assessment, consisting of homework (5%), tree 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 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: specify vectors and matrices operations and their properties apply vectors operations to determine line and plane equations apply properties of matrices operations to solve system of linear equations use derivation rules to calculate the derivative of explicit, implicit and parametric functions apply differential calculus to sketching a function graph present applications of the definite integral to calculate area and distance traveled use the properties of inverting functions to determine the properties of logarithmic and arcus functions

Lectures

1. Vectors and elementary vector operations

2. Analytical geometry in space

3. Matrices and elementary matrix operations

4. Linear systems, Gaussian eliminations

5. Eigenvalues, eigenvectors, 1st midterm exam

6. Basic idea of a derivative, rules for differentiation, differential

7. Chain rule, differentiation of implicit functions

8. Parametric differentiation, anti-derivatives

9. Investigation of the graph of a function by using differentiation, local and global extremes

10. Definite integral, rules of integration, Newton-Leibniz formula 2nd midterm exam

11. Trigonometric functions

12. Inverse functions, polar coordinates

13. Exponential and logarithmic functions,

14. Taylor series formula

15. Power series 3nd midterm exam, final exam

Exercises

1. Vectors and elementary vector operations

2. Analytical geometry in space

3. Matrices and elementary matrix operations

4. Linear systems, Gaussian eliminations

5. Eigenvalues, eigenvectors, 1st midterm exam

6. Basic idea of a derivative, rules for differentiation, differential

7. Chain rule, differentiation of implicit functions

8. Parametric differentiation, anti-derivatives

9. Investigation of the graph of a function by using differentiation, local and global extremes

10. Definite integral, rules of integration, Newton-Leibniz formula 2nd midterm exam

11. Trigonometric functions

12. Inverse functions, polar coordinates

13. Exponential and logarithmic functions,

14. Taylor series formula

15. Power series 3nd midterm exam, final exam

Compulsory literature:

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

- 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

- A. Aglić, N. Elezović - "Linearna Algebra - zbirka", Element, Zagreb, 1995.

Recommended literature:

e-textbooks:

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

http: //e-ucenje.fsb.hr/course/view.php?id=364