1. komponenta

Lecture type	Total
Lectures	45
Seminar	45

* Load is given in academic hour (1 academic hour = 45 minutes)

COURSE OBJECTIVE
To introduce the basic concepts of integral calculus, real functions of two or more variables, ordinary and partial differential equations, and their relation to engineering problems.

COURSE IMPLEMENTATION PROGRAM
1. Indefinite integral and methods of calculation
2. Application of indefinite integral in engineering - some important differential equations
3. Area problem - a definite integral. Leibniz-Newton formula
4. Methods of calculating a definite integral. Improper integral
5. Applications of definite integral in geometry
6. Applications of definite integral in natural sciences
7. The concept of the function of two variables, its graph, and partial derivatives
8. Linear and quadratic approximation of functions of several variables
9. Local extrema for functions of several variables
10. Multiple integrals - successive integration
11. Applications of multiple integrals
12. Ordinary differential equations of 1st order
13. Ordinary differential equations of 2nd order
14. The concept of a partial differential equation, its solution, and initial and boundary conditions (elective)
15. Applications of partial differential equations (elective)

PREREQUISITES FOR COURSE ENROLLMENT
The student has enrolled in Mathematics 1

PREREQUISITES FOR ATTENDING THE COURSE EXAM
The student has successfully passed Mathematics 1

DEVELOPMENT OF GENERAL AND SPECIFIC SKILLS BY STUDENTS
Acquire basic techniques for integrating functions of one variable, differentiating functions of several variables, multiple integrals, solving ordinary differential equations, and offer a physical and engineering-related interpretation of the solutions

STUDENTS OBLIGATIONS AND PERFORMANCE MONITORING METHODS
Participate in and follow lessons, acquire the material covered and solve the problems offered

TEACHING METHODS
Classical lecture, demonstration, presentation

EXAMINATION METHODS
Two colloquia during the lecture period, written exams, MatLab or GNU Octave programming language test (optional), possible short knowledge tests during the semester

METHODS FOR MONITORING THE COURSE QUALITY
Student survey

1. Apply the indefinite integral to problems inverse to derivative problems
2. Use the definite integral to solve area problems and apply it to engineering problems
3. Adopt the concept of a function of several variables, their derivatives, and integrals, and apply it by analogy to the function of one variable to the study of relationships among several dependent variables
4. Apply first- and second-order differential equations to solve mathematical and physical problems
5. Apply the appropriate basic procedures in Matlab or GNU Octave programming languages
6. Explain the scientific principles that are important for eco-engineering, especially fundamental knowledge of chemistry, mathematics, physics, biology, and eco-engineering
7. Model processes that occur in or interact with the environment using appropriate computer databases and programs
8. Theoretically interpret the results of experimental work
9. Develop a work ethic, personal responsibility, and a drive for continuous learning

1. Lekcije iz Matematike 2, http://matematika.fkit.hr, I. Gusić,
2. Matematika 2, vježbe, http://matematika.fkit.hr, I. Baranović, M. Jerković,
3. Primjeri kolokvija i pismenih ispita, http://matematika.fkit.hr, Zavod za matematiku,
4. Matematika 2, http://lavica.fesb.hr/mat2/predavanja, I. Slapničar,

Enrollment :
Attended : Calculus I

Examination :
Passed : Calculus I

Mandatory course - Regular studij - Environmental Engineering