COURSE OBJECTIVES
To introduce students to the basic concepts of integral calculus, real functions of two or more variables, and ordinary and partial differential equations, as well as their connection to engineering problems.
PREREQUISITE COURSES
Completed attendance of the course Mathematics 1
COURSE LEARNING OUTCOMES
1. Apply the indefinite integral to problems inverse to the problem of differentiation.
2. Use the definite integral to solve the area problem and apply it to engineering problems.
3. Acquire the concept of a function of several variables, its derivatives and integrals by analogy with a function of one variable, and apply it to the study of relationships between several dependent quantities.
4. Apply first- and second-order differential equations in solving mathematical and physical problems.
5. Actively use the relevant basic procedures in the MATLAB or GNU Octave programming language.
LEARNING OUTCOMES OF THE STUDY PROGRAM TO WHICH THE LEARNING OUTCOMES OF THIS COURSE CONTRIBUTE
1. Explain the scientific foundations relevant to eco-engineering, in particular fundamental knowledge in chemistry, mathematics, physics, biology and eco-engineering
2. Model processes taking place in the environment or in interaction with the environment using appropriate computer databases and software
3. Interpret the results of experimental work theoretically
4. Develop work ethics, personal responsibility and a commitment to further professional development
COURSE CONTENT BY UNITS OR WEEKS
Lectures and seminars:
1. The indefinite integral and methods of integration.
2. Applications of the indefinite integral in engineering - some important differential equations.
3. The area problem - the definite integral. The Newton-Leibniz formula.
4. Methods of computing the definite integral. Improper integrals.
5. Applications of the definite integral in geometry.
6. Applications of the definite integral in the natural sciences.
7. The concept of a function of two variables, its graph and partial derivatives.
8. Linear and quadratic approximation of functions of several variables.
9. Local extrema of functions of several variables.
10. Multiple integrals - iterated integration.
11. Applications of multiple integrals.
12. First-order ordinary differential equations.
13. Second-order ordinary differential equations.
14. The concept of a partial differential equation, its solutions, and initial and boundary conditions.
15. Applications of partial differential equations.
MODES OF INSTRUCTION
- Lectures
- Seminars and workshops
STUDENT OBLIGATIONS
Attending and following classes, mastering the material covered, and solving the assigned problems.
MONITORING OF STUDENTS' WORK
- Class attendance
- Class participation
- Written exam
- Continuous assessment
GRADING AND ASSESSMENT DURING CLASS AND ON THE FINAL EXAM
- Midterm exam 1 - theoretical and seminar part. Maximum 25 + 25 points, with a minimum of 5 points on each part required to pass.
- Midterm exam 2 - theoretical and seminar part. Maximum 25 + 25 points, with a minimum of 5 points on each part required to pass.
- Exam - theoretical and seminar part. Maximum 50 + 50 points, with a minimum of 10 points on each part.
- Class participation. Maximum 10 points, 5 in lectures and 5 in seminars.
- Computer seminar in the MATLAB or GNU Octave programming language. Maximum 10 points.
Total: 120 points
Grades:
- 60 - 69 sufficient (2)
- 70 - 79 good (3)
- 80 - 89 very good (4)
- 90 - 120 excellent (5)
MANDATORY LITERATURE
- Gusić, I., Jerković, M., teaching materials, Matematika 2, predavanja (Mathematics 2, Lectures), 2022. (Course website: https://matematika.fkit.hr/matematika2.html)
- Bužančić, M., Vlahek Štrok, A., teaching materials, Matematika 2, seminari (Mathematics 2, Seminars), 2022. (Course website: https://matematika.fkit.hr/matematika2.html)
QUALITY ASSURANCE METHODS THAT ENSURE THE ACQUISITION OF OUTPUT KNOWLEDGE, SKILLS AND COMPETENCES
Student survey, pass rate analysis
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