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 I
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. Define 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. Describe phenomena in the field of chemical engineering using the vocabulary and tools of the fundamental sciences - mathematics, physics and chemistry
2. Select appropriate methods of analysis, modelling, simulation and optimisation
3. Apply a scientific approach to real chemical engineering problems
4. Apply techniques and methods with an awareness of their limitations
5. Demonstrate the ability to learn independently and recognise the need for lifelong learning
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
- Practical work
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.
- 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.
- Exam - theoretical and seminar part. Maximum 50 + 50 points, with a minimum of 10 points on each part and 33 points in total required to pass.
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 - FKIT)
- Bužančić, M., Vlahek Štrok, A., teaching materials, Matematika 2 - seminari (Mathematics 2 - Seminars), 2022. (Course website - FKIT)
QUALITY ASSURANCE METHODS THAT ENSURE THE ACQUISITION OF OUTPUT KNOWLEDGE, SKILLS AND COMPETENCES
Student survey, pass rate analysis
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