COURSE OBJECTIVES
To introduce students to number systems, the basic concepts of linear algebra, elementary functions, and the concept and meaning of the derivative, as well as their connection to engineering problems.
PREREQUISITE COURSES
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COURSE LEARNING OUTCOMES
1. Distinguish and use types of numbers, their representations, and arithmetic operations with them.
2. Apply the coordinate system (in the plane, in space and in higher dimensions) and the basic mathematical constructions associated with it: vectors, matrices, systems of linear equations.
3. Use elementary functions, distinguish their graphs, and interpret the corresponding relationship between dependent quantities.
4. Master the concept of the derivative and its physical and geometric interpretation, and apply it in solving and modelling practical 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. Real and complex numbers
2. Two-dimensional, three-dimensional and n-dimensional real vector spaces.
3. Representation of some transformations of the plane and space - the concept of a matrix and a linear operator.
4. Matrix algebra. Inverse matrix. Determinant.
5. Dot product, cross product and scalar triple product of vectors.
6. Systems of linear equations and their solution.
7. The concept and the geometric and physical meaning of eigenvalues and eigenvectors (optional content)
8. The concept of a function, its graph and the inverse function.
9. Elementary functions. Functions important in applications.
10. The concepts of a sequence, the limit of a sequence, a series and the limit of a function.
11. The concept of the derivative, its geometric and physical meaning.
12. Properties of derivatives. Derivatives of elementary functions.
13. Linear approximation, quadratic approximation and Taylor series.
14. Decrease, increase, local extrema, convexity, concavity, inflection points and their physical meaning.
15. Analysing the behaviour of functions using derivatives.
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 1 - predavanja (Mathematics 1 - Lectures), 2022. (Course website - FKIT)
- Adlešić, T., teaching materials, Matematika 1 - seminari (Mathematics 1 - Seminars), 2024. (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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