1. komponenta

Lecture type	Total
Lectures	45
Seminar	45

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

COURSE OBJECTIVE
Introduction to number systems, basic concepts of linear algebra, elementary functions, the concept and importance of the derivative and its relation to engineering problems

COURSE IMPLEMENTATION PROGRAM
1. Real and complex numbers
2. Two-dimensional, three-dimensional, and n-dimensional real vector space
3. Notation of some transformations of plane and space - the concept of matrix and linear operator
4. Matrix algebra. Inverse matrix. Determinant
5. Scalar, vector, and mixed product of vectors
6. Linear system and its solution
7. The concept and geometrical and physical meaning of eigenvalue and eigenvector (elective)
8. The concept of function, graph, and inverse function
9. Elementary functions. Functions important in applications
10. The concept of sequence, limit of sequences, series, and limits of functions
11. The concept of derivative, geometrical and physical significance
12. Properties of derivatives. Derivatives of elementary functions
13. Linear approximation, quadratic approximation, and Taylor series
14. Decline, growth, local extrema, convexity, concavity, inflection points, and their physical significance
15. Analysis of functions using derivatives

PREREQUISITES FOR COURSE ENROLLMENT
None

PREREQUISITES FOR ATTENDING THE COURSE EXAM
None

DEVELOPMENT OF GENERAL AND SPECIFIC SKILLS BY STUDENTS
Acquire techniques for working with vectors, matrices, determinants, functions of one variable, their graphs and derivatives and acquire the ability to relate these techniques to physical and engineering problems

STUDENTS OBLIGATIONS AND PERFORMANCE MONITORING METHODS
Participate and follow along in class, 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. Distinguish and apply number systems, their notations, and arithmetic operations
2. Demonstrate the ability to learn independently and recognize the need for lifelong learning
3. Use the coordinate system (in the plane, in space, and in higher dimensions) and basic mathematical constructions with it: vectors, matrices, systems of linear equations
4. Apply elementary functions, distinguish their graphs and interpret the corresponding relationship between dependent quantities
5. Master the concept of derivative, its physical and geometrical interpretation and apply it in solving and modeling practical problems
6. Actively apply the appropriate basic procedures in the programming languages MatLab or GNU Octave
7. Describe phenomena in chemical engineering using a dictionary and the tools of fundamental sciences - mathematics, physics, and chemistry
8. Select appropriate methods of analysis, modeling, simulation, and optimization
9. Apply a scientific approach to real-world chemical engineering problems
10. Apply techniques and methods with an awareness of their limitations

1. Lekcije iz Matematike 1, http://matematika.fkit.hr, I. Gusić,
2. Matematika 1, vježbe, http://matematika.fkit.hr, I. Baranović, M. Jerković,
3. Primjeri kolokvija i pismenih ispita, http://matematika.fkit.hr, Zavod za matematiku,
4. Matematika 1, http://lavica.fesb.hr/mat1/predavanja, I. Slapničar,
5. Račun - diferencijalni i integralni, Z. Šikić, L. Krnić, Školska knjiga, 1992.

Mandatory course - Regular studij - Chemical Engineering