1. komponenta

Lecture type	Total
Lectures	30
Seminar	15

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

COURSE OBJECTIVE
To introduce students to Fourier expansion, partial differential equations, dynamical systems, and their relation to engineering problems.

COURSE IMPLEMENTATION PROGRAM
1. Introductory lesson
2. Basic partial differential equations
3. Fourier expansion
4. One-dimensional wave equation
5. Two-dimensional wave equation
6. Thermal equation
7. Introduction to dynamical systems. The exponential and logistic equation
8. Two-dimensional dynamical systems. Examples of linear systems
9. Classification of two-dimensional linear systems
10. - 11. Nonlinear systems important in applications
12. - 13. Graphical solution of nonlinear systems
14. Three-dimensional dynamical systems. Lorenz equations (optional content)
15. Chaos (optional content)

PREREQUISITES FOR COURSE ENROLLMENT.
Fundamentals of differential and integral calculus (Mathematics 1, Mathematics 2)

PREREQUISITES FOR ATTENDING THE COURSE EXAM
None

DEVELOPMENT OF GENERAL AND SPECIFIC SKILLS BY STUDENTS
Students should be able to model basic engineering problems involving ordinary differential equations, partial differential equations, and autonomous systems of ordinary differential equations and solve these equations directly or graphically.

STUDENTS OBLIGATIONS AND PERFORMANCE MONITORING METHODS
Class participation, preparation, and presentation of seminar papers

TEACHING METHODS
Lectures, seminars, exercises (MatLab, GNU Octave), consultations

EXAMINATION METHODS
Seminar paper

METHODS FOR MONITORING THE COURSE QUALITY
Student Survey

1. Distinguish the types of partial differential equations and their physical interpretations
2. Critically evaluate data and draw conclusions
3. Interpret boundary and initial conditions
4. Apply Fourier expansion in solving some important partial differential equations
5. Understand the concept of the logistic equation and its role in modeling processes
6. Interpret a two-dimensional dynamical system and its solution and distinguish between linear and nonlinear systems
7. Actively apply the appropriate basic procedures in the MatLab or GNU Octave programming languages
8. Apply a broad and deep knowledge of mathematics, chemistry, chemical engineering, and other sciences to solve scientific, professional, and general social problems in the field of expertise
9. Solve problems using a scientific approach, even if having an incomplete or unusual formulation, and offer a range of possible solutions
10. Apply a scientific approach to real-world chemical engineering problems

1. Interni materijali Zavoda za matematiku, http://matematika.fkit.hr, I. Gusić,
2. Advanced Engineering Mathematics, E. Kreyszig, John Wiley & Sons Inc, 2006.
3. Differential Equations, Dynamical Systems - Introduction to Chaos, second edition, M.W.Hirsch, S.Smale, R.L.Devaney, Elsevier Academic Press, 2003.
4. Uvod u matematičku teoriju kaosa za inženjere, Skripta FER, M. Pašić,
5. Nonlinear Dynamics and Chaos: with application to physics, biology, chemistry, and engineering, S.H. Strogatz, Addison - Wesley, 1994.
6. A First Course in Chaotic Dynamical Systems, theory and experiment, R. L.Devaney, Addison Wesley, 1992.
7. An Introduction to Dynamical Systems and Chaos, http://www.ldeo.columbia.edu/~mspieg, M. Spiegelman,

Izborni kolegij - Regular modul - Chemical Engineering in Environmental Protection
Izborni kolegij - Regular modul - Chemical Process Engineering
Izborni kolegij - Regular modul - Chemical Technologies and Products
Izborni kolegij - Regular studij - Material Science and Engineering