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  1. Faculty of Chemical Engineering and Technology
  2. Introduction to mathematical methods in engineering

Introduction to mathematical methods in engineering

en hr
Code:
156899
ECTS:
6.0
Lecturers in charge:
Erna Begović Kovač, Associate Professor, PhD
Miroslav Jerković, Assistant Professor, PhD
Lecturers:
Lectures:
Erna Begović Kovač, Associate Professor, PhD
Miroslav Jerković, Assistant Professor, PhD
Take exam:
Studomat
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1. komponenta
Lecture type Total
Lectures 45
Seminar 15
Description:
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
Learning outcomes:
  1. Distinguish the types of partial differential equations and their physical interpretations
  2. Demonstrate the ability to work independently with minimal guidance
  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 ideas in the context of a scientific research work
  9. Form opinions based on incomplete or limited information
  10. Objectively evaluate the results of the work in order to present them concisely
Literature:
  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,
2. semester
Izborni kolegij - Regular modul - Advanced Materials and Technologies
Izborni kolegij - Regular modul - Applied Organic Chemistry
Izborni kolegij - Regular modul - Environmental Chemistry and Green Technologies
Consultations schedule:
  • For consultation hours, please contact the course lecturers.