Objectives and competences
Objectives:
- Students understand the importance and key attributes of numerical solutions.
- They know the theoretical basics of different numerical methods and their purpose.
- Use of a programming language for numerical solutions.
- Understand the source and propagation of numerical errors.
- Use of different numerical methods for solving equations and system of equations.
- understand the process and techniques of solving differential equations as algebraic systems with initial and boundary conditions.
Competences:
- Define and describe the meaning of numerical solutions.
- Identify physical properties and select numerical method for mathematical description.
- Identify types of domain discretization.
- Distinguish approaches to numerical simulations.
Content (Syllabus outline)
- The purpose of numerical modelling.
- Basic methods of numerical modelling and mathematical formulation.
- Discretization problems and computational errors.
- Numerical approximations and interpolations.
- Taylor series.
- Physical descriptions of processes in energy: leading equations, boundary, and initial conditions.
- Finite difference method, formulation, discretization, advantages, weaknesses.
- The use of numerical modelling: selection of methods, preparation of simulations, analysis of results.
Learning and teaching methods
- Frontal lectures
- Tutorials
- Seminar assignment
Intended learning outcomes - knowledge and understanding
Knowledge and understanding:
- Students understand the discrete systems in computer notation.
- Can describe and define the characteristics of different numerical methods.
- Understand the purpose and limitations of numerical analysis.
- Approaches to the correct interpretation of the results of numerical solutions.
Intended learning outcomes - transferable/key skills and other attributes
Transferable/key competences and other abilities:
- Communication skills: oral defence of seminar assignment.
- Computer skills: use of programming language for numerical solutions of problems and use of advanced computer programs.
- Problem solving: preparation, execution, and interpretation of results of numerical analyses.
Readings
M.Hriberšek, J.Ravnik: Numerično modeliranje in računalniške simulacije; 1 del. Gradniki numeričnega računanja, Fakulteta za strojništvo, UM, 2012
B.Orel: Uvod v numerične metode, Fakulteta za računalništvo in informatiko, ULJ, 2021
B.Jurčič Zlobec, Numerične metode, Fakulteta za elektrotehniko, ULJ, 2007
Dodatna literatura/additional literature:
A.Kaw, E.E.Kalu: Numerical Methods with Applications, 2nd Ed.University of South Florida, 2008
T.Young, M.J.Mohlenkamp: Introduction to Numerical Methods and Matlab Programming for Engineers, Department of Mathematics, Ohio University, 2018
S.Calogero: Introduction to finite difference method; Geteborg Univeristet, Chalmers, 2015
Additional information on implementation and assessment Method (written or oral exam, coursework, project):
-coursework
-oral/quiz exam
-written exam
