Numerical Methods for Engineers

Course Information
TitleΑριθμητικές Μέθοδοι για Μηχανικούς / Numerical Methods for Engineers
SchoolChemical Engineering
Cycle / Level1st / Undergraduate
Teaching PeriodSpring
Course ID20000684

Programme of Study: PPS Tmīmatos CΗīmikṓn Mīchanikṓn (2021-sīmera)

Registered students: 0
OrientationAttendance TypeSemesterYearECTS
KORMOSCompulsory Course425

Class Information
Academic Year2019 – 2020
Class PeriodSpring
Faculty Instructors
Instructors from Other Categories
Weekly Hours4
Class ID
Course Type 2016-2020
  • Background
  • General Knowledge
  • Skills Development
Course Type 2011-2015
General Foundation
Mode of Delivery
  • Face to face
Digital Course Content
Language of Instruction
  • Greek (Instruction, Examination)
General Prerequisites
Advanced Mathematics, Introduction to Computers
Learning Outcomes
1. Learning of simple numerical methods for the solution of algebraic and ordirary differential equations. 2. Getting familiar with MATLAB environment 3. Application of numerical methods in MATLAB for the solution of common Chem.Eng. problems.
General Competences
  • Apply knowledge in practice
  • Retrieve, analyse and synthesise data and information, with the use of necessary technologies
  • Work autonomously
Course Content (Syllabus)
Introduction. Need for numerical analysis in chemical engineering. Numerical solution of SYSTEMS OF LINEAR ALGEBRAIC EQUATIONS. Gauss Elimination – Pivoting – LU Decomposition. Iterative Methods. NON LINEAR ALGEBRAIC EQUATIONS. Picard and Newton methods for a single equation. Newton-Raphson method – solution of systems of non linear algebraic equations. INTERPOLATION AND CURVE FITTING: Lagrange interpolation, Newton interpolation, Splines. NUMERICAL INTEGRATION: Newton- Cotes formulas, the trapezoidal rule, Simpson's rules, Gauss quadrature. ORDINARY DIFFERENTIAL EQUATIONS – INITIAL VALUE PROBLEMS. Explicit and implicit Euler methods. Euler Predictor-Corrector. 4th order Runge-Kutta. Systems of ODE-IVP. Numerical Stability. Stiffness, step size control, errors. ORDINARY DIFFERENTIAL EQUATIONS – BOUNDARY VALUE PROBLEMS. Finite Differences for the solution of a single equation. Systems of equations. COMPUTER LAB: Introduction to MATLAB. Plotting. M-files. Application of Gauss Elimination for the solution of systems of linear algebraic equations. Computational cost. Ill Conditioning. Jacobi and Gauss-Seidel methods. Convergence. Picard and Newton-Raphson method – solution of a unique NL algebraic equation. Solution of systems on NL algebraic equations. Application of Euler and Runge-Kutta Method methods for the solution of an ODE-IVP equation. Effect of step size. Solution of systems of ODE-IVP. Stability. Stiffness.
linear systems, non-linear systems, ODE-IVP, ODE-BVP, numerical error, matrix condition, iterative method, stiffness, finite differences
Educational Material Types
  • Slide presentations
  • Video lectures
  • Book
Use of Information and Communication Technologies
Use of ICT
  • Use of ICT in Course Teaching
  • Use of ICT in Laboratory Teaching
  • Use of ICT in Communication with Students
Course Organization
Laboratory Work30
Interactive Teaching in Information Center45
Student Assessment
30% homework 20% intermediate test (optional) 50% final test
Student Assessment methods
  • Written Assignment (Formative, Summative)
  • Written Exam with Problem Solving (Formative, Summative)
  • Labortatory Assignment (Formative, Summative)
Course Bibliography (Eudoxus)
Αριθμητικές μέθοδοι για προβλήματα μηχανικής, Πρ. ΝΤΑΟΥΤΙΔΗΣ, Σπ. ΜΑΣΤΡΟΓΕΩΡΓΟΠΟΥΛΟΣ, Ευμ. ΣΙΔΗΡΟΠΟΥΛΟΥ, εκδ.ΑΝΙΚΟΥΛΑ 2010 Αριθμητικές μέθοδοι για μηχανικούς, S. C. Chapra S. & R. P. Canale, (7η εκδοση)., εκδ. ΤΖΙΟΛΑ 2017 Αριθμητικές υπολογιστικές μέθοδοι στην επιστήμη και τη μηχανική,C.POZRIKIDIS, εκδ. ΤΖΙΟΛΑ 2006
Last Update