Numerical Methods for Engineers
| Title | Αριθμητικές Μέθοδοι για Μηχανικούς / Numerical Methods for Engineers |
| Code | HY4 |
| Faculty | Engineering |
| School | Chemical Engineering |
| Cycle / Level | 1st / Undergraduate |
| Teaching Period | Spring |
| Common | No |
| Status | Active |
| Course ID | 20000684 |
Programme of Study: PPS Tmīmatos CΗīmikṓn Mīchanikṓn (2021-2026
Registered students: 215
| Orientation | Attendance Type | Semester | Year | ECTS |
|---|---|---|---|---|
| KORMOS | Compulsory Course | 4 | 2 | 5 |
| Academic Year | 2025 – 2026 |
| Class Period | Spring |
| Faculty Instructors |
|
| Instructors from Other Categories |
|
| Weekly Hours | 4 |
| Total Hours | 52 |
| Class ID | 600280286
|
Type Of Offer
- Disciplinary Course
- Challenge-Based Training Offer
Course Type 2021
Specific Foundation
Course Type 2016-2020
- Background
- General Knowledge
- Skills Development
Course Type 2011-2015
General Foundation
Mode of Delivery
- Face to face
Digital Course Content
- e-Study Guide https://qa.auth.gr/en/class/1/600280286
- At the Website of the School: https://cheng.auth.gr/
- eLearning (Moodle): https://elearning.auth.gr/course/view.php?id=6285
Erasmus
The course is also offered to exchange programme students.
Language of Instruction
- Greek (Instruction, Examination)
- English (Instruction, Examination)
Prerequisites
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.
Keywords
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
- Use of ICT in Student Assessment
Course Organization
| Activities | Workload | ECTS | Individual | Teamwork | Erasmus |
|---|---|---|---|---|---|
| Lectures | 26 | ✓ | ✓ | ||
| Reading Assigment | 50 | ✓ | ✓ | ||
| Interactive Teaching in Information Center | 26 | ✓ | |||
| Project | ✓ | ||||
| Written assigments | 24 | ✓ | ✓ | ||
| Exams | 24 | ✓ | ✓ | ||
| Total | 150 |
Student Assessment
Description
- With Lab Attendance and Completion of Assignments (Mandatory for 4th Semester):
-- Method: Oral and written examination on four distinct assignments.
-- Criteria: a) 40% Theory – correct application of numerical methods and understanding of the underlying mathematical concepts. b) 30% Implementation of algorithms using MATLAB in individual assignments. c) 30% Problem solving and troubleshooting during the four progress assessments throughout the semester.
- Without Lab Attendance – Final Examination:
-- Method: Final Examination
-- Criteria: First, submission of preparatory assignments before the final exam (pass/fail). Second Final examination : a) 30% solution of exam problems using MATLAB. b) Oral examination (40% theory, 30% application) guided by the preparatory assignments.
Student Assessment methods
- Written Assignment (Formative, Summative)
- Oral Exams (Formative, Summative)
- Written Exam with Problem Solving (Formative, Summative)
- Labortatory Assignment (Formative, Summative)
Bibliography
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
30-05-2025
