Subject Datasheet
Download PDFBudapest University of Technology and Economics  
Faculty of Transportation Engineering and Vehicle Engineering 
1. Subject name  Numerical methods  
2. Subject name in Hungarian  Numerikus módszerek  
3. Code  BMEKOVRM121  4. Evaluation type  midterm grade  5. Credits  4 
6. Weekly contact hours  2 (9) Lecture  0 (0) Practice  1 (5) Lab  
7. Curriculum  Autonomous Vehicle Control Engineering MSc (A) Vehicle Engineering MSc (J) Transportation Engineering MSc (K) 
8. Role  Mandatory (mc) at Autonomous Vehicle Control Engineering MSc (A) Mandatory (mc) at Vehicle Engineering MSc (J) Mandatory (mc) at Transportation Engineering MSc (K) 

9. Working hours for fulfilling the requirements of the subject  120  
Contact hours  42  Preparation for seminars  11  Homework  20 
Reading written materials  35  Midterm preparation  12  Exam preparation  0 
10. Department  Department of Aeronautics and Naval Architectures  
11. Responsible lecturer  Dr. Rohács József  
12. Lecturers  Dr. Bicsák György  
13. Prerequisites  
14. Description of lectures  
Introduction: scope of lectures, content and requirements. System analysis, model generation, modelling and simulation. General models, simplifications. Source of errors, model types and solution possibilities. Analytic, geometric and numerical solutions. Functions, vectors, matrices, basic operations. Classical and floatingpoint errorcalculation. Sensitivity and numerical stability. Investigation of solution technics. Representing the solutions, evaluation. Solution of system of equations. Single variable, nonlinear equations. Successive approximation, Newton iteration and secant method. Solution of polynomial equation. Horner method and Newtonmethod. Numerical solution of linear system of equations. Gausselimination and LU decomposition. Numerical solution of Eigenvalue problem. Extremum problems, optimization. Linear programming, simplex method. Optimization of nonlinear functions. Nonlinear programming. Gradient method. Functions, series of functions, approximation. Taylor series, MacLaurin series, Fourier series. Polynomialinterpolation, Newton, Lagrange and Hermite interpolation. Application of Splines. Generating curves and surfaces with using Splines. Bezier polynomials, NURBS surfaces. Approximation, Chebyshev and Padé approximation. Harmonical analysis, fast Fourier transformation (FFT). Numerical differentiation, integration. Approximation of derivatives using finite difference method. Approximation of derivatives using Lagrange and Newton interpolation formulas. Numerical integration, general quadrature formula. Trapezoidal and Simpson formula. Romberg iteration. Initial value problems, ordinary differential equations. Explicit formulas: Euler method, 4th order RungeKutta method. Implicit formulas, predictorcorrector methods. Approximation of partial differential equations. Boundary conditions, finite difference method, finite volume method, finite element method. Stochastic process modelling. System input data generation. MonteCarlo simulation. 

15. Description of practices  
16. Description of labortory practices  
MATLAB application of the introduced methods.  
17. Learning outcomes  
A. Knowledge


18. Requirements, way to determine a grade (obtain a signature)  
2 midterm exams from the theoretical part, 50 points / exam. 1 project work for a group of 45 students, for n*100 points (n is the number of students). The points can be divided between the group members according to their whish. Grade calculation: summing all the points, the total points gives the final grade as follows: 0 – 79  1; 80 – 109  2; 110 – 139  3; 140 – 169  4; 170 – 5 

19. Opportunity for repeat/retake and delayed completion  
Because of the pointcollection system, no minimum points are determined for the midterm exams or for the project work. The retake possibilities are the following: on the replacement week the 1st midterm exam, or the 2nd midterm exam can be tried again for 50 points, or a combined 1st+2nd midterm exam retake for 100 points.  
20. Learning materials  
Examples, documents and training materials, given out during lectures, presentations. György Bicsák, Dávid Sziroczák, Aaron Latty: Numerical Methods Ramin S. Esfandiari: Numerical methods for engineers and scientists using MATLAB, ISBN 9781466585706 Erwin Kreyszig: Advanced engineering mathematics, 10th edition, ISBN 9780470458365 

Effective date  10 October 2019  This Subject Datasheet is valid for  2023/2024 semester II 