Module also offered within study programmes:
General information:
Name:
Numerical methods and statistics
Course of study:
2013/2014
Code:
RMS-1-306-s
Faculty of:
Mechanical Engineering and Robotics
Study level:
First-cycle studies
Specialty:
-
Field of study:
Mechatronics with English as instruction languagege
Semester:
3
Profile of education:
Academic (A)
Lecture language:
English
Form and type of study:
Full-time studies
Course homepage:
 
Responsible teacher:
dr hab. inż. Iwaniec Joanna (jiwaniec@agh.edu.pl)
Academic teachers:
dr hab. inż. Iwaniec Joanna (jiwaniec@agh.edu.pl)
Module summary

Description of learning outcomes for module
MLO code Student after module completion has the knowledge/ knows how to/is able to Connections with FLO Method of learning outcomes verification (form of completion)
Skills
M_U001 The student can formulate algorithms of the concerned issues and represent them by means of flowcharts. Activity during classes
M_U002 The student knows the MATLAB environment for numerical calculations and can use it for the purposes of solving practical engineering issues. Execution of laboratory classes
M_U003 The student is able to evaluate the computational complexity of (some) algorithms of numerical methods and, on this basis, to assess their suitability for engineering tasks to be solved. Execution of exercises
Knowledge
M_W001 The student has extensive and in-depth knowledge of linear algebra numerical methods, including methods of solving linear systems of equations. Test
M_W002 The student knows selected method of numerical integration and methods of solving differential equations. Execution of exercises
M_W003 The student knows numerical methods of eigen problem solving, singular value decomposition, condition number estimation and statistical analysis, the knowledge of which is essential for analyzing experimental results. Test
FLO matrix in relation to forms of classes
MLO code Student after module completion has the knowledge/ knows how to/is able to Form of classes
Lecture
Audit. classes
Lab. classes
Project classes
Conv. seminar
Seminar classes
Pract. classes
Others
Zaj. terenowe
Zaj. warsztatowe
E-learning
Skills
M_U001 The student can formulate algorithms of the concerned issues and represent them by means of flowcharts. - + + - - - - - - - -
M_U002 The student knows the MATLAB environment for numerical calculations and can use it for the purposes of solving practical engineering issues. + - + - - - - - - - -
M_U003 The student is able to evaluate the computational complexity of (some) algorithms of numerical methods and, on this basis, to assess their suitability for engineering tasks to be solved. + + + - - - - - - - -
Knowledge
M_W001 The student has extensive and in-depth knowledge of linear algebra numerical methods, including methods of solving linear systems of equations. + + + - - - - - - - -
M_W002 The student knows selected method of numerical integration and methods of solving differential equations. + + + - - - - - - - -
M_W003 The student knows numerical methods of eigen problem solving, singular value decomposition, condition number estimation and statistical analysis, the knowledge of which is essential for analyzing experimental results. + + + - - - - - - - -
Module content
Lectures:
  1. Basic concepts of statistical analysis.
  2. Selected methods of function interpolation.
  3. Selected methods of function approximation.
  4. Numerical integration.
  5. Numerical methods of solving nonlinear equations.
  6. Methods of solving ordinary differential equations.
  7. Methods of solving partial differential equations.
  8. Methods of eigenproblem solution estimation.
  9. MATLAB – environment for numerical computations.
  10. Basic concepts and fields of applications of numerical analysis.
  11. Sources of numerical errors. Numerical errors assessing.
  12. Conditioning of numerical problems and stability of algorithms.
  13. Review of matrix algebra. Methods of solving sets of linear equations.
Auditorium classes:
  1. Numerical errors assessing.
  2. Conditioning of numerical problems and stability of algorithms.
  3. Matrix algebra. Determining inverse and pseudo-inverse matrices.
  4. Methods of solving sets of linear equations.
  5. Example applications of numerical methods of solving nonlinear equations.
  6. Analysis of accuracy of solutions estimated with the use of selected methods of numerical integration.
  7. Methods of solving ordinary differential equations.
  8. Methods of solving partial differential equations.
  9. Methods of eigenproblem solution estimation.
  10. Numerical representation. Number systems.
  11. Flowcharts of selected numerical algorithms.
Laboratory classes:
  1. Methods of solving sets of linear equations.
  2. Basic operations of matrix algebra.

    (Multiplication and division of matrices, computations of determinants, condition numbers and decomposition into singular values).

  3. Applications of numerical integration methods.
  4. Function interpolation by means of Lagrange Interpolation Polynomials, Newton Interpolation Polynomials and splines.
  5. Solving differential equations with the application of the Euler and Runge-Kutta methods.
  6. Estimation of matrix eigenvalues and eigenvectors.
  7. Assessment of numerical errors and stability of selected algorithms.
  8. Applications of bisection, regula falsi, secant and Newton’s methods.
Student workload (ECTS credits balance)
Student activity form Student workload
Summary student workload 149 h
Module ECTS credits 5 ECTS
Participation in lectures 30 h
Participation in laboratory classes 15 h
Participation in auditorium classes 26 h
Preparation for classes 50 h
Examination or Final test 4 h
Realization of independently performed tasks 16 h
Preparation of a report, presentation, written work, etc. 8 h
Additional information
Method of calculating the final grade:

Arithmetic mean of grades from classes and laboratories.

Prerequisites and additional requirements:

Prerequisites and additional requirements not specified

Recommended literature and teaching resources:

1. Fausett L.: Numerical Methods. Algorithms and Applications, Prentice Hall, Pearson Education Inc., Upper Saddle River, New Jersey, 2003.
2. Björck A., Dahlquist G.: Metody Numeryczne, PWN, Warszawa, 1987.
3. Brzózka J., Dorobczyński L.: Programowanie w Matlab, Mikom, 1998.
4. Fortuna Z., Macukow B., Wąsowski J.: Metody numeryczne, WNT, Warszawa, 1982.
5. Jankowska J., Jankowski M.: Przegląd metod i algorytmów numerycznych, część I i II, WNT, Warszawa, 1981.
6. Mrozek B., Mrozek Z.: MATLAB i Simulink. Poradnik użytkownika, Helion, 2004.
7. Ralston A.: Wstęp do analizy numerycznej, PWN, 1983.
8. Regel W.: Statystyka matematyczna w Matlab, Mikom, 2003.
9. Turowicz A.: Teoria macierzy, Skrypt uczelniany AGH nr 895, Kraków, 1982.
10. http://www.mathworks.com

Scientific publications of module course instructors related to the topic of the module:

Additional scientific publications not specified

Additional information:

None