1. SylabUZ
2. Wydział Mechaniczny
3. semestr zimowy 2023/2024
4. Management and Production Engineering - pierwszego stopnia z tyt. inżyniera
5. Numerical Algorithms

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Numerical Algorithms - opis przedmiotu

Cel przedmiotu

The aim of the course is to provide information on basic numerical algorithms, developing the ability to use numerical algorithms to solve simple engineering problems.

Wymagania wstępne

Zapisz zmiany

basic computer skills, basic mathematics course

Zakres tematyczny

Lecture

L1: Presentation of the basic topics of numerical methods.

L2: Solving systems of linear equations by Gaussian elimination and simple iterations.

L3: Polynomial and and spline interpolation. Least square approximation with polynomials and orthogonal polynomials.

L4: Integration of univariate functions: midpointS, trapezoids and Simpson methods.

L5: Solving non-linear equations: bisection, false position, secant, Newton's methods. One-dimensional unconstrained optimization: golden-section search, parabolic interpolation.

L6: Solving ordinary differential equations by Euler and Runge-Kutta methods.

L7: Final test.

 

Laboratory

L1: Introduction to Google Colab environment, variables, arithmetic operators and standard functions in Python,

L2: Creating scripts and functions.

L3: Graphical presentation of data.

L4: Solving problems requiring the use of matrix calculus.

L5: Solving systems of linear equations.

L6: Problems requiring determination of eigenvalues and eigenvectors.

L7: Polynomial interpolation and spline interpolation.

L8: Approximation of measurement data.

L9: Interpolation and approximation of multivariate functions.

L10: Solving computational problems requiring numerical integration.

L11: Solving systems of non-linear equations.

L12. Searching for the minimum of univariate and multivariate functions.

L13: Numerical differentiation.

L14: Solving ordinary differential equations by Runge-Kutta methods.

L15: Final test.

Metody kształcenia

Lecture: a conventional lecture

Laboratory: practical classes in the computer laboratory

Efekty uczenia się i metody weryfikacji osiągania efektów uczenia się

Opis efektu	Symbole efektów	Metody weryfikacji	Forma zajęć

Warunki zaliczenia

Lecture: a positive result of the assessment via a written test

Laboratory: the condition for passing the laboratory is to pass all laboratory tasks and a positive grade in the final test

Final grade: the condition for passing the course is to pass all its forms, the final grade for the course is the arithmetic mean of the grades for individual forms of classes

Literatura podstawowa

1. Chapra S., Canale R., Numerical Methods for Engineers, McGraw Hill, 2020.
2. Gupta R. K., Numerical Methods - Fundamentals and Applications, Cambridge University Press, 2019.
3. Kong Q., Siauw T., Bayen A., Python Programming and Numerical Methods - A Guide for Engineers and Scientists,  Elsevier, 2020.
4. Miles W., Numerical Methods with Python for the Sciences, De Gruyter, 2023.

Literatura uzupełniająca

1. Björck A.,  Numerical Methods in Matrix Computations, Springer, 2015.
2. Johansson R., Numerical Python: Scientific Computing and Data Science Applications with Numpy, SciPy and Matplotlib, Apress, 2018.
3. Nazareth J. L., Concise Guide to Numerical Algorithmics: The Foundations and Spirit of Scientific Computing, Springer, 2023.

Uwagi

Zmodyfikowane przez dr inż. Grzegorz Pająk (ostatnia modyfikacja: 03-05-2023 11:48)