This course, in slight variations and different names, is offered in different study programs:
- Computational methods, Mechanical Engineering, Bachelor degree
- Computational methods, Mechatronics and Robotics, Bachelor degree
- Numerical methods, Computer Science, Bachelor degree
Course objectives
Identification of numerical problems in engineering. Understanding and application of basic numerical methods. Basic knowledge of the Python programming language and relevant numerical and visualization modules. Independent writing of short computer programs and use of existing software for solving numerical tasks.
Expected course learning outcomes
Identify appropriate computational methods for simple mathematical formulations of engineering problems. Properly interpret the fundamental idea of each computational method. Correctly assess the advantages and disadvantages of each computational method. Compare computational methods applicable to the same type of problem. Apply existing computer programs to simple problems. Develop simple computer programs in the Python programming language for specific computational methods following instructions. Evaluate the results of computational methods.
Course content
Examples in engineering for nonlinear equations with one unknown. Corresponding numerical methods and comparison. Convergence criteria of iterative algorithms. Computer programs in Python. Optimization of a single-variable function with examples from engineering. Corresponding numerical methods and comparison. Computer programs in Python. Examples in engineering for systems of linear equations. Corresponding exact and numerical methods and their comparison. Error in solving using computers. Computer programs in Python. Examples in engineering for curve fitting to data. Regression analysis. Interpolation and spline curves in computer graphics. Computer programs in Python. Examples in engineering for definite integrals. Corresponding numerical methods. Increasing the accuracy of calculations versus accumulation of rounding errors. Computer programs in Python. Examples in engineering for ordinary differential equations and systems of ordinary differential equations. Corresponding numerical methods. Local and global errors. Computer programs in Python.