## MTH504 Numerical Analysis for Research of Dynamics of Machines (for Master Students)

 Code MTH504 Name Numerical Analysis for Research of Dynamics of Machines (for Master Students) Status Compulsory/Courses of Limited Choice Level and type Post-graduate Studies, Academic Field of study Mechanics, Mechanical Engineering, Machine Building Faculty Academic staff Jānis Auziņš, Sabīne Upnere Credit points 4.0 (6.0 ECTS) Parts 1 Annotation This is the basic course on the use of numerical methods for the analysis and optimization of machine and mechanism dynamics. In the present field the researchers have to deal with complex problems of numerical mathematics, which demand the proficiency level above the average and is not limited to knowledge of the basic math course. . The main topics of the study subject are:. Ideology of engineering calculation. Preciseness/Exactress, stability, complexity, automation. Analysis of linear systems of freguency and time diapason. Methods of analysis of nonlinear systems. Stability of numerical methods. Hard and badly defined systems. Covered methods. Meshanisms with geometrical sites: differential - algebrical systems. Analysis of machine regulation systems. Simplifying the dynamical models. Programms: MathCad, WorkingModel, MSC ADAMS.. Goals and objectives of the course in terms of competences and skills The aim of the course is to attain the ability to apply the numerical methods for the analysis and optimization of machines, mechanisms and other complex mechanical systems, implemented in universal computer software. After completing this course, students will be able to: (1) estimate the complexity and costs of simulation or optimization tasks as well as predict the main problems before the implementation of the work; (2) be able to use universial software MathCad, specified software WorkingModel, ADAMS/View for simulation of mecanisms and machines and to choose the best of available software and method for solving of given problem. Learning outcomes and assessment 1. Understad the concept of the sources of calculation errors and stability - Questions at the exam 2. Be aware of the main interpolation and approximation methods of functions - Questions at the exam 3. Know the main direct and iterative methods for solving of systems of linear algebraic equations - Questions at the exam 4. Understand the modal analysis of linear systems - Questions at the class and in home works 5. Know the main methods of numerical integration and differentiation of functions - Questions at the exam 6. Know the mainly used methods of numerical solving of ODE systems - Questions in the home works 7. Understand the stability of numerical methods for solving of ODE - Questions at the exam 8. Be able to use commercial software for numerical methods - Questions in the practical works and in the coursework. Course prerequisites Mathematics, theoretical mechanics, computer-aided analysis of mechanisms - basic course

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