## DOP204 Numerical Methods

 Code DOP204 Name Numerical Methods Status Compulsory/Courses of Limited Choice Level and type Undergraduate Studies, Academic Field of study Mathematics and Statistics Faculty Academic staff Ilmārs Iltiņš, Raisa Smirnova, Andrejs Koliškins Credit points 2.0 (3.0 ECTS) Parts 1 Annotation Solution of linear equation systems by direct, iterative and variation methods. Solution of nonlinear equations and systems. Interpolation, aproximation, mean square method, their applications. Incorrect problems. Regularization with Tikhonov method.. Goals and objectives of the course in terms of competences and skills After successful completion of the study course, a student is able to perform the simplest numerical methods; to understand problems that can occur in the process of applying numerical methods; to use the MATHEMATICA software in order to solve the simplest problems; to use the built-in functions of MATHEMATICA. Learning outcomes and assessment After successful completion of the study course, a student is able to demonstrate the understanding of methods of solving simultaneous linear equations based on factoring of matrix. Able to apply these methods by means of MATHEMATICA software. - Homework assignment. Assignments relevant to the material studied are included in the final examination. Able to demonstrate the understanding of Seidel method, Jacobi method, method of simple iteration, method of minimal discrepancy. Able to apply these methods by means of MATHEMATICA software. - Homework assignment. Assignments relevant to the material studied are included in the final examination. Able to demonstrate the understanding of the concept of convergence and the causes of eventual nonconvergence. - Homework assignment. Assignments relevant to the material studied are included in the final examination. Able to perform table interpolation by linear combination of functions, by cubic spline. Able to perform table approximation by means of method of minimal squares. - Homework assignment. Assignments relevant to the material studied are included in the final examination. Able to apply the method of simple iterations and the Newton's method to solve equations and simultaneous equations. - Homework assignment. Assignments relevant to the material studied are included in the final examination. Able to demonstrate the understanding of the main methods of numerical differentiation and integration. - Homework assignment. Assignments relevant to the material studied are included in the final examination. Able to demonstrate the understanding of the concept of difference equations. Able to apply Euler's method and the method of Runge-Kutta to solve Cauchy problem. - Homework assignment. Assignments relevant to the material studied are included in the final examination. Able to demonstrate the understanding of the concept of ill-conditioned problem. Able to demonstrate the understanding of the influence of the coefficient of determination on the quality of solution. - Assignments relevant to the material studied are included in the final examination. Course prerequisites Linear algebra, analytical geometry, calculus and preliminary knowledge of MATHEMATICA software.

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