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## Numerical Methods

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Course Unit Code Number of ECTS Credits Allocated Type of Course Unit * 310-2304/01 5 ECTS credits Compulsory First Cycle Winter, Summer Semester Face-to-face Czech, English Course succeeds to compulsory courses of previous semester KUC14 prof. RNDr. Radek Kučera, Ph.D. The course is devoted to basic numerical methods of the linear algebra and the mathematical analysis. The following topics are presented: direct and iterative methods for solving systems of linear equations; eigenvalue problems; iterative solving of nonlinear equations; interpolation and approximation of the function data; numerical computation of integrals and derivatives; numerical solving of initial value problems for ordinary differential equations; using MATLAB in numerical computations. The course is an introduction to the numerical methods. The main goal consists in explanations of fundamental numerical principles so that students should be able to decide about an appropriate method for problems arising in the other courses or in the technical practice. An important ingredient is the algorithmic implementation of numerical methods and the usage of the standard numerical software. The graduate of this course should know: • to recognize problems suitable for solving by numerical procedures and to find an appropriate numerical method; • to decide whether the computed solution is sufficiently accurate and, in case of need, to assess reasons of inaccuracies; • to propose an algorithmic procedure for solving the problem and to choice a suitable computer environment for its realization. It is necessary to complete Mathematics 1 and Mathematics 2 courses or their equivalents. Program of lectures =================== Week. Lecture ------------- 1st Course contents, the issue of errors, stability calculations. 2nd Solution of nonlinear equations, separation of roots, the simplest method. 3rd Newton's method and simple iterations. 4th Direct methods for solving linear equations, Gaussian elimination and LU-decomposition. 5th Eigenvalues and eigenvectors, numerical calculation. 6th Iterative methods for solving linear equations. 7th Interpolation by polynomials and splines. 8th Least squares approximation. 9th Numerical differentiation and integration. 10th Extrapolation in the calculation of integrals. Gaussian integration formulas. 11th One-step method for solving initial value problems for ordinary differential equations. 12th Multistep methods. 13th Ordinary differential equations of higher order. 14th Systems of differential equations. Program of the excercises and the exam questions are analogous. Matalb program is used in the excersises. 1. Burden, R. L., Faires, J. D.: Numerical Analysis. Cengage Learning, 2011 2. Chapra, S., Canale, R.: Numerical Methods for Engineers. McGraw-Hill Education, 2009. 1. Burden, R. L., Faires, J. D.: Numerical Analysis. Cengage Learning, 2011 2. Chapra, S., Canale, R.: Numerical Methods for Engineers. McGraw-Hill Education, 2009. 1. Qaurteroni, A., Sacco, R., Saleri, F.: Numerical Mathematics. Springer, 2007. 2. Süli, E., Mayers, D.: An introduction to Numerical Analysis. Cambridge University Press, 2003. 3. Van Loan, C. F.: Introduction to scientific computing. Prentice Hall, Upper Saddle River, NJ 07459, 1999. 1. Qaurteroni, A., Sacco, R., Saleri, F.: Numerical Mathematics. Springer, 2007. 2. Süli, E., Mayers, D.: An introduction to Numerical Analysis. Cambridge University Press, 2003. 3. Van Loan, C. F.: Introduction to scientific computing. Prentice Hall, Upper Saddle River, NJ 07459, 1999. Lectures, Individual consultations, Tutorials Tasks are not Defined