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1. |
Course title |
Numerical methods |
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2. |
Course of Study, Speciality |
2, Mathematics and information technologies (majors in) Major in 1-31 03 08-01 Web development and Internet Technologies Major in 1-31 03 08-02 Mathematical and Software of Mobile Devices |
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3. |
Semester |
3 |
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4. |
Credits |
1 |
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5. |
Lecturer |
Candidate of Physical and Mathematical Sciences, Associate Professor IGNATENKO Marina Viktorovna |
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6. |
Course goal |
– construction of mathematical models, determination of their role and significance; – familiarity with the basic principles of developing computational methods for typical and new mathematical models; – study and development of the theory and applications of computing methods, their computer implementations; – analysis of the reliability of numerical results, their interpretation and implementation. |
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7. |
Prerequisites |
– algebra and number theory; – Geometry, mathematical analysis; – modern systems of computer modeling |
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8. |
Course Topics |
Introduction. On some problems and content of computational mathematics. On the content and purpose of the computational experiment in the interpretation of A.A. Samarskiy. Elements of the theory of errors. Significant, true and dubious figures in the recording of an approximate number. Absolute, relative error. The direct problem of the theory of errors. The error of arithmetic operations. Inverse problem of the theory of errors. Examples of unstable algorithms. Interpolation and approximation of functions. Formulation of the problem. Interpolation polynomials of Lagrange and Newton. Estimates of the residual terms of interpolation polynomials and their minimization. Polynomials of Chebyshev. Interpolation by splines. Numerical differentiation of functions and estimation of its error. The concept of numerical interpolation and differentiation of functions of several variables. Discrete and fast Fourier transform. The concept of the method of least squares. |
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9. |
Recommended Literature |
1. Бахвалов Н.С., Жидков Н.П., Кобельков Г.М. Численные методы. – М.: Наука, 1987. 2. Крылов В.И., Бобков В.В., Монастырный П.И. Вычислительные методы высшей математики. В 2 т. – Минск: Выш. шк., 1972, 1975. 3. Крылов В.И., Бобков В.В., Монастырный П.И. Начала теории вычислительных методов. Интерполирование и интегрирование. – Минск: Наука и техника, 1983. 4. Мысовских И.П. Лекции по методам вычислений: учеб. пособие. – СПб.: Изд–во С.-Петерб. ун-та, 1998. 5. Сборник задач по методам вычислений: учеб. пособие / Под ред. П.И. Монастырного, – Минск: Изд. центр БГУ, 2007. 6. Методы вычислений. Интерполирование и интегрирование: курс лекций / М.В. Игнатенко. – Минск: БГУ, 2006. |
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10. |
Teaching Methods |
Passive, active, interactive, verbal, visual, problematic |
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11. |
Teaching language |
Russian |
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12. |
Requirements, current control |
– report on laboratory work; – mathematical dictation; – colloquium. |
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13. |
Method of certification |
Credit |