Кто читает:: Кафедра фундаментальной математики (Факультет информатики, математики и компьютерных наук (Нижний Новгород))

Статус:: Курс по выбору

Когда читается:: 1-й курс, 3, 4 модуль

Abstract

Numerical computations historically play a crucial role in natural sciences and engineering. These days however, it’s not only traditional «hard sciences»: whether you do digital humanities or biotechnology, whether you design novel materials or build artificial intelligence systems, virtually any quantitative work involves some amount of numerical computing . These days, you hardly ever implement the whole computation yourselves from scratch. We rely on libraries which package tried-and-tested, battle-hardened numerical primitives. It is vanishingly rare however that a library contains a single pre-packaged routine which does all what you need. Numerical computing involves assembling these building blocks into computational pipelines. This kind of work requires a general understanding of basic numerical methods, their strengths and weaknesses, their limitations and their failure modes. And this is exactly what this course is about. It is meant to be an introductory, foundational course in numerical analysis, with the focus on basic ideas. We will review and develop basic characteristics of numerical algorithms (convergence, approximation, stability, computational complexity and so on), and will illustrate them with several classic problems in numerical mathematics. You will also work on implementing abstract mathematical constructions into working prototypes of numerical code. Upon completion of this course, you will have an overview of the main ideas of numerical computing, and will have a solid foundation for reading up on and working with more advanced numerical needs of your specific subject area. As prerequisites for this course, we assume a basic command of college-level mathematics (linear algebra and calculus, mostly), and a basic level of programming proficiency.

Learning Objectives

Learn to numerically solve problems from various areas of mathematics (linear algebra, analysis).

Expected Learning Outcomes

Ability to find a solution to algebraic equations in the Matlab environment
The ability to numerically find solutions to differential equations and display their graphs.

Course Contents

Numerical solution of algebraic equations
Numerical integration of ordinary differential equations.

Assessment Elements

Устный опрос
Экзамен

Interim Assessment

2023/2024 4th module
0.3 * Устный опрос + 0.4 * Устный опрос + 0.3 * Экзамен

Bibliography

Recommended Core Bibliography

Mukherjee, K. K. (2019). Numerical Analysis. [N.p.]: New Central Book Agency. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=2239733
Тынкевич, М. А. Введение в численный анализ : учебное пособие / М. А. Тынкевич. — Кемерово : КузГТУ имени Т.Ф. Горбачева, 2017. — 179 с. — ISBN 978-5-906969-35-4. — Текст : электронный // Лань : электронно-библиотечная система. — URL: https://e.lanbook.com/book/115170 (дата обращения: 00.00.0000). — Режим доступа: для авториз. пользователей.

Recommended Additional Bibliography

Timo Heister, Leo G. Rebholz, & Fei Xue. (2019). Numerical Analysis : An Introduction. Berlin/Boston: De Gruyter. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=2103428

Магистерская программа «Математика»

Адрес:

Introduction to Numerical Analysis

Course Syllabus