Математический анализ

2026/2027

Статус: Маго-лего

Кто читает: Институт когнитивных нейронаук

Где читается: Институт когнитивных нейронаук

Охват аудитории: для своего кампуса

Преподаватели: Фроленков Дмитрий Андреевич

Язык: русский

Кредиты: 6

Контактные часы: 40

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Аннотация

The course covers basic definitions and methods of calculus. This course, together with other mathematical courses, provides sufficient condition for students to be ready to participate in quantitative and computational modeling at the Master's Program "Cognitive Sciences and Technologies: From Neuron to Cognition". Students study the theory and applications of continuous functions their derivatives and integrals; solve optimization and approximation problems; study complex numbers and Fourier series as well as some basic material of the theory of differential equations.

Цель освоения дисциплины

know basic skills to start quantitative and computational modeling
know basic principles of calculus

Планируемые результаты обучения

Stiudents should be able to evaluate differnt difficult limits using L'hopital rule
Students should be able to detect composition of functions and to find the inverse function.
Students should be able to evaluate derivatives of complicated functions
Students should be able to evaluate different integrals using integration by parts or the change of variable.
Students should be able to evaluate limit of a function and to check if a function is continious or not
Students should be able to expand a function in Taylor series. Students should be able to evaluate limits using Taylor series
Students should be able to expand periodic functions in Fourier series.
Students should be able to find critical points of a function, to find segment where it is increasing (decreasing), to find maximum (minimum) of a function
Students should be able to rewrite the area under the curve as a definite integral. Students should be able to evaluate indefinite integrals of elementary functions.
Students should be able to sketch graph of a function based on the analysis of this function via derivatives
Students should be able to solve linear differential equations and separable differential equations.
The students should be able to prove basic properties of elementary functions using derivatives
The students should know basic properties of trigonometric and exponential functions. The students should know basic properties of logarithm
The students should understand the definition of sequence and its limit. The students should be able to evaluate limit of a sequence.