2022/2023

Спецкурс по математическому анализу, ICEF Academia

Статус: Дисциплина общефакультетского пула

Кто читает: Международный институт экономики и финансов

Когда читается: 1-4 модуль

Охват аудитории: для своего кампуса

Преподаватели: Патрик Анатолий Евгеньевич

Язык: английский

Кредиты: 6

Контактные часы: 64

Course Syllabus

Abstract

It is expected that students attend classes and lectures of the main ICEF 1st year Calculus subject, and that they successfully completed “Algebra and Introduction to Calculus” subject at the level of secondary school programme. · Module I: rational and irrational numbers, the method of mathematical induction, limits of sequences, properties of continuous functions, differentiable functions, derivatives. · Module II: higher derivatives, the Taylor formula, convergence of infinite series, anti-derivatives and indefinite integrals. · Module III: functions of two real variables, extreme values, constraint maximization, absolute maxima and minima, classical inequalities, double and triple integrals, calculation of volumes and surface areas. · Module IV: topics from AP Calculus BC: differential and functional equations, Taylor series.

Learning Objectives

• enable students to to solve advanced problems from selected chapters of the main Calculus course
• show how to deal with double and triple integrals and use them for calculating volumes, surface areas and for solving various problems from probability theory

Expected Learning Outcomes

• Apply mean value theorem
• Estimate approximation error, apply Taylor formula
• Apply the main theorems (EVT, IVT)
• Integrate rational functions, calculate anti-derivatives
• Calculate limits of sequences and solve advanced related problems
• Calculate masses, volumes, and areas of surfaces
• investigate convergence for infinite series
• Solve Bernoulli equations, second-order equations with constant coefficients
• solve functional equations
• Use extreme values, differentiation, Lagrange method, Polar coordinates
• Change variables, write down iterated integrals

Course Contents

• Prologue
• Sequences. Limit of a sequence.
• Properties of continuous functions
• Differentiable functions.
• Higher derivatives. Taylor formula.
• Infinite series.
• Anti-derivatives.
• Functions of two and several variables.
• Definite integrals
• Double integrals.
• Applications of double integrals
• Triple integrals
• Differentials Equations
• Calculus BC APT questions

Assessment Elements

• April exam
• midterm exam 1
• weakly quizzes
• midterm exam 3
• midterm exam 4
• midterm exam 2

Interim Assessment

• 2022/2023 4th module
  0.1 * weakly quizzes + 0.5 * April exam + 0.1 * midterm exam 4 + 0.1 * midterm exam 2 + 0.1 * midterm exam 3 + 0.1 * midterm exam 1

Bibliography

Recommended Core Bibliography

• Spivak, M. (1998). Calculus On Manifolds : A Modern Approach To Classical Theorems Of Advanced Calculus. New York: CRC Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=421137

Recommended Additional Bibliography

• Binmore, K. G. (1982). Mathematical Analysis : A Straightforward Approach (Vol. Second edition). Cambridge [Cambridgeshire]: Cambridge University Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=510997
• Дифференциальное и интегральное исчисление в примерах и задачах. Функции одной переменной : учеб. пособие для вузов, Марон, И. А., 2008