2022/2023
Математический анализ
Статус:
Маго-лего
Когда читается:
1 модуль
Онлайн-часы:
82
Охват аудитории:
для своего кампуса
Преподаватели:
Лукьяненко Никита Сергеевич
Язык:
английский
Кредиты:
5
Контактные часы:
8
Course Syllabus
Abstract
Our course aims to provide necessary background in Calculus sufficient for up-following Data Science courses.
Course starts with basic introduction to concepts concerning functional mappings. Later students are assumed to study limits (in case of sequences, single- and multivariate functions), differentiability (once again starting from single variable up to multiple cases), integration, thus sequentially building up a base for the basic optimization. To provide an understanding of the practical skills set being taught, the course introduces the final programming project considering the usage of optimization routine in machine learning.
Additional materials provided during the course include interactive plots in GeoGebra environment used during lectures, bonus reading materials with more general methods and more complicated basis for discussed themes.
Learning Objectives
- Students will develop understanding of variety of essential concepts of the single and multi-variable calculus and acquire a range of practical skills regarding aforementioned concepts.
- Amongst the skills and concepts, there should be stressed out the following: • derivatives of single and multi-variate functions • indefinite and definite integration • principle differences of functions of several variables
Expected Learning Outcomes
- Calculate discrete limit and the limit of sequences
- Learn asymptotic comparison of functions, Big- and little-o notations, famous important limits
- Calculate function's derivative
- Learn derivatives of single and multi-variate functions
- Learn indefinite and definite integration
- Learn principle differences of functions of several variables
Course Contents
- 1: Introduction: Numerical Sets, Functions, Limits
- 2: Limits and Multivariate Functions
- 3: Derivatives and Linear Approximations: Single variate Functions
- 4: Derivatives and Linear Approximations: Multivariate Functions
- 5: Integrals: Anti-derivative, Area under Curve
- 6: Optimization: Directional derivative, Extrema and Gradient Descent
Assessment Elements
- Week Final Quizzes (weeks 1-5)Weekly Quizzes
- Practice Quizzes (week 6)
- SGA Open Question: Series
- First Week Extra Quiz
- SGA Open Question: Multivariate limit
- SGA Numerical Differentiation
- SGA Open Question: Extremum
- SGA Open Question: Chain Rule
- SGA Open Question: FTC
- SGA Numerical Integration
- Final Project
Interim Assessment
- 2022/2023 1st module0.09 * SGA Numerical Integration + 0.09 * SGA Numerical Differentiation + 0.3 * Final Project + 0.04 * SGA Open Question: Chain Rule + 0.04 * SGA Open Question: Multivariate limit + 0.04 * SGA Open Question: FTC + 0.02 * First Week Extra Quiz + 0.04 * SGA Open Question: Series + 0.05 * Practice Quizzes (week 6) + 0.04 * SGA Open Question: Extremum + 0.25 * Week Final Quizzes (weeks 1-5)
Bibliography
Recommended Core Bibliography
- Friedman, A. (2007). Advanced Calculus (Vol. Dover edition). Mineola, N.Y.: Dover Publications. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=1153250
- James Stewart. (2016). Calculus, Early Transcendentals, International Metric Edition: Vol. Eighth edition, metric version. Cengage Learning.
- Jennifer F. Wood. (2015). Dowling, P. J., Festing, M., Engle Sr., A. D., International Human Resource Management (6th Edition), Cengage Learning EMEA, 2013. Management International Review, (4), 589. https://doi.org/10.1007/s11575-014-0236-1
Recommended Additional Bibliography
- William H. Press, Saul A. Teukolsky, William T. Vetterling, & Brian P. Flannery. (1992). Numerical Recipes in C: The Art of Scientific Computing. Second Edition. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsbas&AN=edsbas.9CFCD6AE