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Regular version of the site
Master 2022/2023

# Calculus

Type: Compulsory course
Area of studies: Applied Mathematics and Informatics
When: 1 year, 1 module
Mode of studies: distance learning
Online hours: 82
Open to: students of one campus
Instructors: Nikita Lukianenko
Master’s programme: Master of Data Science
Language: English
ECTS credits: 5
Contact hours: 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 module
0.09 * 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)